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"image": "https:https://st.vkuso.ru/data/cache/thumb/1a/0618f9b54b6121a_434x295.jpg"
},
{
"text": "Выпекать банановый кекс с ромом и корицей 40 минут в духовке с температурой 180 градусов.",
"image": null
}
],
"tags": [
{
"name": "Пошаговые фото-рецепты",
"slug": "poshagovye-foto-recepty"
},
{
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},
{
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"slug": "bezdrojjevaya-vypechka"
},
{
"name": "В духовке",
"slug": "v-duhovke"
},
{
"name": "Выпечка без молока",
"slug": "vypechka-bez-moloka"
},
{
"name": "Выпечка на сметане",
"slug": "vypechka-na-smetane"
},
{
"name": "Выпечка с бананами",
"slug": "vypechka-s-bananami"
},
{
"name": "Выпечка с корицей",
"slug": "vypechka-s-koricey"
},
{
"name": "Выпечка с фруктами",
"slug": "vypechka-s-fruktami"
},
{
"name": "Кекс без масла",
"slug": "keks-bez-masla"
},
{
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"slug": "keks-v-duhovke"
},
{
"name": "Кекс на сметане",
"slug": "keks-na-smetane"
},
{
"name": "Кекс с какао",
"slug": "keks-s-kakao"
},
{
"name": "Кексы",
"slug": "keksy"
},
{
"name": "Фруктовый кекс",
"slug": "fruktoviy-keks"
}
]
} |
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{"comment": "0", "idNoticia": "8307", "tags": [], "url": "http://www.valor.com.br/financas/2571064/fluxo-cambial-mostra-marola-e-nao-um-tsunami ", "autor": " Daniela Machado e Eduardo Campos | De São Paulo", "titulo": "Fluxo cambial mostra marola e não um tsunami", "corpo": "Os termos \"tsunami monetário\" e \"enxurrada de dólares\" vêm, com frequência, acompanhando as avaliações do governo sobre a valorização recente do real e servido de pedra fundamental para a adoção de medidas cambiais. Mas, ainda que as expectativas sejam fundamentais na formação de preço de qualquer mercado, a liquidez despejada pelos bancos centrais nas principais economias ainda não se traduziu efetivamente em salto no fluxo cambial para o Brasil. Dados do Banco Central mostram que a diferença entre ingresso e saída de moeda é positiva em US$ 18,095 bilhões neste ano (até 9 de março), uma queda de 40% em relação aos US$ 30,361 bilhões vistos em igual período de 2011. Descontada uma operação específica de captação de recursos da Petrobras no exterior, de cerca de US$ 7 bilhões, os números deste início de 2012 são ainda menos vigorosos. E, como os recursos oriundos dessa operação da estatal já foram retirados do mercado pelo BC por meio de leilões de compra de dólar a termo, a sobra de dólares de 2012, que ajuda a pressionar o câmbio, cairia a algo em torno de US$ 11 bilhões. Colocando na conta as demais atuações do Banco Central com compras no mercado à vista, que somam US$ 2,056 bilhões no período, o excedente no ano cai para US$ 9,039 bilhões. Como base de comparação, entre janeiro e março (mês fechado) de 2006, o saldo do fluxo foi de US$ 17,692 bilhões. Sempre no mesmo período, em 2007, a sobra ficou em US$ 17,394 bilhões. Em 2008, foram US$ 8,940 bilhões. Já em 2009, ano de crise, a saída foi de US$ 2,974 bilhões. E em 2010, o fluxo foi de US$ 2,789 bilhões. O movimento de câmbio pelo segmento financeiro, que responde pelas trocas de moeda decorrentes de empréstimos, financiamentos e investimentos entre o país e o exterior e poderia espelhar mais claramente a busca de investidores por ganhos com \"carry trade\", também não mostra trajetória explosiva (ver gráficos). \"O que efetivamente forçava a apreciação do real era a perspectiva sobre a enxurrada de dólares. Isso levou alguns agentes no mercado futuro a especular sem fazer o hedge do dólar, já que o viés era seguro de baixa\", avalia o diretor da NGO Corretora, Sidnei Nehme. \"É só verificar como alguns compraram hedge após as medidas do governo, simplesmente pela mudança da perspectiva. Isso sim provocou a alta no preço do dólar\", diz Nehme. Os tais agentes são os fundos nacionais, que apresentam uma posição comprada de US$ 12,298 bilhões em dólar futuro e cupom cambial (DDI, o juro em dólar). A alta foi de US$ 5 bilhões no mês. Para o executivo, o governo age mais em reação ao fraco crescimento do Produto Interno Bruto (PIB) no ano passado e, principalmente, em resposta à queda de 2,1% da produção industrial na abertura de 2012. \"O câmbio é a via mais rápida para conter a concorrência das importações e tentar aumentar a competitividade. Contudo, precisa de sustentabilidade e este é um grande desafio para o governo\", diz Nehme. \"Claramente não houve essa enxurrada [esperada pelo governo]\", afirma Vladimir Caramaschi, economista-chefe do Crédit Agricole Brasil, para quem a desvalorização do real vista nos últimos dias está mais ligada a uma mudança na percepção de risco global do que às atuações do governo. \"A prova disso é que o real andou mais ou menos em linha com outras moedas emergentes.\" Isso não quer dizer, segundo ele, que a injeção de liquidez nos países desenvolvidos não venha a ter como possível efeito a migração para emergentes. Para isso se concretizar, no entanto, é preciso que os bancos estrangeiros resolvam seus problemas de nível de capital e o mundo não apresente um novo solavanco. \"É preciso ter confiança no cenário, sem que apareça um novo episódio como o da Grécia. Hoje é difícil que já saiam aumentando seu balanço porque ainda precisam adequar seu nível de capital\", acrescenta. O economista não é, em princípio, contrário a que o governo atue. \"O que eu não acho correto é que achem que é almoço grátis. Cada vez que o governo avança nessas medidas, a tendência é que tenha menos benefícios e mais custos. Ao estender o IOF para captações de até cinco anos, por exemplo, o governo começa a entrar num campo em que não necessariamente está afetando só fluxo especulativo.\"", "data": "2012-03-15 00:00:00"} |
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"questionMark": {
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["[From: Abbie]\nQuincy Jan\u2019y 1 1797", "\u201cO Blindness to the future kindly given\nThat each may fill the circle mark\u2019d by Heaven[\u201d]", "The new year opens upon us with new Scenes of Life before us.", "what are to be the trials the troubles and vexations of it, are wisely with held from our view.", "The universal cause\nActs not by partial, but by Gen\u2019ral laws\nwho sees and follows that great Scheme the best\nBest knows the blessing, and will most be blest", "To him who sits Supreem let us commit the hour the Day the Year, and fearless view the whole.", "there needs but thinking right, and meaning well, and may this ensure to you, the Souls calm sun shine, and the Heart felt Joy.", "I seldom think twice of a Dreem but last Night I had one of so singular a nature that it has amused My mind to Day with various conjectures.", "I was riding in my Coach, where I know not, but all at once, I perceived flying in the Air a Number of large black Balls of the Size of a 24 pounder.", "they appeard to be all directed at me.", "all of them however burst and fell before they reach\u2019d me, tho I continued going immediatly towards them.", "I saw them crumble all to Attoms, but During this Scene, two Guns were dischargd at My left Ear the flash of which I saw and heard the report.", "I still remaind unhurt, but proceedeed undaunted upon My course", "How would the Sooth sayers interpret this Dream?", "whom do you think has undertaken to read the Defence!", "but Deacon Webb, and declares himself well pleasd with the first volm. as cousin Boylstone informs me.", "I fear the Deleware is frozen up So that Brisler will not be able to send me any flower\u2014", "Billings is just recovering from a visit to Stoughten which has lasted him a week, the Second he has made since you went away.", "from the first, as he went without the Root of all Evil, he returnd steady.", "the occasion of his going was the Sickness & Death of the Man who lived upon his place.", "I have been obliged at his request to purchase for him shirts & other Cloathing.", "Your Mother desires to be rememberd affectionatly to you.", "one Day last week she walkt here, and spent the Day.", "I am my Dearest Friend most / affectionatly Yours\nA Adams."] |
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{"artist": "Tycoon", "timestamp": "2011-07-31 22:19:22.911952", "similars": [], "tags": [], "track_id": "TRCUKRJ128F9303129", "title": "Way Of The World"} |
[{"detail": [{"content": "Optical conveyors: A class of active tractor beams Optical conveyors: A class of active tractor beams References David Grier's Home Page Grier Group Publications Optical conveyors: A class of active tractor beams David B.\u00a0Ruffner and David G.\u00a0Grier Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003 Abstract. We experimentally demonstrate a class of tractor beams created by coherently superposing coaxial Bessel beams. These optical conveyors have periodic intensity variations along their axes that act as highly effective optical traps for micrometer-scale objects. Varying the Bessel beams' relative phase shifts the traps axially thereby selectively transports trapped objects either downstream or upstream along the length of the beam. The same methods used to project a single optical conveyor can project arrays of independent optical conveyors, allowing bi-directional transport in three dimensions. A tractor beam is a traveling wave that can transport illuminated material along its length back to its source. By this definition, an optical tweezer [ 1 ] is not a tractor beam because of its inherently limited range. Nor is an optical conveyor belt [ 2 , 3 ] , which is created from a standing wave rather than a traveling wave. A one-sided variant of the optical conveyor belt created from coaxial Bessel beams has been demonstrated, but relies on auxiliary forces to achieve retrograde motion [ 4 ] . Here, we demonstrate one-sided optical conveyors that act as tractor beams without requiring outside assistance. The same technique we use to project a single optical conveyor also can project arrays of optical conveyors each with independently controlled transport properties. Most beams of light do not act as tractor beams because radiation pressure tends to drive illuminated objects downstream. Recently, however two categories of tractor beams have been described, both of which exploit properties of propagation-invariant or non-diffracting traveling waves [ 5 ] , and thus have promise for long-range material transport. Both rely on the recoil force that an illuminated object experiences if it scatters transverse components of the beam's linear momentum density into the axial direction. The first is based on multipole scattering in Bessel beams, which has been predicted to drive retrograde motion in both acoustic [ 6 ] and optical [ 7 ] waves. Because this mechanism relies on scattering by high-order induced multipole moments, however, the direction of induced transport depends sensitively on the properties of the illuminated object; tractor beams based on pure Bessel modes have not yet been demonstrated experimentally. The other approach utilizes periodic axial intensity gradients in beams with discrete propagation invariance [ 5 ] to achieve forward scattering from the interference between the incident field and the dipole radiation field of an illuminated object. Such tractor beams have been realized experimentally with solenoidal waves that have transported micrometer-scale colloidal spheres over an axial range of 10\u00a0 \u00a0 [ 8 ] . Figure 1. (color online) (a) Schematic representation of holographic projection of a Bessel beam with axial wavenumber by a lens of focal length . Shaded region indicates volume of invariant propagation. (b) Volumetric reconstruction of a holographically projected Bessel beam. (c) Phase hologram encoding an optical conveyor. Diagonal blazing tilts the projected conveyor away from the optical axis. (d) Volumetric reconstruction of the beam projected by the hologram in (c). The color bar indicates relative intensities in (b) and (d). Here, we describe another category of tractor beams derived from the optical conveyor belts introduced in Refs.\u00a0 [ 2 , 3 , 4 ] that can be projected from a single source and can transport material bidirectionally without the aid of outside forces. A one-sided optical conveyor is formed by projecting two or more coherent Bessel beams along the same axis and systematically varying their relative phase. The vector potential for a two-component optical conveyor of frequency and polarization may be written in cylindrical coordinates as ( 1 ) where is the wavenumber of light in a medium with refractive index and is a Bessel function of the first kind of order . The two beams differ in their axial wavenumbers, and , which are reduced from by factors . They also differ in their relative phase , whose time variation makes the conveyor work. The prefactor is the beam's amplitude. Setting the relative amplitude to unity, , maximizes the conveyor's axial intensity gradients and thus optimizes its performance for optical manipulation. In the special case , , the component Bessel beams have unit amplitude along the optical axis, , and the conveyor's axial intensity is ( 2 ) ( 3 ) where . The beam thus has intensity maxima at axial positions ( 4 ) that are evenly spaced by multiples, , of the wavelength in the medium, and thus can be indexed by the integer . Objects trapped along can be displaced either up or down the axis by appropriately varying the relative phase . Continuous variations translate trapped objects deterministically along with axial velocity, ( 5 ) regardless of their size, shape, or optical properties. This differs from the action of Bessel-based tractor beams [ 6 ] in which even the sign of the induced motion depends on each object's properties. It differs also from the motion induced by solenoidal tractor beams [ 8 ] which is unidirectional but not uniformly fast. We implemented optical conveyors using the holographic optical trapping technique [ 9 ] in which a computer-designed phase profile is imprinted onto the wavefronts of a Gaussian beam, which then is projected into the sample with a high-numerical-aperture objective lens of focal length . In practice, the trap-forming hologram is implemented with a computer-addressable spatial light modulator (SLM) (Hamamatsu X8267-16) that imposes a selected phase shift at each pixel in a array. If the field described by Eq.\u00a0( 1 ) is to be projected into the objective's focal plane, the field in the plane of the hologram is given in the scalar diffraction approximation [ 11 ] by its Fourier transform, ( 6 ) where is the Dirac delta function, and , The ideal hologram for each Bessel beam comprising the conveyor thus is a thin ring in the plane of the SLM, as indicated schematically in Fig.\u00a0 1 (a). A holographically projected Bessel beam then propagates without diffraction over the range indicated by the shaded region. Increasing the transverse wave number increases the radius of the hologram and therefore reduces the non-diffracting range. Figure\u00a0 1 (b) shows a volumetric reconstruction [ 12 ] of a Bessel beam projected with a ring-like hologram. Increasing the ring's thickness of the ring by increases diffraction efficiency, but is equivalent to superposing Bessel beams with a range of axial wavenumbers, . This superposition contributes an overall axial envelope to the projected Bessel beam, limiting its axial range to . The axial range in Fig.\u00a0 1 (b) is consistent with this estimate and so is smaller than the ray-optics estimate suggested by the overlap volume in Fig.\u00a0 1 (a). Figure\u00a0 1 (c) shows the two-ringed phase-only hologram that encodes an optical conveyor with an overall cone angle of . This function corresponds to the phase of the beam's vector potential, which the SLM imprints on an incident Gaussian plane wave. The relative phase offset between the two rings determines . The relative widths of the two phase rings can be used to establish the components' relative amplitudes through , the range of the projected conveyor then being the smaller of and . The large featureless regions in Fig.\u00a0 1 (c) do not contribute to the desired optical conveyor. Light passing through these regions is not diffracted and therefore converges at the focal point of the optical train. To prevent interference between the diffracted and undiffracted beams, the two phase rings contributing to the conveyor are offset and blazed with a linear phase gradient [ 13 ] to displace the projected Bessel beams by 24\u00a0 \u00a0from the optical axis. Figure 2. (color online) (a) Trajectories of two 1.5\u00a0 \u00a0diameter colloidal silica spheres moving along a pair of optical conveyors, superimposed with a holographic snapshot of the two spheres. Colored orbs indicate the spheres' positions in the hologram, and are plotted at the same scale as the actual spheres. Rings are added for emphasis. (b) Measured time dependence of the spheres' axial positions as one moves downstream ( ) along its conveyor and the other moves upstream ( ). (c) Three-dimensional reconstruction of a holographic snapshot of two colloidal spheres moving along a single optical conveyor. The volumetric reconstruction in Fig.\u00a0 1 (d) shows the three-dimensional intensity distribution projected by the hologram in Fig.\u00a0 1 (c), with oriented along the diffracted beam's direction of propagation. This beam clearly displays the pattern of periodically alternating bright and dark regions predicted by Eqs.\u00a0( 1 ) through ( 4 ). The unused regions of the hologram need not go to waste. They can be used to project additional independent conveyors, much as has been demonstrated for spatially multiplexed optical traps of other types [ 14 ] . An appropriately designed array of conveyors therefore can make full use of the light falling on the SLM and thus can be projected with very high diffraction efficiency. Each conveyor, moreover, can be operated independently of the others by selectively offsetting the phase in appropriate regions of the multiplexed hologram. The data in Fig.\u00a0 2 were obtained with two separate optical conveyors projected simultaneously with equal intensity and equal axial period by a single hologram. The conveyors' phases were ramped at the same rate, but with opposite sign. This single structured beam of light therefore should transport material in opposite directions simultaneously. To demonstrate this, we projected the pair of conveyors into a sample of 1.5\u00a0 \u00a0diameter colloidal silica spheres dispersed in water (Polysciences, Lot # 600424). The sample is contained in the 100\u00a0 \u00a0deep gap between a clean glass microscope slide and a cover-slip that was formed by and sealed with UV-curing optical adhesive (Norland 68). The slide was mounted on the stage of a Nikon TE-2000U optical microscope outfitted with a custom-built holographic optical trapping system [ 17 ] operating at a vacuum wavelength of . An estimated 17\u00a0 \u00a0of linearly polarized light were projected into each conveyor with a numerical aperture 1.4 oil-immersion objective lens (Nikon Plan-Apo DIC H) at an overall efficiency of 0.5 percent. To facilitate tracking the spheres as they move along the optical axis, the microscope's conventional illuminator was replaced with a 10\u00a0 \u00a03\u00a0 -diameter collimated laser beam at a vacuum wavelength of 445\u00a0 . Interference between light scattered by the spheres and the rest of the illumination forms a hologram of the spheres in the focal plane of the objective lens that is magnified and recorded at 30 frames per second with a conventional greyscale video camera (NEC TI-324A-II). A typical holographic snapshot is reproduced in Fig.\u00a0 2 (a). These holograms then can be analyzed [ 18 , 20 ] to obtain the spheres' three-dimensional positions with nanometer-scale resolution. The traces in Fig.\u00a0 2 (a) show the full trajectories of both spheres over the course of the experiment. Colored orbs indicate the measured positions of the spheres at the instant of the holographic snapshot and are scaled to represent the actual sizes of the spheres. Starting from the configuration in Fig.\u00a0 2 (a), the two conveyors were run through total phase ramps of in steps of , yielding the axial trajectories plotted in Fig.\u00a0 2 (b). Reversing the phase ramps reverses the process. These measurements confirm that arrays of optical conveyors can selectively induce bidirectional transport over their entire lengths. The self-healing nature of Bessel beams [ 5 , 21 ] furthermore suggests that multiple objects can be trapped and moved by a single optical conveyor despite light scattering by each of the trapped objects [ 2 , 3 , 4 ] . This is confirmed by Fig.\u00a0 2 (c), which shows a volumetric reconstruction [ 22 ] of the light scattered by two colloidal spheres simultaneously trapped on an optical conveyor. The plotted intensity distribution was computed from the inset hologram by Rayleigh-Sommerfeld back-propagation. Maxima representing the positions of the spheres are separated by two periods of the underlying optical conveyor. To characterize and optimize the transport properties of optical conveyors, we model the forces they exert in the Rayleigh approximation, which is appropriate for objects smaller than the wavelength of light. Considering both induced-dipole attraction and radiation pressure, the axial component of the force is ( 7 ) where the coefficients and parameterize the light-matter interaction for a particle with electric polarizability . For simplicity, Eq.\u00a0( 7 ) omits contributions due to the curl of the spin density [ 23 ] , and thus is appropriate for linearly polarized light. Further assuming a conveyor of the form described by Eq.\u00a0( 2 ) with continuously ramped phase, , the equation of motion for a colloidal particle with drag coefficient is ( 8 ) where is the downstream drift speed due to radiation pressure, and where describes the relative axial trapping strength. Particles that are trapped by intensity gradients are translated upstream with the conveyor's phase velocity, . From Eq.\u00a0( 8 ), the maximum upstream transport speed is then limited by viscous drag to ( 9 ) This remarkable result suggests that an optical conveyor can act as a tractor beam for any particle with provided that it is not run too fast. Both light-seeking ( ) and dark-seeking ( ) particles should move in the same direction with the same speed, although the dark-seeking particles will sit near the beam's minima. Optical conveyors thus have the potential to out-perform optical tweezers, which cannot always achieve stable axial trapping even in the Rayleigh regime. Equation\u00a0( 9 ) also suggests straightforward optimization strategies for optical conveyors. Brighter conveyors can run faster. Reducing the conveyor's spatial period proportionately increases the maximum transport rate at the cost of reducing the maximum range. Higher-order conveyors with also have intensity maxima at positions given by Eq.\u00a0( 4 ). They differ from zero-order conveyors in that their principal maxima are displaced from to transverse radii that depend on , , and . This larger transverse range may be useful for conveying irregular or asymmetrically shaped objects, or objects with inhomogeneous optical properties. Higher-order conveyors also carry orbital angular momentum and so will exert torques on trapped objects. The transport direction predicted by Eq.\u00a0( 8 ) reverses sign in the limit of large , illuminated objects then traveling steadily downstream at the drift speed . The crossover between upstream and downstream transport is marked by a dynamical state in which the particle alternately is transported upstream and slips back downstream. The transition to this state is established by Eq.\u00a0( 9 ) in the deterministic case described by Eq.\u00a0( 8 ). It will be strongly affected by thermal fluctuations, however, and may feature anomalous velocity fluctuations. Still other dynamical states are possible if the relative phase varies discontinuously, for example in a Brownian ratchet protocol [ 25 ] . Even more complicated behavior may be expected for optical conveyor transport in underdamped systems for which inertia plays a role. This work was supported by the National Science Foundation under Grant Number DMR-0922680. The authors are grateful for enlightening conversations with Paul Stysley, Demetrios Poulios and Donald Coyle. References 1 A.\u00a0Ashkin, J.\u00a0M. Dziedzic, J.\u00a0E. Bjorkholm and S.\u00a0Chu. \u201cObservation of a single-beam gradient force optical trap for dielectric particles.\u201d Opt. Lett. 11 , 288\u2013290 (1986). 2 T.\u00a0\u010ci\u017emar, V.\u00a0Garc\u00e9s-Ch\u00e1vez, K.\u00a0Dhokalia and P.\u00a0Zem\u00e1nek. \u201cOptical conveyor belt for delivery of submicron objects.\u201d Appl. Phys. Lett. 86 , 174101 (2005). 3 T.\u00a0\u010ci\u017em\u00e1r, M.\u00a0\u0160iler and P.\u00a0Zem\u00e1nek. \u201cAn optical nanotrap array movable over a milimetre range.\u201d Appl. Phys. B 84 , 197\u2013203 (2006). 4 T.\u00a0\u010ci\u017em\u00e1r, V.\u00a0Koll\u00e1rov\u00e1, Z.\u00a0Bouchal and P.\u00a0Zem\u00e1nek. \u201cSub-micron particle organization by self-imaging of non-diffracting beams.\u201d New J. Phys. 8 , 43 (2006). 5 J.\u00a0Durnin. \u201cDiffraction-free beams.\u201d Phys. Rev. Lett. 58 , 1499\u20131501 (1987). 6 P.\u00a0L. Marston. \u201cAxial radiation force of a Bessel beam on a sphere and direction reversal of the force.\u201d J. Acoust. Soc. Am. 120 , 3518\u20133524 (2006). 7 J.\u00a0Chen, J.\u00a0Ng, Z.\u00a0Lin and C.\u00a0T. Chan. \u201cOptical pulling force.\u201d Nature Photonics 5 , 531\u2013534 (2011). 8 S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptical solenoid beams.\u201d Opt. Express 18 , 6988\u20136993 (2010). 9 E.\u00a0R. Dufresne and D.\u00a0G. Grier. \u201cOptical tweezer arrays and optical substrates created with diffractive optical elements.\u201d Rev. Sci. Instrum. 69 , 1974\u20131977 (1998). 10 D.\u00a0G. Grier. \u201cA revolution in optical manipulation.\u201d Nature 424 , 810\u2013816 (2003). 11 J.\u00a0W. Goodman. Introduction to Fourier Optics (McGraw-Hill, New York, 2005), 3rd ed. 12 Y.\u00a0Roichman, I.\u00a0Cholis and D.\u00a0G. Grier. \u201cVolumetric imaging of holographic optical traps.\u201d Opt. Express 14 , 10907\u201310912 (2006). 13 J.\u00a0E. Curtis, B.\u00a0A. Koss and D.\u00a0G. Grier. \u201cDynamic holographic optical tweezers.\u201d Opt. Commun. 207 , 169\u2013175 (2002). 14 C.-S. Guo, X.\u00a0Liu, J.-L. He and H.-T. Wang. \u201cOptimal annulus structures of optical vortices.\u201d Opt. Express 12 , 4625\u20134634 (2004). 15 K.\u00a0Ladavac and D.\u00a0G. Grier. \u201cColloidal hydrodynamic coupling in concentric optical vortices.\u201d Europhys. Lett. 70 , 548\u2013554 (2005). 16 Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cProjecting extended optical traps with shape-phase holography.\u201d Opt. Lett. 31 , 1675\u20131677 (2006). 17 M.\u00a0Polin, K.\u00a0Ladavac, S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptimized holographic optical traps.\u201d Opt. Express 13 , 5831\u20135845 (2005). 18 S.-H. Lee, Y.\u00a0Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A.\u00a0van Blaaderen, P.\u00a0van Oostrum and D.\u00a0G. Grier. ``Characterizing and tracking single colloidal particles with video holographic microscopy.\u201d Opt. Express 15 , 18275\u201318282 (2007). 19 F.\u00a0C. Cheong, B.\u00a0J. Krishnatreya and D.\u00a0G. Grier. \u201cStrategies for three-dimensional particle tracking with holographic video microscopy.\u201d Opt. Express 18 , 13563\u201313573 (2010). 20 F.\u00a0C. Cheong, B.\u00a0Sun, R.\u00a0Dreyfus, J.\u00a0Amato-Grill, K.\u00a0Xiao, L.\u00a0Dixon and D.\u00a0G. Grier. \u201cFlow visualization and flow cytometry with holographic video microscopy.\u201d Opt. Express 17 , 13071\u201313079 (2009). 21 V.\u00a0Garc\u00e9s-Ch\u00e1vez, D.\u00a0McGloin, H.\u00a0Melville, W.\u00a0Sibbett and K.\u00a0Dholakia. \u201cSimultaneous micromanipulation in multiple planes using a self-reconstructing light beam.\u201d Nature 419 , 145\u2013147 (2002). 22 S.-H. Lee and D.\u00a0G. Grier. ``Holographic microscopy of holographically trapped three-dimensional structures.\u201d Opt. Express 15 , 1505\u20131512 (2007). 23 S.\u00a0Albaladejo, M.\u00a0I. Marqu\u00e9s, F.\u00a0Scheffold and J.\u00a0J. S\u00e1enz. \u201cGiant enhanced diffusion of gold nanoparticles in optical vortex fields.\u201d Nano Lett. 9 , 3527\u20133531 (2009). 24 D.\u00a0B. Ruffner and D.\u00a0G. Grier. \u201cOptical forces and torques in non-uniform beams of light.\u201d Phys. Rev. Lett. 108 , 173602 (2012). 25 S.-H. Lee, K.\u00a0Ladavac, M.\u00a0Polin and D.\u00a0G. Grier. \u201cObservation of flux reversal in a symmetric optical thermal ratchet.\u201d Phys. Rev. Lett. 94 , 110601 (2005). 26 S.-H. Lee and D.\u00a0G. Grier. \u201cFlux reversal in a two-state symmetric optical thermal ratchet.\u201d Phys. Rev. E 71 , 060102(R) (2005). 27 S.-H. Lee and D.\u00a0G. Grier. \u201cOne-dimensional optical thermal ratchets.\u201d J. Phys.: Condens. Matter 17 , S3685\u2013S3695 (2006). D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012)"}]},
{"detail": [{"content": "Optical conveyors: A class of active tractor beams Optical conveyors: A class of active tractor beams References David Grier's Home Page Grier Group Publications Optical conveyors: A class of active tractor beams David B.\u00a0Ruffner and David G.\u00a0Grier Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003 Abstract. We experimentally demonstrate a class of tractor beams created by coherently superposing coaxial Bessel beams. These optical conveyors have periodic intensity variations along their axes that act as highly effective optical traps for micrometer-scale objects. Varying the Bessel beams' relative phase shifts the traps axially thereby selectively transports trapped objects either downstream or upstream along the length of the beam. The same methods used to project a single optical conveyor can project arrays of independent optical conveyors, allowing bi-directional transport in three dimensions. A tractor beam is a traveling wave that can transport illuminated material along its length back to its source. By this definition, an optical tweezer [ 1 ] is not a tractor beam because of its inherently limited range. Nor is an optical conveyor belt [ 2 , 3 ] , which is created from a standing wave rather than a traveling wave. A one-sided variant of the optical conveyor belt created from coaxial Bessel beams has been demonstrated, but relies on auxiliary forces to achieve retrograde motion [ 4 ] . Here, we demonstrate one-sided optical conveyors that act as tractor beams without requiring outside assistance. The same technique we use to project a single optical conveyor also can project arrays of optical conveyors each with independently controlled transport properties. Most beams of light do not act as tractor beams because radiation pressure tends to drive illuminated objects downstream. Recently, however two categories of tractor beams have been described, both of which exploit properties of propagation-invariant or non-diffracting traveling waves [ 5 ] , and thus have promise for long-range material transport. Both rely on the recoil force that an illuminated object experiences if it scatters transverse components of the beam's linear momentum density into the axial direction. The first is based on multipole scattering in Bessel beams, which has been predicted to drive retrograde motion in both acoustic [ 6 ] and optical [ 7 ] waves. Because this mechanism relies on scattering by high-order induced multipole moments, however, the direction of induced transport depends sensitively on the properties of the illuminated object; tractor beams based on pure Bessel modes have not yet been demonstrated experimentally. The other approach utilizes periodic axial intensity gradients in beams with discrete propagation invariance [ 5 ] to achieve forward scattering from the interference between the incident field and the dipole radiation field of an illuminated object. Such tractor beams have been realized experimentally with solenoidal waves that have transported micrometer-scale colloidal spheres over an axial range of 10\u00a0 \u00a0 [ 8 ] . Figure 1. (color online) (a) Schematic representation of holographic projection of a Bessel beam with axial wavenumber by a lens of focal length . Shaded region indicates volume of invariant propagation. (b) Volumetric reconstruction of a holographically projected Bessel beam. (c) Phase hologram encoding an optical conveyor. Diagonal blazing tilts the projected conveyor away from the optical axis. (d) Volumetric reconstruction of the beam projected by the hologram in (c). The color bar indicates relative intensities in (b) and (d). Here, we describe another category of tractor beams derived from the optical conveyor belts introduced in Refs.\u00a0 [ 2 , 3 , 4 ] that can be projected from a single source and can transport material bidirectionally without the aid of outside forces. A one-sided optical conveyor is formed by projecting two or more coherent Bessel beams along the same axis and systematically varying their relative phase. The vector potential for a two-component optical conveyor of frequency and polarization may be written in cylindrical coordinates as ( 1 ) where is the wavenumber of light in a medium with refractive index and is a Bessel function of the first kind of order . The two beams differ in their axial wavenumbers, and , which are reduced from by factors . They also differ in their relative phase , whose time variation makes the conveyor work. The prefactor is the beam's amplitude. Setting the relative amplitude to unity, , maximizes the conveyor's axial intensity gradients and thus optimizes its performance for optical manipulation. In the special case , , the component Bessel beams have unit amplitude along the optical axis, , and the conveyor's axial intensity is ( 2 ) ( 3 ) where . The beam thus has intensity maxima at axial positions ( 4 ) that are evenly spaced by multiples, , of the wavelength in the medium, and thus can be indexed by the integer . Objects trapped along can be displaced either up or down the axis by appropriately varying the relative phase . Continuous variations translate trapped objects deterministically along with axial velocity, ( 5 ) regardless of their size, shape, or optical properties. This differs from the action of Bessel-based tractor beams [ 6 ] in which even the sign of the induced motion depends on each object's properties. It differs also from the motion induced by solenoidal tractor beams [ 8 ] which is unidirectional but not uniformly fast. We implemented optical conveyors using the holographic optical trapping technique [ 9 ] in which a computer-designed phase profile is imprinted onto the wavefronts of a Gaussian beam, which then is projected into the sample with a high-numerical-aperture objective lens of focal length . In practice, the trap-forming hologram is implemented with a computer-addressable spatial light modulator (SLM) (Hamamatsu X8267-16) that imposes a selected phase shift at each pixel in a array. If the field described by Eq.\u00a0( 1 ) is to be projected into the objective's focal plane, the field in the plane of the hologram is given in the scalar diffraction approximation [ 11 ] by its Fourier transform, ( 6 ) where is the Dirac delta function, and , The ideal hologram for each Bessel beam comprising the conveyor thus is a thin ring in the plane of the SLM, as indicated schematically in Fig.\u00a0 1 (a). A holographically projected Bessel beam then propagates without diffraction over the range indicated by the shaded region. Increasing the transverse wave number increases the radius of the hologram and therefore reduces the non-diffracting range. Figure\u00a0 1 (b) shows a volumetric reconstruction [ 12 ] of a Bessel beam projected with a ring-like hologram. Increasing the ring's thickness of the ring by increases diffraction efficiency, but is equivalent to superposing Bessel beams with a range of axial wavenumbers, . This superposition contributes an overall axial envelope to the projected Bessel beam, limiting its axial range to . The axial range in Fig.\u00a0 1 (b) is consistent with this estimate and so is smaller than the ray-optics estimate suggested by the overlap volume in Fig.\u00a0 1 (a). Figure\u00a0 1 (c) shows the two-ringed phase-only hologram that encodes an optical conveyor with an overall cone angle of . This function corresponds to the phase of the beam's vector potential, which the SLM imprints on an incident Gaussian plane wave. The relative phase offset between the two rings determines . The relative widths of the two phase rings can be used to establish the components' relative amplitudes through , the range of the projected conveyor then being the smaller of and . The large featureless regions in Fig.\u00a0 1 (c) do not contribute to the desired optical conveyor. Light passing through these regions is not diffracted and therefore converges at the focal point of the optical train. To prevent interference between the diffracted and undiffracted beams, the two phase rings contributing to the conveyor are offset and blazed with a linear phase gradient [ 13 ] to displace the projected Bessel beams by 24\u00a0 \u00a0from the optical axis. Figure 2. (color online) (a) Trajectories of two 1.5\u00a0 \u00a0diameter colloidal silica spheres moving along a pair of optical conveyors, superimposed with a holographic snapshot of the two spheres. Colored orbs indicate the spheres' positions in the hologram, and are plotted at the same scale as the actual spheres. Rings are added for emphasis. (b) Measured time dependence of the spheres' axial positions as one moves downstream ( ) along its conveyor and the other moves upstream ( ). (c) Three-dimensional reconstruction of a holographic snapshot of two colloidal spheres moving along a single optical conveyor. The volumetric reconstruction in Fig.\u00a0 1 (d) shows the three-dimensional intensity distribution projected by the hologram in Fig.\u00a0 1 (c), with oriented along the diffracted beam's direction of propagation. This beam clearly displays the pattern of periodically alternating bright and dark regions predicted by Eqs.\u00a0( 1 ) through ( 4 ). The unused regions of the hologram need not go to waste. They can be used to project additional independent conveyors, much as has been demonstrated for spatially multiplexed optical traps of other types [ 14 ] . An appropriately designed array of conveyors therefore can make full use of the light falling on the SLM and thus can be projected with very high diffraction efficiency. Each conveyor, moreover, can be operated independently of the others by selectively offsetting the phase in appropriate regions of the multiplexed hologram. The data in Fig.\u00a0 2 were obtained with two separate optical conveyors projected simultaneously with equal intensity and equal axial period by a single hologram. The conveyors' phases were ramped at the same rate, but with opposite sign. This single structured beam of light therefore should transport material in opposite directions simultaneously. To demonstrate this, we projected the pair of conveyors into a sample of 1.5\u00a0 \u00a0diameter colloidal silica spheres dispersed in water (Polysciences, Lot # 600424). The sample is contained in the 100\u00a0 \u00a0deep gap between a clean glass microscope slide and a cover-slip that was formed by and sealed with UV-curing optical adhesive (Norland 68). The slide was mounted on the stage of a Nikon TE-2000U optical microscope outfitted with a custom-built holographic optical trapping system [ 17 ] operating at a vacuum wavelength of . An estimated 17\u00a0 \u00a0of linearly polarized light were projected into each conveyor with a numerical aperture 1.4 oil-immersion objective lens (Nikon Plan-Apo DIC H) at an overall efficiency of 0.5 percent. To facilitate tracking the spheres as they move along the optical axis, the microscope's conventional illuminator was replaced with a 10\u00a0 \u00a03\u00a0 -diameter collimated laser beam at a vacuum wavelength of 445\u00a0 . Interference between light scattered by the spheres and the rest of the illumination forms a hologram of the spheres in the focal plane of the objective lens that is magnified and recorded at 30 frames per second with a conventional greyscale video camera (NEC TI-324A-II). A typical holographic snapshot is reproduced in Fig.\u00a0 2 (a). These holograms then can be analyzed [ 18 , 20 ] to obtain the spheres' three-dimensional positions with nanometer-scale resolution. The traces in Fig.\u00a0 2 (a) show the full trajectories of both spheres over the course of the experiment. Colored orbs indicate the measured positions of the spheres at the instant of the holographic snapshot and are scaled to represent the actual sizes of the spheres. Starting from the configuration in Fig.\u00a0 2 (a), the two conveyors were run through total phase ramps of in steps of , yielding the axial trajectories plotted in Fig.\u00a0 2 (b). Reversing the phase ramps reverses the process. These measurements confirm that arrays of optical conveyors can selectively induce bidirectional transport over their entire lengths. The self-healing nature of Bessel beams [ 5 , 21 ] furthermore suggests that multiple objects can be trapped and moved by a single optical conveyor despite light scattering by each of the trapped objects [ 2 , 3 , 4 ] . This is confirmed by Fig.\u00a0 2 (c), which shows a volumetric reconstruction [ 22 ] of the light scattered by two colloidal spheres simultaneously trapped on an optical conveyor. The plotted intensity distribution was computed from the inset hologram by Rayleigh-Sommerfeld back-propagation. Maxima representing the positions of the spheres are separated by two periods of the underlying optical conveyor. To characterize and optimize the transport properties of optical conveyors, we model the forces they exert in the Rayleigh approximation, which is appropriate for objects smaller than the wavelength of light. Considering both induced-dipole attraction and radiation pressure, the axial component of the force is ( 7 ) where the coefficients and parameterize the light-matter interaction for a particle with electric polarizability . For simplicity, Eq.\u00a0( 7 ) omits contributions due to the curl of the spin density [ 23 ] , and thus is appropriate for linearly polarized light. Further assuming a conveyor of the form described by Eq.\u00a0( 2 ) with continuously ramped phase, , the equation of motion for a colloidal particle with drag coefficient is ( 8 ) where is the downstream drift speed due to radiation pressure, and where describes the relative axial trapping strength. Particles that are trapped by intensity gradients are translated upstream with the conveyor's phase velocity, . From Eq.\u00a0( 8 ), the maximum upstream transport speed is then limited by viscous drag to ( 9 ) This remarkable result suggests that an optical conveyor can act as a tractor beam for any particle with provided that it is not run too fast. Both light-seeking ( ) and dark-seeking ( ) particles should move in the same direction with the same speed, although the dark-seeking particles will sit near the beam's minima. Optical conveyors thus have the potential to out-perform optical tweezers, which cannot always achieve stable axial trapping even in the Rayleigh regime. Equation\u00a0( 9 ) also suggests straightforward optimization strategies for optical conveyors. Brighter conveyors can run faster. Reducing the conveyor's spatial period proportionately increases the maximum transport rate at the cost of reducing the maximum range. Higher-order conveyors with also have intensity maxima at positions given by Eq.\u00a0( 4 ). They differ from zero-order conveyors in that their principal maxima are displaced from to transverse radii that depend on , , and . This larger transverse range may be useful for conveying irregular or asymmetrically shaped objects, or objects with inhomogeneous optical properties. Higher-order conveyors also carry orbital angular momentum and so will exert torques on trapped objects. The transport direction predicted by Eq.\u00a0( 8 ) reverses sign in the limit of large , illuminated objects then traveling steadily downstream at the drift speed . The crossover between upstream and downstream transport is marked by a dynamical state in which the particle alternately is transported upstream and slips back downstream. The transition to this state is established by Eq.\u00a0( 9 ) in the deterministic case described by Eq.\u00a0( 8 ). It will be strongly affected by thermal fluctuations, however, and may feature anomalous velocity fluctuations. Still other dynamical states are possible if the relative phase varies discontinuously, for example in a Brownian ratchet protocol [ 25 ] . Even more complicated behavior may be expected for optical conveyor transport in underdamped systems for which inertia plays a role. This work was supported by the National Science Foundation under Grant Number DMR-0922680. The authors are grateful for enlightening conversations with Paul Stysley, Demetrios Poulios and Donald Coyle. References 1 A.\u00a0Ashkin, J.\u00a0M. Dziedzic, J.\u00a0E. Bjorkholm and S.\u00a0Chu. \u201cObservation of a single-beam gradient force optical trap for dielectric particles.\u201d Opt. Lett. 11 , 288\u2013290 (1986). 2 T.\u00a0\u010ci\u017emar, V.\u00a0Garc\u00e9s-Ch\u00e1vez, K.\u00a0Dhokalia and P.\u00a0Zem\u00e1nek. \u201cOptical conveyor belt for delivery of submicron objects.\u201d Appl. Phys. Lett. 86 , 174101 (2005). 3 T.\u00a0\u010ci\u017em\u00e1r, M.\u00a0\u0160iler and P.\u00a0Zem\u00e1nek. \u201cAn optical nanotrap array movable over a milimetre range.\u201d Appl. Phys. B 84 , 197\u2013203 (2006). 4 T.\u00a0\u010ci\u017em\u00e1r, V.\u00a0Koll\u00e1rov\u00e1, Z.\u00a0Bouchal and P.\u00a0Zem\u00e1nek. \u201cSub-micron particle organization by self-imaging of non-diffracting beams.\u201d New J. Phys. 8 , 43 (2006). 5 J.\u00a0Durnin. \u201cDiffraction-free beams.\u201d Phys. Rev. Lett. 58 , 1499\u20131501 (1987). 6 P.\u00a0L. Marston. \u201cAxial radiation force of a Bessel beam on a sphere and direction reversal of the force.\u201d J. Acoust. Soc. Am. 120 , 3518\u20133524 (2006). 7 J.\u00a0Chen, J.\u00a0Ng, Z.\u00a0Lin and C.\u00a0T. Chan. \u201cOptical pulling force.\u201d Nature Photonics 5 , 531\u2013534 (2011). 8 S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptical solenoid beams.\u201d Opt. Express 18 , 6988\u20136993 (2010). 9 E.\u00a0R. Dufresne and D.\u00a0G. Grier. \u201cOptical tweezer arrays and optical substrates created with diffractive optical elements.\u201d Rev. Sci. Instrum. 69 , 1974\u20131977 (1998). 10 D.\u00a0G. Grier. \u201cA revolution in optical manipulation.\u201d Nature 424 , 810\u2013816 (2003). 11 J.\u00a0W. Goodman. Introduction to Fourier Optics (McGraw-Hill, New York, 2005), 3rd ed. 12 Y.\u00a0Roichman, I.\u00a0Cholis and D.\u00a0G. Grier. \u201cVolumetric imaging of holographic optical traps.\u201d Opt. Express 14 , 10907\u201310912 (2006). 13 J.\u00a0E. Curtis, B.\u00a0A. Koss and D.\u00a0G. Grier. \u201cDynamic holographic optical tweezers.\u201d Opt. Commun. 207 , 169\u2013175 (2002). 14 C.-S. Guo, X.\u00a0Liu, J.-L. He and H.-T. Wang. \u201cOptimal annulus structures of optical vortices.\u201d Opt. Express 12 , 4625\u20134634 (2004). 15 K.\u00a0Ladavac and D.\u00a0G. Grier. \u201cColloidal hydrodynamic coupling in concentric optical vortices.\u201d Europhys. Lett. 70 , 548\u2013554 (2005). 16 Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cProjecting extended optical traps with shape-phase holography.\u201d Opt. Lett. 31 , 1675\u20131677 (2006). 17 M.\u00a0Polin, K.\u00a0Ladavac, S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptimized holographic optical traps.\u201d Opt. Express 13 , 5831\u20135845 (2005). 18 S.-H. Lee, Y.\u00a0Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A.\u00a0van Blaaderen, P.\u00a0van Oostrum and D.\u00a0G. Grier. ``Characterizing and tracking single colloidal particles with video holographic microscopy.\u201d Opt. Express 15 , 18275\u201318282 (2007). 19 F.\u00a0C. Cheong, B.\u00a0J. Krishnatreya and D.\u00a0G. Grier. \u201cStrategies for three-dimensional particle tracking with holographic video microscopy.\u201d Opt. Express 18 , 13563\u201313573 (2010). 20 F.\u00a0C. Cheong, B.\u00a0Sun, R.\u00a0Dreyfus, J.\u00a0Amato-Grill, K.\u00a0Xiao, L.\u00a0Dixon and D.\u00a0G. Grier. \u201cFlow visualization and flow cytometry with holographic video microscopy.\u201d Opt. Express 17 , 13071\u201313079 (2009). 21 V.\u00a0Garc\u00e9s-Ch\u00e1vez, D.\u00a0McGloin, H.\u00a0Melville, W.\u00a0Sibbett and K.\u00a0Dholakia. \u201cSimultaneous micromanipulation in multiple planes using a self-reconstructing light beam.\u201d Nature 419 , 145\u2013147 (2002). 22 S.-H. Lee and D.\u00a0G. Grier. ``Holographic microscopy of holographically trapped three-dimensional structures.\u201d Opt. Express 15 , 1505\u20131512 (2007). 23 S.\u00a0Albaladejo, M.\u00a0I. Marqu\u00e9s, F.\u00a0Scheffold and J.\u00a0J. S\u00e1enz. \u201cGiant enhanced diffusion of gold nanoparticles in optical vortex fields.\u201d Nano Lett. 9 , 3527\u20133531 (2009). 24 D.\u00a0B. Ruffner and D.\u00a0G. Grier. \u201cOptical forces and torques in non-uniform beams of light.\u201d Phys. Rev. Lett. 108 , 173602 (2012). 25 S.-H. Lee, K.\u00a0Ladavac, M.\u00a0Polin and D.\u00a0G. Grier. \u201cObservation of flux reversal in a symmetric optical thermal ratchet.\u201d Phys. Rev. Lett. 94 , 110601 (2005). 26 S.-H. Lee and D.\u00a0G. Grier. \u201cFlux reversal in a two-state symmetric optical thermal ratchet.\u201d Phys. Rev. E 71 , 060102(R) (2005). 27 S.-H. Lee and D.\u00a0G. Grier. \u201cOne-dimensional optical thermal ratchets.\u201d J. Phys.: Condens. Matter 17 , S3685\u2013S3695 (2006). D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012)"}, {"content": "Optical solenoid beams Optical solenoid beams References David Grier's Home Page Grier Group Publications Optical solenoid beams Sang-Hyuk Lee Department of Molecular and Cell Biology, Institute for Quantitative Biology, University of California, Berkeley, CA 94720-3220 Yohai Roichman David G. Grier Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003 Abstract. We introduce optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction-limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. Unlike other collimated beams of light, appropriately designed solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light's propagation. We demonstrate this through video microscopy observations of a colloidal sphere moving upstream along a holographically projected optical solenoid beam. pacs: (350.5500) Propagation; (260.1960) Diffraction theory; (090.1760) Computer holography; (350.4855) Optical tweezers or optical manipulation. Radiation pressure due to the momentum flux in a beam of light drives illuminated objects along the direction of the light's wave vector. Additional forces arising from intensity gradients tend to draw small objects toward extrema of the intensity. These forces are exploited in single-beam optical traps known as optical tweezers (1) , which capture microscopic objects at the focus of a strongly converging beam of light. Stable three-dimensional trapping results when axial intensity gradients are steep enough that the intensity-gradient force overcomes radiation pressure downstream of the focus. The beam of light in a tightly focused optical tweezer therefore has the remarkable property of drawing particles upstream against radiation pressure, at least near its focal point (1) . Collimated beams of light generally have no axial intensity gradients, and therefore ought not to be able to exert such retrograde forces. In this Letter, we introduce optical solenoid beams whose principal intensity maximum spirals around the optical axis and whose wavefronts are characterized by an independent helical pitch. Figure\u00a0 1 (Media 1) shows theoretical and experimentally realized examples. These beams are solutions of the Helmholtz equation, and thus propagate without diffraction (2) ; (3) , their radial intensity profiles remaining invariant in the spiraling frame of reference (4) . Intensity gradients in a solenoid beam tend to draw small objects such as colloidal particles toward the one-dimensional spiral of maximum intensity. Radiation pressure directed by the beam's phase gradients (5) then can drive the particle around the spiral. Under appropriate circumstances, the combination of intensity-gradient localization and phase-gradient driving can create a component of the total optical force directed opposite to the light's direction of propagation, which can pull matter upstream along the beam's entire length. The vector potential for a beam of light at frequency propagating along the direction may be written as ( 1 ) where is the wave number of the light, is its polarization vector and measures the two-dimensional displacement from the beam's axis. We derive the three-dimensional optical solenoid field by considering the two-dimensional field in the plane, . Because the light propagating to must first pass through the plane , the field in this plane completely specifies the beam. Moreover, a featureless beam imprinted with the complex field in the plane will propagate into the far field as . In this sense, may be considered the hologram encoding the desired beam. Figure 1. (a) Calculated three-dimensional intensity distribution of a solenoid beam propagating in the direction. (b) Volumetric rendering of the measured intensity in an experimental realization. Media 1 shows a rotating view of this static beam. Quite generally, may be obtained from by formally back-propagating the three-dimensional field to . This can be accomplished in scalar diffraction theory with the Rayleigh-Sommerfeld formula (6) , ( 2 ) ( 3 ) is the Rayleigh-Sommerfeld propagator, and where the convolution is given by ( 4 ) This formalism can be useful even if the desired field, , is not a solution of the Helmholtz equation, and so does not describe a physically realizable beam of light. In that case, the physical beam, , associated with can be obtained by propagating forward, again using the Rayleigh-Sommerfeld propagator, ( 5 ) Those solutions for which , is independent of are said to be non-diffracting (2) ; (3) . We now apply this formalism to designing beams of light whose intensity maxima trace out specified one-dimensional curves in three dimensions, with arbitrary amplitude and phase profiles along these curves. Such beams may be represented as ( 6 ) Here, is the position of the beam's maximum at axial position , is its amplitude, and is its phase. This representation does not describe a physically realizable beam of light because it neither incorporates self-diffraction nor locally conserves energy or momentum. Equations\u00a0( 2 ) through ( 5 ) nevertheless yield a physically realizable beam that has the desired properties along , provided that self-diffraction may be neglected. Equation\u00a0( 4 ) is most easily computed with the Fourier convolution theorem. In that case, the two-dimensional Fourier transform of is ( 7 ) An inverse Fourier transform then provides , and Eq.\u00a0( 5 ) yields the associated beam of light. This result extends to three dimensions our previous descriptions of holographic line traps and holographic ring traps in the plane (7) ; (8) . As a step toward deriving the solenoid beam, we first consider the case of an infinite line of light propagating along the optical axis, , with uniform amplitude, , but with a specified axial phase gradient, . For , Eq.\u00a0( 7 ) has solutions ( 8 ) and , which is the zeroth-order Bessel beam (9) ; (10) ; (11) . Whereas we specified an infinitesimally finely resolved thread of light, formal back-propagation with Eq.\u00a0( 7 ) implicitly accounts for the beam's self-diffraction. The limit corresponds to a plane wave propagating along . Smaller values of yield more finely resolved beams that carry less momentum along . To create a solenoidal beam, we set and , where is the azimuthal angle around the optical axis in a spiral of radius and pitch . In addition to establishing a spiral structure for the beam's principal intensity maximum, we also impose a helical phase profile in the plane, , where the helical pitch, , is independent of . This helical phase profile will enable us to exert tunable phase-gradient forces (5) along the solenoid. As for the Bessel beam, we seek a non-diffracting solution of Eq.\u00a0( 7 ), and so integrate over all to obtain ( 9 ) where and where is the integer part of . The solenoid beam thus is a particular superposition of -th order Bessel beams. Superposition of non-diffracting modes previously has been used to synthesize multi-lobed spiral (12) ; (13) ; (14) and localized (15) ; (16) modes. More generally, Eq.\u00a0( 9 ) is a particular example of a rotating scale-invariant electromagnetic field (4) . Figure\u00a0 1 (a) shows the three-dimensional intensity distribution computed according to Eq.\u00a0( 9 ) for , and . As intended, the locus of maximum intensity spirals around the optical axis. Quite clearly, the intensity distribution of a solenoid depends on , and so is not strictly invariant under propagation. Nonetheless, the in-plane intensity distribution remains invariant, merely rotating about the optical axis. Such a generalization of the notion of non-diffracting propagation previously was introduced in the context of spiral waves (12) . Solenoid beams therefore may be considered to be non-diffracting in this more general sense. Distinct solenoid beams satisfy the orthogonality condition ( 10 ) except if is an integer that falls in the range . This additional condition defines classes of -congruent solenoid beams whose members are not mutually orthogonal and results from the solenoid modes' non-trivial periodicity along the optical axis. Figure 2. Retrograde forces in a helical solenoid beam. The local wave vector is normal to the light's wavefronts, with a component in the direction. (a) : is directed along the solenoid, resulting in a downstream phase-gradient force. (b) : Wavefronts are parallel to the solenoid so that is everywhere normal to the spiral. Particles trapped by intensity-gradient forces experience no net force. (c) : A component of is directed back down the spiral. A particle confined to the spiral therefore moves upstream. Figure\u00a0 2 shows the effect of changing the helicity of a solenoid beam with a fixed spiral pitch, . When , as in Fig.\u00a0 2 (a), the wave vector is directed along the solenoid. A particle confined to the spiral by intensity-gradient forces therefore is driven downstream by this component of the radiation pressure. Changing does not alter , but changes the wavefronts' pitch relative to . At , the wavefronts are parallel to the solenoid's pitch. as shown in Fig.\u00a0 2 (b). In this case, radiation pressure is directed normal to the spiral, and so can be balanced by intensity-gradient forces. Setting tilts the wavefronts in the retrograde direction, as shown in Fig.\u00a0 2 (c). The resulting reverse-sense phase-gradient force can move the particle upstream along the spiral in the negative direction. We experimentally projected solenoid beams using methods developed for holographic optical trapping (17) ; (18) ; (19) . In this system, a phase-only liquid crystal spatial light modulator (SLM) (Hamamatsu X7690-16 PPM) is used to imprint the hologram associated with onto the wavefronts of a linearly polarized laser beam with a vacuum wavelength (Coherent Verdi). This hologram then is projected into the far field with a microscope objective lens (Nikon Plan Apo, 100 , oil immersion) mounted in a conventional inverted optical microscope (Nikon TE 2000U). The computed complex hologram is encoded on the phase-only SLM using the shape-phase holography algorithm (7) . The resulting beam includes the intended solenoid mode superposed with higher diffraction orders (20) . To visualize the projected beam, we mount a front-surface mirror on the microscope's stage. The reflected light is collected by the objective lens, and relayed to a CCD camera (NEC TI-324AII). Images acquired at a sequence of focal depths then are combined to create a volumetric rendering of the three-dimensional intensity field (21) . The example in Fig.\u00a0 1 (b) (Media 1) shows the serpentine structure of a holographically projected solenoid beam with . To demonstrate the solenoid beam's ability to exert retrograde forces on microscopic objects, we projected it into a sample of colloidal silica spheres 1.5\u00a0 in diameter dispersed in water. The sample was contained in the 50\u00a0 thick gap between a glass microscope slide and a glass no.\u00a01 cover slip, and was mounted on the microscope's stage. Bright-field images of individual spheres interacting with the solenoid beam were obtained with the same objective lens used to project the hologram, and were recorded by the video camera at 1/30\u00a0 intervals. The sphere's appearance changes as it moves in in a manner that can be calibrated (22) to measure the particle's axial position. Combining this with simultaneous measurements of the particle's in-plane position (22) yields the three-dimensional trajectory data that are plotted in Fig.\u00a0 3 (Media 2). The gray-scale image in Fig.\u00a0 3 was created by superimposing six snapshots of a single sphere that was trapped on a solenoid beam and moving along its length. This and the video sequence in Media 2 illustrate how the sphere's image changes as it moves in . Figure 3. Three-dimensional trajectory of a colloidal sphere moving along one turn of an optical solenoid beam together with a multiply-exposed image of the sphere at six points in its motion (Media 2). Alternating between switches the direction of the particle's motion relative to the propagation direction, . Arrows indicate the direction of motion for the downstream (blue) and retrograde upstream (red) trajectories. The data plotted in Fig.\u00a0 3 (Media 2) were obtained by alternately setting and without changing any other properties of the solenoid beam. The three blue traces show trajectories obtained with in which the particle moved downstream along the curve of the solenoid, advancing in the direction of the light's propagation. These alternate with two red traces obtained with in which the particle moves back upstream, opposite to the direction of the light's propagation. These latter traces confirm that the combination of phase- and intensity-gradient forces in helical solenoid beams can exert retrograde forces on illuminated objects and transport them upstream over large distances. Although the solenoid beam was designed to be uniformly bright, the particle does not move along it smoothly in practice. Interference between the holographically projected solenoid beam and higher diffraction orders creates unintended intensity variations along the solenoid that tend to localize the particle. Achieving retrograde motions over distances larger than the 8\u00a0 in our demonstration will require improved methods for projecting solenoid modes. The foregoing results introduce solenoidal beams of light whose non-diffracting transverse intensity profiles spiral periodically around the optical axis and whose wavefronts can be independently inclined through specified azimuthal phase profiles. We have demonstrated that solenoid beams can trap microscopic objects in three dimensions and that phase-gradient forces can be used to transport trapped objects not only down the optical axis but also up. The ability to balance radiation pressure with phase-gradient forces in solenoidal beams opens a previously unexplored avenue for single-beam control of microscopic objects. In principle, solenoid beams can transport objects over large distances, much as do Bessel beams (11) ; (23) and related non-diffracting modes (24) , without the need for high-numerical-aperture optics. Solenoid beams, moreover, offer the additional benefit of bidirectional transport along the optical axis. This work was supported by the National Science Foundation through Grant Number DMR-0855741 and by the W. M. Keck Foundation. S.H.L.\u00a0acknowledges support from the Kessler Family Foundation. References (1) A.\u00a0Ashkin, J.\u00a0M. Dziedzic, J.\u00a0E. Bjorkholm, and S.\u00a0Chu, \u201cObservation of a single-beam gradient force optical trap for dielectric particles,\u201d Opt. Lett. 11 , 288\u2013290 (1986). (2) J.\u00a0Durnin, \u201cExact-solutions for nondiffracting beams. 1. The scalar theory,\u201d J. Opt. Soc. Am. A 4 , 651\u2013654 (1987). (3) J.\u00a0Durnin, \u201cDiffraction-free beams,\u201d Phys. Rev. Lett. 58 , 1499\u20131501 (1987). (4) J.\u00a0Tervo and J.\u00a0Turunen, \u201cRotating scale-invariant electromagnetic fields,\u201d Opt. Express 9 , 9\u201315 (2001). (5) Y.\u00a0Roichman, B.\u00a0Sun, Y.\u00a0Roichman, J.\u00a0Amato-Grill, and D.\u00a0G. Grier, \u201cOptical forces arising from phase gradients,\u201d Phys. Rev. Lett. 100 , 013602 (2008). (6) J.\u00a0W. Goodman, Introduction to Fourier Optics , 2nd ed. (McGraw-Hill, New York, 1996). (7) Y.\u00a0Roichman and D.\u00a0G. Grier, \u201cProjecting extended optical traps with shape-phase holography,\u201d Opt. Lett. 31 , 1675\u20131677 (2006). (8) Y.\u00a0Roichman and D.\u00a0G. Grier, \u201cThree-dimensional holographic ring traps,\u201d Proc. SPIE 6483 , 64830F (2007). (9) A.\u00a0Vasara, J.\u00a0Turunen, and A.\u00a0T. Friberg, \u201cRealization of general nondiffracting beams with computer-generated holograms,\u201d J. Opt. Soc. Am. A 6 (11), 1748\u20131754 (1989). (10) P.\u00a0L. Overfelt, \u201cScalar optical beams with helical symmetry,\u201d Phys. Rev. A 46 , 3516\u20133522 (1992). (11) J.\u00a0Arlt, V.\u00a0Garc\u00e9s-Ch\u00e1vez, W.\u00a0Sibbett, and K.\u00a0Dholakia, \u201cOptical micromanipulation using a Bessel light beam,\u201d Opt. Commun. 197 , 239\u2013245 (2001). (12) S.\u00a0Ch\u00e1vez-Cerda, G.\u00a0S. McDonald, and G.\u00a0H.\u00a0C. New, \u201cNondiffracting beams: travelling, standing, rotating and spiral waves,\u201d Opt. Commun. 123 , 225\u2013233 (1996). (13) V.\u00a0V. Kotlyar, V.\u00a0A. Soifer, and S.\u00a0N. Khonina, \u201cAn algorithm for the generation of laser beams with longitudinal periodicity: Rotating images,\u201d J. Mod. Opt. 44 , 1409\u20131416 (1997). (14) P.\u00a0P\u00e4\u00e4kk\u00f6nen, J.\u00a0Lautanen, M.\u00a0Honkanen, M.\u00a0Kuittinen, J.\u00a0Turunen, S.\u00a0N. Khonina, V.\u00a0V. Kotlyar, V.\u00a0A. Soifer, and A.\u00a0T. Friberg, \u201cRotating optical fields: experimental demonstration with diffractive optics,\u201d J. Mod. Opt. 45 , 2355\u20132369 (1998). (15) Z.\u00a0Bouchal and J.\u00a0Kyvalsky, \u201cControllable 3D spatial localization of light fields synthesized by non-diffracting modes,\u201d J. Mod. Opt. 51 , 157\u2013176 (2004). (16) J.\u00a0Courtial, G.\u00a0Whyte, Z.\u00a0Bouchal, and J.\u00a0Wagner, \u201cIterative algorithms for holographic shaping of non-diffracting and self-imaging light beams,\u201d Opt. Express 14 , 2108\u20132116 (2006). (17) E.\u00a0R. Dufresne and D.\u00a0G. Grier, \u201cOptical tweezer arrays and optical substrates created with diffractive optical elements,\u201d Rev. Sci. Instrum. 69 , 1974\u20131977 (1998). (18) D.\u00a0G. Grier, \u201cA revolution in optical manipulation,\u201d Nature 424 , 810\u2013816 (2003). (19) M.\u00a0Polin, K.\u00a0Ladavac, S.-H. Lee, Y.\u00a0Roichman, and D.\u00a0G. Grier, \u201cOptimized holographic optical traps,\u201d Opt. Express 13 (15), 5831\u20135845 (2005). (20) S.-H. Lee and D.\u00a0G. Grier, \u201cRobustness of holographic optical traps against phase scaling errors,\u201d Opt. Express 13 , 7458\u20137465 (2005). (21) Y.\u00a0Roichman, I.\u00a0Cholis, and D.\u00a0G. Grier, \u201cVolumetric imaging of holographic optical traps,\u201d Opt. Express 14 , 10,907\u201310,912 (2006). (22) J.\u00a0C. Crocker and D.\u00a0G. Grier, \u201cMethods of digital video microscopy for colloidal studies,\u201d J. Colloid Interface Sci. 179 , 298\u2013310 (1996). (23) V.\u00a0Garc\u00e9s-Ch\u00e1vez, D.\u00a0McGloin, H.\u00a0Melville, W.\u00a0Sibbett, and K.\u00a0Dholakia, \u201cSimultaneous micromanipulation in multiple planes using a self-reconstructing light beam,\u201d Nature 419 , 145\u2013147 (2002). (24) T.\u00a0\u010ci\u017em\u00e1r, V.\u00a0Koll\u00e1rov\u00e1, Z.\u00a0Bouchal, and P.\u00a0Zem\u00e1nek, \u201cSub-micron particle organization by self-imaging of non-diffracting beams,\u201d New J. Phys. 8 , 43 (2006). S.\u00a0Lee, Y.\u00a0Roichman and D.\u00a0G.\u00a0Grier, Optics Express 18, 6988-6993 (2010)"}, {"content": "Mass Mass is the amount of matter an object has. We often use a triple-balance beam to measure mass. A triple-beam balance gets its name because it has three beams that allow you to move known masses along the beam. Here is a picture of a triple beam balance. You probably have used one in school. To read more about the triple-beam balances shown above click here There are also many other types of balances. Scientists need balances that can measure very small amounts of mass. If you are interested at looking at the many other types of balances click here . If you are using a triple beam balance in school you might want to brush up on your skills on how to use a triple-beam balance Now it's time to practice your skills using the triple-beam balance . Problem 1: A block is put onto a triple beam balance. What is the mass of the object? Click on the picture below and get a closer look at reading the scale after the scale has been balanced. Type your answer in the space provided below, then hit the submit button . The mass of the object is: grams Do you often get confused between mass and weight? Check out the Mass vs. Weight Page Please continue to Part II ."}]},
{"detail": [{"content": "Optical conveyors: A class of active tractor beams Optical conveyors: A class of active tractor beams References David Grier's Home Page Grier Group Publications Optical conveyors: A class of active tractor beams David B.\u00a0Ruffner and David G.\u00a0Grier Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003 Abstract. We experimentally demonstrate a class of tractor beams created by coherently superposing coaxial Bessel beams. These optical conveyors have periodic intensity variations along their axes that act as highly effective optical traps for micrometer-scale objects. Varying the Bessel beams' relative phase shifts the traps axially thereby selectively transports trapped objects either downstream or upstream along the length of the beam. The same methods used to project a single optical conveyor can project arrays of independent optical conveyors, allowing bi-directional transport in three dimensions. A tractor beam is a traveling wave that can transport illuminated material along its length back to its source. By this definition, an optical tweezer [ 1 ] is not a tractor beam because of its inherently limited range. Nor is an optical conveyor belt [ 2 , 3 ] , which is created from a standing wave rather than a traveling wave. A one-sided variant of the optical conveyor belt created from coaxial Bessel beams has been demonstrated, but relies on auxiliary forces to achieve retrograde motion [ 4 ] . Here, we demonstrate one-sided optical conveyors that act as tractor beams without requiring outside assistance. The same technique we use to project a single optical conveyor also can project arrays of optical conveyors each with independently controlled transport properties. Most beams of light do not act as tractor beams because radiation pressure tends to drive illuminated objects downstream. Recently, however two categories of tractor beams have been described, both of which exploit properties of propagation-invariant or non-diffracting traveling waves [ 5 ] , and thus have promise for long-range material transport. Both rely on the recoil force that an illuminated object experiences if it scatters transverse components of the beam's linear momentum density into the axial direction. The first is based on multipole scattering in Bessel beams, which has been predicted to drive retrograde motion in both acoustic [ 6 ] and optical [ 7 ] waves. Because this mechanism relies on scattering by high-order induced multipole moments, however, the direction of induced transport depends sensitively on the properties of the illuminated object; tractor beams based on pure Bessel modes have not yet been demonstrated experimentally. The other approach utilizes periodic axial intensity gradients in beams with discrete propagation invariance [ 5 ] to achieve forward scattering from the interference between the incident field and the dipole radiation field of an illuminated object. Such tractor beams have been realized experimentally with solenoidal waves that have transported micrometer-scale colloidal spheres over an axial range of 10\u00a0 \u00a0 [ 8 ] . Figure 1. (color online) (a) Schematic representation of holographic projection of a Bessel beam with axial wavenumber by a lens of focal length . Shaded region indicates volume of invariant propagation. (b) Volumetric reconstruction of a holographically projected Bessel beam. (c) Phase hologram encoding an optical conveyor. Diagonal blazing tilts the projected conveyor away from the optical axis. (d) Volumetric reconstruction of the beam projected by the hologram in (c). The color bar indicates relative intensities in (b) and (d). Here, we describe another category of tractor beams derived from the optical conveyor belts introduced in Refs.\u00a0 [ 2 , 3 , 4 ] that can be projected from a single source and can transport material bidirectionally without the aid of outside forces. A one-sided optical conveyor is formed by projecting two or more coherent Bessel beams along the same axis and systematically varying their relative phase. The vector potential for a two-component optical conveyor of frequency and polarization may be written in cylindrical coordinates as ( 1 ) where is the wavenumber of light in a medium with refractive index and is a Bessel function of the first kind of order . The two beams differ in their axial wavenumbers, and , which are reduced from by factors . They also differ in their relative phase , whose time variation makes the conveyor work. The prefactor is the beam's amplitude. Setting the relative amplitude to unity, , maximizes the conveyor's axial intensity gradients and thus optimizes its performance for optical manipulation. In the special case , , the component Bessel beams have unit amplitude along the optical axis, , and the conveyor's axial intensity is ( 2 ) ( 3 ) where . The beam thus has intensity maxima at axial positions ( 4 ) that are evenly spaced by multiples, , of the wavelength in the medium, and thus can be indexed by the integer . Objects trapped along can be displaced either up or down the axis by appropriately varying the relative phase . Continuous variations translate trapped objects deterministically along with axial velocity, ( 5 ) regardless of their size, shape, or optical properties. This differs from the action of Bessel-based tractor beams [ 6 ] in which even the sign of the induced motion depends on each object's properties. It differs also from the motion induced by solenoidal tractor beams [ 8 ] which is unidirectional but not uniformly fast. We implemented optical conveyors using the holographic optical trapping technique [ 9 ] in which a computer-designed phase profile is imprinted onto the wavefronts of a Gaussian beam, which then is projected into the sample with a high-numerical-aperture objective lens of focal length . In practice, the trap-forming hologram is implemented with a computer-addressable spatial light modulator (SLM) (Hamamatsu X8267-16) that imposes a selected phase shift at each pixel in a array. If the field described by Eq.\u00a0( 1 ) is to be projected into the objective's focal plane, the field in the plane of the hologram is given in the scalar diffraction approximation [ 11 ] by its Fourier transform, ( 6 ) where is the Dirac delta function, and , The ideal hologram for each Bessel beam comprising the conveyor thus is a thin ring in the plane of the SLM, as indicated schematically in Fig.\u00a0 1 (a). A holographically projected Bessel beam then propagates without diffraction over the range indicated by the shaded region. Increasing the transverse wave number increases the radius of the hologram and therefore reduces the non-diffracting range. Figure\u00a0 1 (b) shows a volumetric reconstruction [ 12 ] of a Bessel beam projected with a ring-like hologram. Increasing the ring's thickness of the ring by increases diffraction efficiency, but is equivalent to superposing Bessel beams with a range of axial wavenumbers, . This superposition contributes an overall axial envelope to the projected Bessel beam, limiting its axial range to . The axial range in Fig.\u00a0 1 (b) is consistent with this estimate and so is smaller than the ray-optics estimate suggested by the overlap volume in Fig.\u00a0 1 (a). Figure\u00a0 1 (c) shows the two-ringed phase-only hologram that encodes an optical conveyor with an overall cone angle of . This function corresponds to the phase of the beam's vector potential, which the SLM imprints on an incident Gaussian plane wave. The relative phase offset between the two rings determines . The relative widths of the two phase rings can be used to establish the components' relative amplitudes through , the range of the projected conveyor then being the smaller of and . The large featureless regions in Fig.\u00a0 1 (c) do not contribute to the desired optical conveyor. Light passing through these regions is not diffracted and therefore converges at the focal point of the optical train. To prevent interference between the diffracted and undiffracted beams, the two phase rings contributing to the conveyor are offset and blazed with a linear phase gradient [ 13 ] to displace the projected Bessel beams by 24\u00a0 \u00a0from the optical axis. Figure 2. (color online) (a) Trajectories of two 1.5\u00a0 \u00a0diameter colloidal silica spheres moving along a pair of optical conveyors, superimposed with a holographic snapshot of the two spheres. Colored orbs indicate the spheres' positions in the hologram, and are plotted at the same scale as the actual spheres. Rings are added for emphasis. (b) Measured time dependence of the spheres' axial positions as one moves downstream ( ) along its conveyor and the other moves upstream ( ). (c) Three-dimensional reconstruction of a holographic snapshot of two colloidal spheres moving along a single optical conveyor. The volumetric reconstruction in Fig.\u00a0 1 (d) shows the three-dimensional intensity distribution projected by the hologram in Fig.\u00a0 1 (c), with oriented along the diffracted beam's direction of propagation. This beam clearly displays the pattern of periodically alternating bright and dark regions predicted by Eqs.\u00a0( 1 ) through ( 4 ). The unused regions of the hologram need not go to waste. They can be used to project additional independent conveyors, much as has been demonstrated for spatially multiplexed optical traps of other types [ 14 ] . An appropriately designed array of conveyors therefore can make full use of the light falling on the SLM and thus can be projected with very high diffraction efficiency. Each conveyor, moreover, can be operated independently of the others by selectively offsetting the phase in appropriate regions of the multiplexed hologram. The data in Fig.\u00a0 2 were obtained with two separate optical conveyors projected simultaneously with equal intensity and equal axial period by a single hologram. The conveyors' phases were ramped at the same rate, but with opposite sign. This single structured beam of light therefore should transport material in opposite directions simultaneously. To demonstrate this, we projected the pair of conveyors into a sample of 1.5\u00a0 \u00a0diameter colloidal silica spheres dispersed in water (Polysciences, Lot # 600424). The sample is contained in the 100\u00a0 \u00a0deep gap between a clean glass microscope slide and a cover-slip that was formed by and sealed with UV-curing optical adhesive (Norland 68). The slide was mounted on the stage of a Nikon TE-2000U optical microscope outfitted with a custom-built holographic optical trapping system [ 17 ] operating at a vacuum wavelength of . An estimated 17\u00a0 \u00a0of linearly polarized light were projected into each conveyor with a numerical aperture 1.4 oil-immersion objective lens (Nikon Plan-Apo DIC H) at an overall efficiency of 0.5 percent. To facilitate tracking the spheres as they move along the optical axis, the microscope's conventional illuminator was replaced with a 10\u00a0 \u00a03\u00a0 -diameter collimated laser beam at a vacuum wavelength of 445\u00a0 . Interference between light scattered by the spheres and the rest of the illumination forms a hologram of the spheres in the focal plane of the objective lens that is magnified and recorded at 30 frames per second with a conventional greyscale video camera (NEC TI-324A-II). A typical holographic snapshot is reproduced in Fig.\u00a0 2 (a). These holograms then can be analyzed [ 18 , 20 ] to obtain the spheres' three-dimensional positions with nanometer-scale resolution. The traces in Fig.\u00a0 2 (a) show the full trajectories of both spheres over the course of the experiment. Colored orbs indicate the measured positions of the spheres at the instant of the holographic snapshot and are scaled to represent the actual sizes of the spheres. Starting from the configuration in Fig.\u00a0 2 (a), the two conveyors were run through total phase ramps of in steps of , yielding the axial trajectories plotted in Fig.\u00a0 2 (b). Reversing the phase ramps reverses the process. These measurements confirm that arrays of optical conveyors can selectively induce bidirectional transport over their entire lengths. The self-healing nature of Bessel beams [ 5 , 21 ] furthermore suggests that multiple objects can be trapped and moved by a single optical conveyor despite light scattering by each of the trapped objects [ 2 , 3 , 4 ] . This is confirmed by Fig.\u00a0 2 (c), which shows a volumetric reconstruction [ 22 ] of the light scattered by two colloidal spheres simultaneously trapped on an optical conveyor. The plotted intensity distribution was computed from the inset hologram by Rayleigh-Sommerfeld back-propagation. Maxima representing the positions of the spheres are separated by two periods of the underlying optical conveyor. To characterize and optimize the transport properties of optical conveyors, we model the forces they exert in the Rayleigh approximation, which is appropriate for objects smaller than the wavelength of light. Considering both induced-dipole attraction and radiation pressure, the axial component of the force is ( 7 ) where the coefficients and parameterize the light-matter interaction for a particle with electric polarizability . For simplicity, Eq.\u00a0( 7 ) omits contributions due to the curl of the spin density [ 23 ] , and thus is appropriate for linearly polarized light. Further assuming a conveyor of the form described by Eq.\u00a0( 2 ) with continuously ramped phase, , the equation of motion for a colloidal particle with drag coefficient is ( 8 ) where is the downstream drift speed due to radiation pressure, and where describes the relative axial trapping strength. Particles that are trapped by intensity gradients are translated upstream with the conveyor's phase velocity, . From Eq.\u00a0( 8 ), the maximum upstream transport speed is then limited by viscous drag to ( 9 ) This remarkable result suggests that an optical conveyor can act as a tractor beam for any particle with provided that it is not run too fast. Both light-seeking ( ) and dark-seeking ( ) particles should move in the same direction with the same speed, although the dark-seeking particles will sit near the beam's minima. Optical conveyors thus have the potential to out-perform optical tweezers, which cannot always achieve stable axial trapping even in the Rayleigh regime. Equation\u00a0( 9 ) also suggests straightforward optimization strategies for optical conveyors. Brighter conveyors can run faster. Reducing the conveyor's spatial period proportionately increases the maximum transport rate at the cost of reducing the maximum range. Higher-order conveyors with also have intensity maxima at positions given by Eq.\u00a0( 4 ). They differ from zero-order conveyors in that their principal maxima are displaced from to transverse radii that depend on , , and . This larger transverse range may be useful for conveying irregular or asymmetrically shaped objects, or objects with inhomogeneous optical properties. Higher-order conveyors also carry orbital angular momentum and so will exert torques on trapped objects. The transport direction predicted by Eq.\u00a0( 8 ) reverses sign in the limit of large , illuminated objects then traveling steadily downstream at the drift speed . The crossover between upstream and downstream transport is marked by a dynamical state in which the particle alternately is transported upstream and slips back downstream. The transition to this state is established by Eq.\u00a0( 9 ) in the deterministic case described by Eq.\u00a0( 8 ). It will be strongly affected by thermal fluctuations, however, and may feature anomalous velocity fluctuations. Still other dynamical states are possible if the relative phase varies discontinuously, for example in a Brownian ratchet protocol [ 25 ] . Even more complicated behavior may be expected for optical conveyor transport in underdamped systems for which inertia plays a role. This work was supported by the National Science Foundation under Grant Number DMR-0922680. The authors are grateful for enlightening conversations with Paul Stysley, Demetrios Poulios and Donald Coyle. References 1 A.\u00a0Ashkin, J.\u00a0M. Dziedzic, J.\u00a0E. Bjorkholm and S.\u00a0Chu. \u201cObservation of a single-beam gradient force optical trap for dielectric particles.\u201d Opt. Lett. 11 , 288\u2013290 (1986). 2 T.\u00a0\u010ci\u017emar, V.\u00a0Garc\u00e9s-Ch\u00e1vez, K.\u00a0Dhokalia and P.\u00a0Zem\u00e1nek. \u201cOptical conveyor belt for delivery of submicron objects.\u201d Appl. Phys. Lett. 86 , 174101 (2005). 3 T.\u00a0\u010ci\u017em\u00e1r, M.\u00a0\u0160iler and P.\u00a0Zem\u00e1nek. \u201cAn optical nanotrap array movable over a milimetre range.\u201d Appl. Phys. B 84 , 197\u2013203 (2006). 4 T.\u00a0\u010ci\u017em\u00e1r, V.\u00a0Koll\u00e1rov\u00e1, Z.\u00a0Bouchal and P.\u00a0Zem\u00e1nek. \u201cSub-micron particle organization by self-imaging of non-diffracting beams.\u201d New J. Phys. 8 , 43 (2006). 5 J.\u00a0Durnin. \u201cDiffraction-free beams.\u201d Phys. Rev. Lett. 58 , 1499\u20131501 (1987). 6 P.\u00a0L. Marston. \u201cAxial radiation force of a Bessel beam on a sphere and direction reversal of the force.\u201d J. Acoust. Soc. Am. 120 , 3518\u20133524 (2006). 7 J.\u00a0Chen, J.\u00a0Ng, Z.\u00a0Lin and C.\u00a0T. Chan. \u201cOptical pulling force.\u201d Nature Photonics 5 , 531\u2013534 (2011). 8 S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptical solenoid beams.\u201d Opt. Express 18 , 6988\u20136993 (2010). 9 E.\u00a0R. Dufresne and D.\u00a0G. Grier. \u201cOptical tweezer arrays and optical substrates created with diffractive optical elements.\u201d Rev. Sci. Instrum. 69 , 1974\u20131977 (1998). 10 D.\u00a0G. Grier. \u201cA revolution in optical manipulation.\u201d Nature 424 , 810\u2013816 (2003). 11 J.\u00a0W. Goodman. Introduction to Fourier Optics (McGraw-Hill, New York, 2005), 3rd ed. 12 Y.\u00a0Roichman, I.\u00a0Cholis and D.\u00a0G. Grier. \u201cVolumetric imaging of holographic optical traps.\u201d Opt. Express 14 , 10907\u201310912 (2006). 13 J.\u00a0E. Curtis, B.\u00a0A. Koss and D.\u00a0G. Grier. \u201cDynamic holographic optical tweezers.\u201d Opt. Commun. 207 , 169\u2013175 (2002). 14 C.-S. Guo, X.\u00a0Liu, J.-L. He and H.-T. Wang. \u201cOptimal annulus structures of optical vortices.\u201d Opt. Express 12 , 4625\u20134634 (2004). 15 K.\u00a0Ladavac and D.\u00a0G. Grier. \u201cColloidal hydrodynamic coupling in concentric optical vortices.\u201d Europhys. Lett. 70 , 548\u2013554 (2005). 16 Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cProjecting extended optical traps with shape-phase holography.\u201d Opt. Lett. 31 , 1675\u20131677 (2006). 17 M.\u00a0Polin, K.\u00a0Ladavac, S.-H. Lee, Y.\u00a0Roichman and D.\u00a0G. Grier. \u201cOptimized holographic optical traps.\u201d Opt. Express 13 , 5831\u20135845 (2005). 18 S.-H. Lee, Y.\u00a0Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A.\u00a0van Blaaderen, P.\u00a0van Oostrum and D.\u00a0G. Grier. ``Characterizing and tracking single colloidal particles with video holographic microscopy.\u201d Opt. Express 15 , 18275\u201318282 (2007). 19 F.\u00a0C. Cheong, B.\u00a0J. Krishnatreya and D.\u00a0G. Grier. \u201cStrategies for three-dimensional particle tracking with holographic video microscopy.\u201d Opt. Express 18 , 13563\u201313573 (2010). 20 F.\u00a0C. Cheong, B.\u00a0Sun, R.\u00a0Dreyfus, J.\u00a0Amato-Grill, K.\u00a0Xiao, L.\u00a0Dixon and D.\u00a0G. Grier. \u201cFlow visualization and flow cytometry with holographic video microscopy.\u201d Opt. Express 17 , 13071\u201313079 (2009). 21 V.\u00a0Garc\u00e9s-Ch\u00e1vez, D.\u00a0McGloin, H.\u00a0Melville, W.\u00a0Sibbett and K.\u00a0Dholakia. \u201cSimultaneous micromanipulation in multiple planes using a self-reconstructing light beam.\u201d Nature 419 , 145\u2013147 (2002). 22 S.-H. Lee and D.\u00a0G. Grier. ``Holographic microscopy of holographically trapped three-dimensional structures.\u201d Opt. Express 15 , 1505\u20131512 (2007). 23 S.\u00a0Albaladejo, M.\u00a0I. Marqu\u00e9s, F.\u00a0Scheffold and J.\u00a0J. S\u00e1enz. \u201cGiant enhanced diffusion of gold nanoparticles in optical vortex fields.\u201d Nano Lett. 9 , 3527\u20133531 (2009). 24 D.\u00a0B. Ruffner and D.\u00a0G. Grier. \u201cOptical forces and torques in non-uniform beams of light.\u201d Phys. Rev. Lett. 108 , 173602 (2012). 25 S.-H. Lee, K.\u00a0Ladavac, M.\u00a0Polin and D.\u00a0G. Grier. \u201cObservation of flux reversal in a symmetric optical thermal ratchet.\u201d Phys. Rev. Lett. 94 , 110601 (2005). 26 S.-H. Lee and D.\u00a0G. Grier. \u201cFlux reversal in a two-state symmetric optical thermal ratchet.\u201d Phys. Rev. E 71 , 060102(R) (2005). 27 S.-H. Lee and D.\u00a0G. Grier. \u201cOne-dimensional optical thermal ratchets.\u201d J. Phys.: Condens. Matter 17 , S3685\u2013S3695 (2006). D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 109, 163903 (2012)"}, {"content": "Optical solenoid beams Optical solenoid beams References David Grier's Home Page Grier Group Publications Optical solenoid beams Sang-Hyuk Lee Department of Molecular and Cell Biology, Institute for Quantitative Biology, University of California, Berkeley, CA 94720-3220 Yohai Roichman David G. Grier Department of Physics and Center for Soft Matter Research, New York University, New York, NY 10003 Abstract. We introduce optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction-limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. Unlike other collimated beams of light, appropriately designed solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light's propagation. We demonstrate this through video microscopy observations of a colloidal sphere moving upstream along a holographically projected optical solenoid beam. pacs: (350.5500) Propagation; (260.1960) Diffraction theory; (090.1760) Computer holography; (350.4855) Optical tweezers or optical manipulation. Radiation pressure due to the momentum flux in a beam of light drives illuminated objects along the direction of the light's wave vector. Additional forces arising from intensity gradients tend to draw small objects toward extrema of the intensity. These forces are exploited in single-beam optical traps known as optical tweezers (1) , which capture microscopic objects at the focus of a strongly converging beam of light. Stable three-dimensional trapping results when axial intensity gradients are steep enough that the intensity-gradient force overcomes radiation pressure downstream of the focus. The beam of light in a tightly focused optical tweezer therefore has the remarkable property of drawing particles upstream against radiation pressure, at least near its focal point (1) . Collimated beams of light generally have no axial intensity gradients, and therefore ought not to be able to exert such retrograde forces. In this Letter, we introduce optical solenoid beams whose principal intensity maximum spirals around the optical axis and whose wavefronts are characterized by an independent helical pitch. Figure\u00a0 1 (Media 1) shows theoretical and experimentally realized examples. These beams are solutions of the Helmholtz equation, and thus propagate without diffraction (2) ; (3) , their radial intensity profiles remaining invariant in the spiraling frame of reference (4) . Intensity gradients in a solenoid beam tend to draw small objects such as colloidal particles toward the one-dimensional spiral of maximum intensity. Radiation pressure directed by the beam's phase gradients (5) then can drive the particle around the spiral. Under appropriate circumstances, the combination of intensity-gradient localization and phase-gradient driving can create a component of the total optical force directed opposite to the light's direction of propagation, which can pull matter upstream along the beam's entire length. The vector potential for a beam of light at frequency propagating along the direction may be written as ( 1 ) where is the wave number of the light, is its polarization vector and measures the two-dimensional displacement from the beam's axis. We derive the three-dimensional optical solenoid field by considering the two-dimensional field in the plane, . Because the light propagating to must first pass through the plane , the field in this plane completely specifies the beam. Moreover, a featureless beam imprinted with the complex field in the plane will propagate into the far field as . In this sense, may be considered the hologram encoding the desired beam. Figure 1. (a) Calculated three-dimensional intensity distribution of a solenoid beam propagating in the direction. (b) Volumetric rendering of the measured intensity in an experimental realization. Media 1 shows a rotating view of this static beam. Quite generally, may be obtained from by formally back-propagating the three-dimensional field to . This can be accomplished in scalar diffraction theory with the Rayleigh-Sommerfeld formula (6) , ( 2 ) ( 3 ) is the Rayleigh-Sommerfeld propagator, and where the convolution is given by ( 4 ) This formalism can be useful even if the desired field, , is not a solution of the Helmholtz equation, and so does not describe a physically realizable beam of light. In that case, the physical beam, , associated with can be obtained by propagating forward, again using the Rayleigh-Sommerfeld propagator, ( 5 ) Those solutions for which , is independent of are said to be non-diffracting (2) ; (3) . We now apply this formalism to designing beams of light whose intensity maxima trace out specified one-dimensional curves in three dimensions, with arbitrary amplitude and phase profiles along these curves. Such beams may be represented as ( 6 ) Here, is the position of the beam's maximum at axial position , is its amplitude, and is its phase. This representation does not describe a physically realizable beam of light because it neither incorporates self-diffraction nor locally conserves energy or momentum. Equations\u00a0( 2 ) through ( 5 ) nevertheless yield a physically realizable beam that has the desired properties along , provided that self-diffraction may be neglected. Equation\u00a0( 4 ) is most easily computed with the Fourier convolution theorem. In that case, the two-dimensional Fourier transform of is ( 7 ) An inverse Fourier transform then provides , and Eq.\u00a0( 5 ) yields the associated beam of light. This result extends to three dimensions our previous descriptions of holographic line traps and holographic ring traps in the plane (7) ; (8) . As a step toward deriving the solenoid beam, we first consider the case of an infinite line of light propagating along the optical axis, , with uniform amplitude, , but with a specified axial phase gradient, . For , Eq.\u00a0( 7 ) has solutions ( 8 ) and , which is the zeroth-order Bessel beam (9) ; (10) ; (11) . Whereas we specified an infinitesimally finely resolved thread of light, formal back-propagation with Eq.\u00a0( 7 ) implicitly accounts for the beam's self-diffraction. The limit corresponds to a plane wave propagating along . Smaller values of yield more finely resolved beams that carry less momentum along . To create a solenoidal beam, we set and , where is the azimuthal angle around the optical axis in a spiral of radius and pitch . In addition to establishing a spiral structure for the beam's principal intensity maximum, we also impose a helical phase profile in the plane, , where the helical pitch, , is independent of . This helical phase profile will enable us to exert tunable phase-gradient forces (5) along the solenoid. As for the Bessel beam, we seek a non-diffracting solution of Eq.\u00a0( 7 ), and so integrate over all to obtain ( 9 ) where and where is the integer part of . The solenoid beam thus is a particular superposition of -th order Bessel beams. Superposition of non-diffracting modes previously has been used to synthesize multi-lobed spiral (12) ; (13) ; (14) and localized (15) ; (16) modes. More generally, Eq.\u00a0( 9 ) is a particular example of a rotating scale-invariant electromagnetic field (4) . Figure\u00a0 1 (a) shows the three-dimensional intensity distribution computed according to Eq.\u00a0( 9 ) for , and . As intended, the locus of maximum intensity spirals around the optical axis. Quite clearly, the intensity distribution of a solenoid depends on , and so is not strictly invariant under propagation. Nonetheless, the in-plane intensity distribution remains invariant, merely rotating about the optical axis. Such a generalization of the notion of non-diffracting propagation previously was introduced in the context of spiral waves (12) . Solenoid beams therefore may be considered to be non-diffracting in this more general sense. Distinct solenoid beams satisfy the orthogonality condition ( 10 ) except if is an integer that falls in the range . This additional condition defines classes of -congruent solenoid beams whose members are not mutually orthogonal and results from the solenoid modes' non-trivial periodicity along the optical axis. Figure 2. Retrograde forces in a helical solenoid beam. The local wave vector is normal to the light's wavefronts, with a component in the direction. (a) : is directed along the solenoid, resulting in a downstream phase-gradient force. (b) : Wavefronts are parallel to the solenoid so that is everywhere normal to the spiral. Particles trapped by intensity-gradient forces experience no net force. (c) : A component of is directed back down the spiral. A particle confined to the spiral therefore moves upstream. Figure\u00a0 2 shows the effect of changing the helicity of a solenoid beam with a fixed spiral pitch, . When , as in Fig.\u00a0 2 (a), the wave vector is directed along the solenoid. A particle confined to the spiral by intensity-gradient forces therefore is driven downstream by this component of the radiation pressure. Changing does not alter , but changes the wavefronts' pitch relative to . At , the wavefronts are parallel to the solenoid's pitch. as shown in Fig.\u00a0 2 (b). In this case, radiation pressure is directed normal to the spiral, and so can be balanced by intensity-gradient forces. Setting tilts the wavefronts in the retrograde direction, as shown in Fig.\u00a0 2 (c). The resulting reverse-sense phase-gradient force can move the particle upstream along the spiral in the negative direction. We experimentally projected solenoid beams using methods developed for holographic optical trapping (17) ; (18) ; (19) . In this system, a phase-only liquid crystal spatial light modulator (SLM) (Hamamatsu X7690-16 PPM) is used to imprint the hologram associated with onto the wavefronts of a linearly polarized laser beam with a vacuum wavelength (Coherent Verdi). This hologram then is projected into the far field with a microscope objective lens (Nikon Plan Apo, 100 , oil immersion) mounted in a conventional inverted optical microscope (Nikon TE 2000U). The computed complex hologram is encoded on the phase-only SLM using the shape-phase holography algorithm (7) . The resulting beam includes the intended solenoid mode superposed with higher diffraction orders (20) . To visualize the projected beam, we mount a front-surface mirror on the microscope's stage. The reflected light is collected by the objective lens, and relayed to a CCD camera (NEC TI-324AII). Images acquired at a sequence of focal depths then are combined to create a volumetric rendering of the three-dimensional intensity field (21) . The example in Fig.\u00a0 1 (b) (Media 1) shows the serpentine structure of a holographically projected solenoid beam with . To demonstrate the solenoid beam's ability to exert retrograde forces on microscopic objects, we projected it into a sample of colloidal silica spheres 1.5\u00a0 in diameter dispersed in water. The sample was contained in the 50\u00a0 thick gap between a glass microscope slide and a glass no.\u00a01 cover slip, and was mounted on the microscope's stage. Bright-field images of individual spheres interacting with the solenoid beam were obtained with the same objective lens used to project the hologram, and were recorded by the video camera at 1/30\u00a0 intervals. The sphere's appearance changes as it moves in in a manner that can be calibrated (22) to measure the particle's axial position. Combining this with simultaneous measurements of the particle's in-plane position (22) yields the three-dimensional trajectory data that are plotted in Fig.\u00a0 3 (Media 2). The gray-scale image in Fig.\u00a0 3 was created by superimposing six snapshots of a single sphere that was trapped on a solenoid beam and moving along its length. This and the video sequence in Media 2 illustrate how the sphere's image changes as it moves in . Figure 3. Three-dimensional trajectory of a colloidal sphere moving along one turn of an optical solenoid beam together with a multiply-exposed image of the sphere at six points in its motion (Media 2). Alternating between switches the direction of the particle's motion relative to the propagation direction, . Arrows indicate the direction of motion for the downstream (blue) and retrograde upstream (red) trajectories. The data plotted in Fig.\u00a0 3 (Media 2) were obtained by alternately setting and without changing any other properties of the solenoid beam. The three blue traces show trajectories obtained with in which the particle moved downstream along the curve of the solenoid, advancing in the direction of the light's propagation. These alternate with two red traces obtained with in which the particle moves back upstream, opposite to the direction of the light's propagation. These latter traces confirm that the combination of phase- and intensity-gradient forces in helical solenoid beams can exert retrograde forces on illuminated objects and transport them upstream over large distances. Although the solenoid beam was designed to be uniformly bright, the particle does not move along it smoothly in practice. Interference between the holographically projected solenoid beam and higher diffraction orders creates unintended intensity variations along the solenoid that tend to localize the particle. Achieving retrograde motions over distances larger than the 8\u00a0 in our demonstration will require improved methods for projecting solenoid modes. The foregoing results introduce solenoidal beams of light whose non-diffracting transverse intensity profiles spiral periodically around the optical axis and whose wavefronts can be independently inclined through specified azimuthal phase profiles. We have demonstrated that solenoid beams can trap microscopic objects in three dimensions and that phase-gradient forces can be used to transport trapped objects not only down the optical axis but also up. The ability to balance radiation pressure with phase-gradient forces in solenoidal beams opens a previously unexplored avenue for single-beam control of microscopic objects. In principle, solenoid beams can transport objects over large distances, much as do Bessel beams (11) ; (23) and related non-diffracting modes (24) , without the need for high-numerical-aperture optics. Solenoid beams, moreover, offer the additional benefit of bidirectional transport along the optical axis. This work was supported by the National Science Foundation through Grant Number DMR-0855741 and by the W. M. Keck Foundation. S.H.L.\u00a0acknowledges support from the Kessler Family Foundation. References (1) A.\u00a0Ashkin, J.\u00a0M. Dziedzic, J.\u00a0E. Bjorkholm, and S.\u00a0Chu, \u201cObservation of a single-beam gradient force optical trap for dielectric particles,\u201d Opt. Lett. 11 , 288\u2013290 (1986). (2) J.\u00a0Durnin, \u201cExact-solutions for nondiffracting beams. 1. The scalar theory,\u201d J. Opt. Soc. Am. A 4 , 651\u2013654 (1987). (3) J.\u00a0Durnin, \u201cDiffraction-free beams,\u201d Phys. Rev. Lett. 58 , 1499\u20131501 (1987). (4) J.\u00a0Tervo and J.\u00a0Turunen, \u201cRotating scale-invariant electromagnetic fields,\u201d Opt. Express 9 , 9\u201315 (2001). (5) Y.\u00a0Roichman, B.\u00a0Sun, Y.\u00a0Roichman, J.\u00a0Amato-Grill, and D.\u00a0G. Grier, \u201cOptical forces arising from phase gradients,\u201d Phys. Rev. Lett. 100 , 013602 (2008). (6) J.\u00a0W. Goodman, Introduction to Fourier Optics , 2nd ed. (McGraw-Hill, New York, 1996). (7) Y.\u00a0Roichman and D.\u00a0G. Grier, \u201cProjecting extended optical traps with shape-phase holography,\u201d Opt. Lett. 31 , 1675\u20131677 (2006). (8) Y.\u00a0Roichman and D.\u00a0G. Grier, \u201cThree-dimensional holographic ring traps,\u201d Proc. SPIE 6483 , 64830F (2007). (9) A.\u00a0Vasara, J.\u00a0Turunen, and A.\u00a0T. Friberg, \u201cRealization of general nondiffracting beams with computer-generated holograms,\u201d J. Opt. Soc. Am. A 6 (11), 1748\u20131754 (1989). (10) P.\u00a0L. Overfelt, \u201cScalar optical beams with helical symmetry,\u201d Phys. Rev. A 46 , 3516\u20133522 (1992). (11) J.\u00a0Arlt, V.\u00a0Garc\u00e9s-Ch\u00e1vez, W.\u00a0Sibbett, and K.\u00a0Dholakia, \u201cOptical micromanipulation using a Bessel light beam,\u201d Opt. Commun. 197 , 239\u2013245 (2001). (12) S.\u00a0Ch\u00e1vez-Cerda, G.\u00a0S. McDonald, and G.\u00a0H.\u00a0C. New, \u201cNondiffracting beams: travelling, standing, rotating and spiral waves,\u201d Opt. Commun. 123 , 225\u2013233 (1996). (13) V.\u00a0V. Kotlyar, V.\u00a0A. Soifer, and S.\u00a0N. Khonina, \u201cAn algorithm for the generation of laser beams with longitudinal periodicity: Rotating images,\u201d J. Mod. Opt. 44 , 1409\u20131416 (1997). (14) P.\u00a0P\u00e4\u00e4kk\u00f6nen, J.\u00a0Lautanen, M.\u00a0Honkanen, M.\u00a0Kuittinen, J.\u00a0Turunen, S.\u00a0N. Khonina, V.\u00a0V. Kotlyar, V.\u00a0A. Soifer, and A.\u00a0T. Friberg, \u201cRotating optical fields: experimental demonstration with diffractive optics,\u201d J. Mod. Opt. 45 , 2355\u20132369 (1998). (15) Z.\u00a0Bouchal and J.\u00a0Kyvalsky, \u201cControllable 3D spatial localization of light fields synthesized by non-diffracting modes,\u201d J. Mod. Opt. 51 , 157\u2013176 (2004). (16) J.\u00a0Courtial, G.\u00a0Whyte, Z.\u00a0Bouchal, and J.\u00a0Wagner, \u201cIterative algorithms for holographic shaping of non-diffracting and self-imaging light beams,\u201d Opt. Express 14 , 2108\u20132116 (2006). (17) E.\u00a0R. Dufresne and D.\u00a0G. Grier, \u201cOptical tweezer arrays and optical substrates created with diffractive optical elements,\u201d Rev. Sci. Instrum. 69 , 1974\u20131977 (1998). (18) D.\u00a0G. Grier, \u201cA revolution in optical manipulation,\u201d Nature 424 , 810\u2013816 (2003). (19) M.\u00a0Polin, K.\u00a0Ladavac, S.-H. Lee, Y.\u00a0Roichman, and D.\u00a0G. Grier, \u201cOptimized holographic optical traps,\u201d Opt. Express 13 (15), 5831\u20135845 (2005). (20) S.-H. Lee and D.\u00a0G. Grier, \u201cRobustness of holographic optical traps against phase scaling errors,\u201d Opt. Express 13 , 7458\u20137465 (2005). (21) Y.\u00a0Roichman, I.\u00a0Cholis, and D.\u00a0G. Grier, \u201cVolumetric imaging of holographic optical traps,\u201d Opt. Express 14 , 10,907\u201310,912 (2006). (22) J.\u00a0C. Crocker and D.\u00a0G. Grier, \u201cMethods of digital video microscopy for colloidal studies,\u201d J. Colloid Interface Sci. 179 , 298\u2013310 (1996). (23) V.\u00a0Garc\u00e9s-Ch\u00e1vez, D.\u00a0McGloin, H.\u00a0Melville, W.\u00a0Sibbett, and K.\u00a0Dholakia, \u201cSimultaneous micromanipulation in multiple planes using a self-reconstructing light beam,\u201d Nature 419 , 145\u2013147 (2002). (24) T.\u00a0\u010ci\u017em\u00e1r, V.\u00a0Koll\u00e1rov\u00e1, Z.\u00a0Bouchal, and P.\u00a0Zem\u00e1nek, \u201cSub-micron particle organization by self-imaging of non-diffracting beams,\u201d New J. Phys. 8 , 43 (2006). S.\u00a0Lee, Y.\u00a0Roichman and D.\u00a0G.\u00a0Grier, Optics Express 18, 6988-6993 (2010)"}, {"content": "Mass Mass is the amount of matter an object has. We often use a triple-balance beam to measure mass. A triple-beam balance gets its name because it has three beams that allow you to move known masses along the beam. Here is a picture of a triple beam balance. You probably have used one in school. To read more about the triple-beam balances shown above click here There are also many other types of balances. Scientists need balances that can measure very small amounts of mass. If you are interested at looking at the many other types of balances click here . If you are using a triple beam balance in school you might want to brush up on your skills on how to use a triple-beam balance Now it's time to practice your skills using the triple-beam balance . Problem 1: A block is put onto a triple beam balance. What is the mass of the object? Click on the picture below and get a closer look at reading the scale after the scale has been balanced. Type your answer in the space provided below, then hit the submit button . The mass of the object is: grams Do you often get confused between mass and weight? Check out the Mass vs. Weight Page Please continue to Part II ."}]}] |
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"under": "General Orders"
},
{
"acted_at": "2008-09-26",
"references": [
{
"reference": "CR S9595-9599",
"type": "consideration"
},
{
"reference": "CR S9595-9596",
"type": "text of measure as reported in Senate"
}
],
"text": "Measure laid before Senate by unanimous consent.",
"type": "action"
},
{
"acted_at": "2008-09-26",
"references": [],
"text": "The committee substitute as amended agreed to by Unanimous Consent.",
"type": "action"
},
{
"acted_at": "2008-09-26",
"how": "by Unanimous Consent",
"references": [],
"result": "pass",
"status": "PASS_OVER:SENATE",
"text": "Passed Senate with an amendment by Unanimous Consent.",
"type": "vote",
"vote_type": "vote",
"where": "s"
},
{
"acted_at": "2008-09-26T15:34:00-04:00",
"references": [],
"text": "Received in the House.",
"type": "action"
},
{
"acted_at": "2008-09-26",
"references": [],
"text": "Message on Senate action sent to the House.",
"type": "action"
},
{
"acted_at": "2008-09-26T16:34:00-04:00",
"references": [],
"text": "Held at the desk.",
"type": "action"
},
{
"acted_at": "2008-09-27T19:06:00-04:00",
"references": [],
"text": "Ms. Lofgren, Zoe moved to suspend the rules and pass the bill.",
"type": "action"
},
{
"acted_at": "2008-09-27T19:06:00-04:00",
"references": [
{
"reference": "CR H10268-10270",
"type": "consideration"
}
],
"text": "Considered under suspension of the rules.",
"type": "action"
},
{
"acted_at": "2008-09-27T19:06:00-04:00",
"references": [],
"text": "DEBATE - The House proceeded with forty minutes of debate on S. 2304.",
"type": "action"
},
{
"acted_at": "2008-09-27T19:10:00-04:00",
"references": [],
"text": "At the conclusion of debate, the chair put the question on the motion to suspend the rules. Mr. Smith (TX) objected to the vote on the grounds that a quorum was not present. Further proceedings on the motion were postponed. The point of no quorum was withdrawn.",
"type": "action"
},
{
"acted_at": "2008-09-29T14:59:00-04:00",
"references": [
{
"reference": "CR H10631",
"type": "consideration"
}
],
"text": "Considered as unfinished business.",
"type": "action"
},
{
"acted_at": "2008-09-29T14:59:00-04:00",
"how": "by voice vote",
"references": [
{
"reference": "CR 9/27/2008 H10268-10269",
"type": "text"
}
],
"result": "pass",
"status": "PASSED:BILL",
"suspension": null,
"text": "On motion to suspend the rules and pass the bill Agreed to by voice vote.",
"type": "vote",
"vote_type": "vote2",
"where": "h"
},
{
"acted_at": "2008-09-29T14:59:00-04:00",
"references": [],
"text": "Motion to reconsider laid on the table Agreed to without objection.",
"type": "action"
},
{
"acted_at": "2008-09-29",
"references": [],
"text": "Cleared for White House.",
"type": "topresident"
},
{
"acted_at": "2008-10-03",
"references": [],
"text": "Presented to President.",
"type": "topresident"
},
{
"acted_at": "2008-10-14",
"references": [],
"text": "Signed by President.",
"type": "signed"
},
{
"acted_at": "2008-10-14",
"congress": "110",
"law": "public",
"number": "416",
"references": [],
"status": "ENACTED:SIGNED",
"text": "Became Public Law No: 110-416.",
"type": "enacted"
}
],
"amendments": [
{
"amendment_id": "s5656-110",
"amendment_type": "s",
"chamber": "s",
"number": "5656"
}
],
"bill_id": "s2304-110",
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"committees": [
{
"activity": [
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],
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],
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{
"district": null,
"name": "Kennedy, Edward M.",
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"thomas_id": "01377",
"title": "Sen",
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},
{
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"state": "VT",
"thomas_id": "01383",
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"withdrawn_at": null
},
{
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},
{
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"state": "PA",
"thomas_id": "01437",
"title": "Sen",
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},
{
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"name": "Webb, Jim",
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}
],
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},
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"house_passage_result_at": "2008-09-29T14:59:00-04:00",
"senate_passage_result": "pass",
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"vetoed": false
},
"introduced_at": "2007-11-05",
"number": "2304",
"official_title": "A bill to amend title I of the Omnibus Crime Control and Safe Streets Act of 1968 to provide grants for the improved mental health treatment and services provided to offenders with mental illnesses, and for other purposes.",
"popular_title": null,
"related_bills": [
{
"bill_id": "hr3992-110",
"reason": "related"
},
{
"bill_id": "hr3992-110",
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}
],
"short_title": "Mentally Ill Offender Treatment and Crime Reduction Reauthorization and Improvement Act of 2008",
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"name": "Domenici, Pete V.",
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},
"status": "ENACTED:SIGNED",
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"subjects": [
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"Authorization",
"Congress",
"Congressional reporting requirements",
"Crime and law enforcement",
"Economics and public finance",
"Education",
"Families",
"Federal aid to Indians",
"Federal aid to law enforcement",
"Government operations and politics",
"Governmental investigations",
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"Indian courts",
"Indian law enforcement",
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"Law",
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"Mental illness",
"Minorities",
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"Students",
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],
"subjects_top_term": "Crime and law enforcement",
"summary": {
"as": "Public Law",
"date": "2008-10-14",
"text": "Mentally Ill Offender Treatment and Crime Reduction Reauthorization and Improvement Act of 2008 - Amends the Omnibus Crime Control and Safe Streets Act of 1968 to extend through 2014 the authorization of appropriations for the adult and juvenile mental health collaboration grant program. Includes within the priorities for awarding grants under such program the identification and treatment of mentally-ill offenders and the expanded use of mental health courts. Authorizes the Attorney General to make grants to states, local governments, Indian tribes, and tribal organizations to: (1) offer law enforcement officers and campus security personnel training to respond appropriately to incidents involving mentally-ill individuals; (2) establish specialized receiving centers to assess the mental health requirements and suicide risk of individuals in law enforcement custody; (3) provide computerized information systems to improve the response of law enforcement and criminal justice personnel to mentally-ill offenders; and (4) establish cooperative programs to promote public safety by using effective intervention for mentally-ill offenders. Requires the Director of the Bureau of Justice Assistance to develop training models for law enforcement personnel for responding to the needs of individuals with mental illnesses, including suicide prevention. Prohibits federal matching funds from exceeding 50% of the cost of a grant program. Directs the Attorney General to examine and report to Congress on mental illness and the criminal justice system, including: (1) the rate of occurrence of serious mental illnesses in individuals (including juveniles) on probation, incarcerated in a jail or prison, or on parole; and (2) the percentage of individuals in each of those populations who have a serious mental illness and have received social security disability benefits. Authorizes appropriations."
},
"titles": [
{
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},
{
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},
{
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"title": "Mentally Ill Offender Treatment and Crime Reduction Reauthorization and Improvement Act of 2008",
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{
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},
{
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},
{
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"title": "A bill to amend title I of the Omnibus Crime Control and Safe Streets Act of 1968 to provide grants for the improved mental health treatment and services provided to offenders with mental illnesses, and for other purposes.",
"type": "official"
}
],
"updated_at": "2013-02-02T20:43:57-05:00"
} |
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{"id": "35943082", "header": "Tại sao thông đột ngột chết hàng loạt khắp TQ vào những năm 1970?", "datetime": "2020-08-06T12:40:00.000+07:00", "summary": "Công nghệ giải mã trình tự gen đã giúp giải đáp câu hỏi hóc búa trong suốt 50 năm đối với các nhà khoa học, đồng thời cải thiện các chương trình về cây trồng ở Trung Quốc.", "content": "Các nhà thực vật học Trung Quốc nói rằng họ đã có thể lý giải cho cái chết hàng loạt của cây thông trên khắp đất nước, điều gây trở ngại cho các nhà khoa học trong suốt 50 năm. Câu trả lời là có thể các cây thông chết do gen.Loài thông Pinus armandii, hay cây thông núi Hua, là một loài có nguồn gốc từ Trung Quốc, và có thể sống sót trong điều kiện khắc nghiệt như vách núi. Cây thông trắng cũng là một biểu tượng của sự trường tồn trong văn hóa Trung Hoa - Thần Đạo trường thọ luôn được nhìn thấy trong các bức tranh với một cây thông núi Hua làm nền.Tuy nhiên, vào những năm 1970, các cây thông đã chết trên diện rộng khi được trồng lại ở nhiều tỉnh. Và nguyên nhân của cái chết này suốt thời gian dài là một dấu hỏi lớn.Giờ đây, các nhà khoa học tại Viện thực vật học Côn Minh ở tỉnh Vân Nam nói rằng họ có thể có câu trả lời. Dẫn đầu bởi nhà thực vật học Liu Jie, nhóm nghiên cứu đã thu thập các mẫu cây từ những vùng trồng thông trên khắp Trung Quốc để xây dựng cơ sở dữ liệu thông tin về loài thông lớn nhất cả nước.Thông qua phân tích di truyền, họ tìm thấy rằng thông có ba chi - và những khác biệt về gen này nghĩa là chúng không phù hợp để sống trong cùng một điều kiện.Điều đó giải thích tại sao những cây được trồng trong chiến dịch trồng rừng lại không thể sống sót - bởi chúng không được trồng trong môi trường tự nhiên của chúng, các nhà khoa học cho biết trong một bài báo được công bố trên tạp chí hồi tháng 7.Họ cũng nói rằng đó có thể là lý do từ đó đến nay không có đợt các cây thông chết nào tương tự.Công nghiệp hóa quy mô lớn bắt đầu ở Trung Quốc vào những năm 1950. Chưa đầy 2 thập kỷ sau, những ngọn núi với các khu rừng rậm rạp một thời đã trơ trụi bởi khai thác gỗ, hay chặt rừng lấy chỗ để xây dựng đường sắt, nhà máy và các khu dân cư.Vấn đề phá rừng gây tác động nghiêm trọng, chính phủ Trung Quốc đã phát động một chiến dịch trồng cây vào cuối những năm 1960.Tuy nhiên, chiến dịch không có kế hoạch hay hướng dẫn cụ thể. Các cây thông chủ yếu được trồng ở những khu vực mà những giống cây tương tự đã từng sống. Cây non được bảo vệ và chăm sóc bởi các cơ quan lâm nghiệp địa phương.Chúng trông có vẻ giống như những cây thông núi Hua khác mọc tự nhiên gần đó, nhưng trình tự di truyền của chúng cho thấy rằng ngay cả trong cùng một dãy núi, chúng cũng có thể khác loài nhau.Họ ước tính rằng chi thông đầu tiên xuất hiện khoảng 9 triệu năm trước khi một dãy núi lớn hình thành trên khắp trung tâm Trung Quốc. Một số loài cây không thể thích nghi với sự thay đổi mạnh mẽ của môi trường và bị diệt vong, nhưng cây thông núi Hua vẫn sống sót và phát triển mạnh.Theo nghiên cứu, ba chi của thông có một bộ gen riêng biệt thích nghi với các môi trường khác nhau và có rất ít trao đổi gen giữa chúng.Tuy nhiên, những người trồng cây cách đây 50 năm không nhận thức được sự khác biệt về gen này. Họ trồng những cây thông hợp với khu vực có độ cao thấp và ngược lại.Một vài năm sau, nhiều cây thông trong số đó đột nhiên bắt đầu chết dần.Các nhà thực vật trong nhiều năm đã đưa ra một số lý thuyết giải thích cho điều này, bao gồm mưa axit và một loại nấm gây bệnh, nhưng tất cả được chứng minh là sai sau đó.Cũng không có bằng chứng nào về nguyên nhân cái chết là do ô nhiễm môi trường, bệnh tật hoặc biến đổi khí hậu.Và cũng chưa có lời giải thích nào cho việc những hiện tượng tương tự không xảy ra lần nữa. Ngày nay, gần như tất cả những ngọn núi bị ảnh hưởng đều đã được trồng lại cây thông núi Hua, và phân tích di truyền cho thấy sự phân bố của chúng tuân theo một mô hình tự nhiên.Các nhà khoa học cho biết có rất ít dấu hiệu ảnh hưởng của con người đối với sự phân bố của các loài thông khác nhau, thứ có xu hướng chiếm đa số trong các khu vực mà chúng phù hợp.Nông dân và giới chức trách cơ quan lâm nghiệp trong những năm 1980 không được tiếp cận với công nghệ giải trình tự gen, như khi họ trồng lại thông, họ đã sử dụng hạt giống từ những cây mọc tự nhiên gần đó. Do đó, không có cái chết hàng loạt nào từ đó đến nay.\"Họ đã tuân thủ nguyên tắc phù hợp với địa hình của loài [chọn một loài phù hợp với địa điểm đó] và giữ cho sự ảnh hưởng của con người đối với cảnh quan thiên nhiên đến mức tối thiểu\", các nhà nghiên cứu khẳng định.Xu Bo, một nhà nghiên cứu của Viện Thực vật hoạc ở Bắc Kinh, dù không tham gia vào nghiên cứu, cho biết những phát hiện này sẽ giúp cải thiện chương trình trồng cây lớn nhất thế giới của Trung Quốc.Ông cũng lưu ý rằng \"những đặc điểm quan trọng của một loài thực vật không thể được nhìn thấy qua vẻ bề ngoài\". Nhà nghiên cứu này cho biết việc phân loại truyền thống theo loài có nghĩa là sự thích nghi của loài thực vật với các môi trường khác nhau có thể bị bỏ qua.Trình tự di truyền đã được thực hiện trên các cây trồng quan trọng như lúa, lúa mì và ngô, những gen của hầu hết thực vật vẫn chưa được giải đáp.\"Chúng ta đang trong thời đại khám phá\", nhà nghiên cứu Xu cho biết. Theo South China Morning Post ", "topic": "Khoa học", "tag": ["Nhà thực vật học", "Cây thông", "Trồng rừng", "Liu Jie", "Chết", "Gene", "Hàng loạt", "Lời giải thích", "Trường thọ", "Trung Quốc", "Thực vật", "Trình tự", "Trồng cây", "Nhà khoa học", "Núi", "Giải đáp", "Núi Lớn", "Hóc búa", "Cây trồng", "Lâm nghiệp"], "link": "https://zingnews.vn/tai-sao-thong-dot-ngot-chet-hang-loat-khap-tq-vao-nhung-nam-1970-post1115456.html"} |
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{"url": "http://www.dtic.mil/docs/citations/ADA620615", "authors": "BA Cotton", "title": "Strategic improvements to TSA SPOT program", "year": "2015", "source": ""} |
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{
"title": "【Swisse女性复合维生素 120片】Swisse斯维诗 女士复合维生素片 120片/瓶 澳洲维他命 女性成人营养 澳洲进口 迪丽热巴同款【行情 报价 价格 评测】-京东",
"comment": "一直吃这个牌子的复合维生素，原来是澳大利亚的外甥女儿给买了寄过来的，后来在京东国际上发现有，价格也不贵，而且京东国际的商品值得信赖，所以就买了，买过来比较了一下，完全一样，是正品哦！快递速度也是非常快的！所以还给女儿买了青少年的复合维生素！以后就在京东国际上买了！",
"date": "2020-03-24 20:52",
"platform": "JD.com"
} |
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"name": "API Management Deployment",
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"publisher": "plukasiak",
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}
],
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],
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},
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{"id": "35898607", "header": "Hình ảnh bệnh viện dã chiến điều trị Covid-19 tại Đà Nẵng", "datetime": "2020-08-02T18:07:03.000+07:00", "summary": "Trưa 2/8, hàng trăm công nhân đang gấp rút thực hiện việc xây dựng Cơ sở điều trị Covid-19 tại Cung thể thao Tiên Sơn (quận Hải Châu – TP Đà Nẵng).", "content": "Đại diện bộ phận thi công cho hay, trong hôm nay và ngày mai, công trình sẽ hoàn thiện phần thô, 2 ngày tiếp theo sẽ lắp đặt điện nước, hệ thống thông gió, giường bệnh...Dự kiến việc thi công được hoàn thiện trong vòng 4 ngày. Ngày 4/8, Bộ Y tế sẽ vào kiểm tra công tác chuẩn bị tại đây.Trước đó, sáng 1/8, ngay sau khi Đà Nẵng thống nhất việc xây dựng cơ sở này, đơn vị phụ trách Cung thể thao Tiên Sơn đã tiến hành thu dọn, tạm thời di chuyển sang địa điểm làm việc mới để phục vụ việc lắp đặt, dựng phòng bệnh điều trị Covid-19.Bà Ngô Thị Kim Yến, Giám đốc Sở Y tế TP Đà Nẵng thông tin, các trang thiết bị phục vụ cho bệnh viện này cơ bản đã đầy đủ. Theo bà Yến, Sở đã chỉ định bà Trần Thanh Thủy, Phó Giám đốc Sở Y tế TP đảm nhiệm chức vụ Giám đốc cơ sở điều trị Covid-19 và phụ trách về hậu cần, tổ chức. Hiện cơ sở này vẫn đang cần một Phó giám đốc hỗ trợ về chuyên môn.Cơ sở điều trị Covid-19 tại Cung thể thao Tiên Sơn dự kiến có quy mô 700 giường bệnh, được dành để điều trị những ca bệnh nhẹ.Tính đến sáng 2/8, Việt Nam ghi nhận 590 ca Covid-19. Chỉ tính riêng từ ngày 25/7 tới nay, nước ta đã phát hiện thêm 177 ca mắc mới, trong đó tới 144 ca được xác định có liên quan đến Đà Nẵng.5 bệnh nhân Covid-19 tử vong chỉ trong vòng 3 ngày từ 31/7 đến 2/8, bao gồm bệnh nhân 428, bệnh nhân 437, bệnh nhân 499, bệnh nhân 524 và bệnh nhân 475. ", "topic": "Nhà đất", "tag": ["Bệnh viện dã chiến", "Cung Thể thao Tiên Sơn", "Đà Nẵng", "Lắp đặt", "Giường bệnh", "Xây dựng cơ sở", "Điều trị", "Ca bệnh", "Gấp rút", "Thi công", "Bộ y tế", "Công nhân", "Thu dọn", "Hải Châu", "Đà Nẵng", "Điện nước", "Ngô Thị Kim Yến", "Trần Thanh Thủy", "Thông gió", "Sở Y tế TP", "Phòng bệnh"], "link": "https://vietnamnet.vn/vn/suc-khoe/hinh-anh-benh-vien-da-chien-dieu-tri-covid-19-tai-da-nang-662859.html"} |
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[
{
"category": "interesting",
"title": "One in every 4 Americans has appeared on television.",
"_id": "572bca9d0cf046574a3dbdac"
},
{
"category": "interesting",
"title": "You share your birthday with at least 9 million other people in the world.",
"_id": "572bca9c0cf046574a3dbdab"
},
{
"category": "interesting",
"title": "Grapes explode when you put them in the microwave. Go on, try it then",
"_id": "572bca9c0cf046574a3dbdaa"
},
{
"category": "interesting",
"title": "The first license plate on a car in the United States was issued in Denver, Colorado in 1908.",
"_id": "572bca9c0cf046574a3dbda9"
},
{
"category": "interesting",
"title": "Butterflies cannot fly if their body temperature is less than 86 degrees.",
"_id": "572bca9c0cf046574a3dbda7"
},
{
"category": "interesting",
"title": "The average person walks the equivalent of three times around the world in their lifetime.",
"_id": "5921837b9c6997953958970c"
},
{
"category": "interesting",
"title": "A human will eat, on average, 70 assorted insects and 10 spiders while sleeping.",
"_id": "5921835e9c6997953958970b"
},
{
"category": "interesting",
"title": "A single cloud can weigh more than a million pounds.",
"_id": "592183399c6997953958970a"
},
{
"category": "interesting",
"title": "Walt Disney created multiple fake companies (like M.T. Lott Real Estate) to buy Florida land in the 1960s. This let him acquire what is now Disney World while avoiding suspicion and keeping prices low. The stores on Main Street shop windows are the names of those original companies.",
"_id": "58fa6e6a9c69979539589656"
},
{
"category": "interesting",
"title": "The weight of all the ants on earth is equivalent to the weight of all the humans on earth.",
"_id": "58e5617b9c699795395895fc"
},
{
"category": "interesting",
"title": "Over 40M people of Irish descent are in the United States, 8x more than the population of Ireland.",
"_id": "58cc0dfa9c699795395895ad"
},
{
"category": "interesting",
"title": "Ugly people are more likely to get harsher prison sentences as opposed to attractive people",
"_id": "58bf352fd25f996713186f1a"
},
{
"category": "interesting",
"title": "Mageirocophobia is the fear of cooking",
"_id": "58b880b6d25f996713186f05"
},
{
"category": "interesting",
"title": "If you lift a kangaroo’s tail off the ground it can’t hop.",
"_id": "58b8775cd25f996713186f00"
},
{
"category": "interesting",
"title": "Facebook is predominantly blue in color because Mark Zuckerberg is red-green colorblind and blue is the \"richest color\" that he can see",
"_id": "58b0faf5d25f996713186ef6"
},
{
"category": "interesting",
"title": "Joe Rogan paid $10,000 for a T1 internet connection in order to play Quake without lag.",
"_id": "58b0fa10d25f996713186ef5"
},
{
"category": "interesting",
"title": "The numbers '172' can be found on the back of the U.S. $5 dollar bill in the bushes at the base of the Lincoln Memorial.",
"_id": "58a1c50e1344c5dc07f371e6"
},
{
"category": "interesting",
"title": "Undergound is the only word in the english language that starts with 'Und' and ends with 'Und'",
"_id": "589681471344c5dc07f371cf"
},
{
"category": "interesting",
"title": "The seats and curtains in theatres are red because red is the first colour that is lost to our sight in low-light conditions, which thus makes the surroundings seem black and unobtrusive when watching a movie or performance",
"_id": "58851ad5cdb32d184aa20f00"
},
{
"category": "interesting",
"title": "The term \"genuine leather\" isn't reassuring you that the item is made of real leather, it as an actual distinct grade of leather and is the second worst type of leather there is.",
"_id": "5871834faedebe8e6bc40909"
},
{
"category": "interesting",
"title": "The Earth orbits the sun at an average speed of 107, 220 kms per hour.",
"_id": "585ca8d0aedebe8e6bc408e4"
},
{
"category": "interesting",
"title": "When Joseph Gayetty invented toilet paper in 1857, he had his name printed on each sheet.",
"_id": "585ca3e3aedebe8e6bc408e1"
},
{
"category": "interesting",
"title": "The Dead Sea is roughly 8.6 times saltier than the ocean.",
"_id": "585ca222aedebe8e6bc408db"
},
{
"category": "interesting",
"title": "There is enough energy in one bolt of lightning to power the average home for two weeks.",
"_id": "585c9ac0aedebe8e6bc408d0"
},
{
"category": "interesting",
"title": "Cigarette butts are the most littered item at the world, with an estimated 4.5 trillion littered annually. Each butt can take 5 to 400 years to completely break down.",
"_id": "58549cf8aedebe8e6bc4086d"
},
{
"category": "animal",
"title": "Polar bears are left handed.",
"_id": "5f0bce306289d33e9a49bbe5"
},
{
"category": "animal",
"title": "To escape the grip of a crocodile’s jaws, push your thumbs into its eyeballs – it will let you go instantly.",
"_id": "5f092b306289d33e9a49bbe3"
},
{
"category": "animal",
"title": "Locusts have leg muscles that are about 1000 times more powerful than an equal weight of human muscle.",
"_id": "5f03e5306289d33e9a49bbde"
},
{
"category": "animal",
"title": "Want to known the appetite of a South American Giant Anteater? Well it eats over 30,000 ants, per day. ",
"_id": "5f0142306289d33e9a49bbdc"
},
{
"category": "animal",
"title": "It’s possible to lead a cow upstairs…but not downstairs.",
"_id": "5ef413306289d33e9a49bbce"
},
{
"category": "animal",
"title": "A crocodile can’t stick it’s tongue out.",
"_id": "5ef01eb06289d33e9a49bbca"
},
{
"category": "animal",
"title": "The fingerprints of koala bears are virtually indistinguishable from those of humans, so much so that they could be confused at a crime scene.",
"_id": "5ee987306289d33e9a49bbc5"
},
{
"category": "animal",
"title": "Snails can sleep for 3 years without eating",
"_id": "5ea104b0d6fc8b40e40d763f"
},
{
"category": "animal",
"title": "The reptiles have 6,000 species crawling in their habitats; and more are discovered each year. ",
"_id": "5e9e61b0d6fc8b40e40d763d"
},
{
"category": "animal",
"title": "Horses and cows sleep while standing up.",
"_id": "5e800f304570f24fba418e23"
},
{
"category": "animal",
"title": "A crocodile can’t move its tongue and cannot chew. Its digestive juices are so strong that it can digest a steel nail.",
"_id": "5e76d4b24570f24fba418e1c"
},
{
"category": "animal",
"title": "Giant Arctic jellyfish have tentacles that can reach over 36 metres in length.",
"_id": "5e30f53216179007a706f319"
},
{
"category": "animal",
"title": "Rats and horses can’t vomit.",
"_id": "5e2123300106c607d9b5c153"
},
{
"category": "animal",
"title": "A duck’s quack doesn’t echo, and no one knows why.",
"_id": "5e1151300106c607d9b5c129"
},
{
"category": "animal",
"title": "As well as being a famous Looney Tunes character, the Tasmanian Devil is a real animal that is only found in the wild in Tasmania, Australia. It is the largest carnivorous marsupial in the world.",
"_id": "5e0ab9b00106c607d9b5c121"
},
{
"category": "animal",
"title": "You do not need cotton buds to clean a giraffe ears. It can do so with its own 50cm-tongue. ",
"_id": "5e02d0b00106c607d9b5c119"
},
{
"category": "animal",
"title": "The sailfish can swim at the speed of 109 km/h, making it the fastest swimmer. ",
"_id": "5df450300106c607d9b5c105"
},
{
"category": "animal",
"title": "Starfish don’t have brains.",
"_id": "5ddb43b00106c607d9b5c0d0"
},
{
"category": "animal",
"title": "Dogs have four toes on their hind feet, and five on their front feet.",
"_id": "5dcb71b00106c607d9b5c0b0"
},
{
"category": "animal",
"title": "An ostrich is the fastest bird and can run up to 70 km/h. ",
"_id": "5db7ab309cb21b0faaf1a12b"
},
{
"category": "animal",
"title": "The Sea Horse is the slowest fish, drifting at approximately 0.016 km/h. ",
"_id": "5d649cb044a4cb07a832f51d"
},
{
"category": "animal",
"title": "The crocodile’s tongue is unmovable, as it is attached to the roof of its mouth.",
"_id": "5d3fb2b0a6b1f2598b7004e6"
},
{
"category": "animal",
"title": "Mammals are the only creatures that have flaps around their ears. ",
"_id": "5d3a6cb0a6b1f2598b7004dc"
},
{
"category": "animal",
"title": "The world has approximately one billion cattle, of which about 200 million belong to India. ",
"_id": "5cff1930a6b1f2598b700470"
},
{
"category": "animal",
"title": "If NASA sent birds into space they would soon die; they need gravity to swallow.",
"_id": "5cf1ea30a6b1f2598b700457"
},
{
"category": "animal",
"title": "The length of an elephant is the same as the tongue of a blue whale. ",
"_id": "5cd24630e8cadf0c2eca4d19"
},
{
"category": "animal",
"title": "Humans are the only primates that don’t have pigment in the palms of their hands.",
"_id": "5cbbdcb01fa1850d3cbb5cc8"
},
{
"category": "animal",
"title": "The average housefly only lives for 2 or 3 weeks.",
"_id": "5cac0ab01fa1850d3cbb5c74"
},
{
"category": "animal",
"title": "Cats use their whiskers to check whether a space is too small for them to fit through or not.",
"_id": "5c7de6301fa1850d3cbb5b97"
},
{
"category": "animal",
"title": "A rat can last longer without water than a camel.",
"_id": "5c78a0301fa1850d3cbb5b8b"
},
{
"category": "animal",
"title": "Instead of bones, sharks have a skeleton made from cartilage.",
"_id": "5c662b301fa1850d3cbb5b44"
},
{
"category": "animal",
"title": "Many hamsters only blink one eye at a time.",
"_id": "5c5f93b01fa1850d3cbb5b1e"
},
{
"category": "animal",
"title": "A dog was the first animal to up in space. ",
"_id": "5c5507b01fa1850d3cbb5afe"
},
{
"category": "animal",
"title": "Butterflies taste with their feet.",
"_id": "5c2c29301fa1850d3cbb5a41"
},
{
"category": "animal",
"title": "Rats breed so quickly that in just 18 months, 2 rats could have created over 1 million relatives.",
"_id": "5c2ad7b01fa1850d3cbb5a40"
},
{
"category": "animal",
"title": "Insects such as bees, mosquitoes and cicadas make noise by rapidly moving their wings.",
"_id": "5c2591b0fdc12b0c019f8d85"
},
{
"category": "animal",
"title": "A male emperor moth can smell a female emperor moth up to 7 miles away.",
"_id": "5c0890b0fdc12b0c019f8d57"
},
{
"category": "animal",
"title": "Porcupines float in water.",
"_id": "5bf0d5b0fdc12b0c019f8d23"
},
{
"category": "animal",
"title": "Denmark has twice as many pigs as there are people. ",
"_id": "5bd7c93037bd5c7bf91b29ab"
},
{
"category": "animal",
"title": "Hummingbirds are so agile and have such good control that they can fly backwards.",
"_id": "5bce8eb037bd5c7bf91b298d"
},
{
"category": "animal",
"title": "Armadillos are the only animal besides humans that can get leprosy.",
"_id": "5bc948b037bd5c7bf91b2984"
},
{
"category": "animal",
"title": "A shrimp’s heart is in it’s head.",
"_id": "5bc6a5b037bd5c7bf91b2980"
},
{
"category": "animal",
"title": "Unlike humans, sheep have four stomachs, each one helps them digest the food they eat.",
"_id": "5bb5823037bd5c7bf91b2960"
},
{
"category": "animal",
"title": "Even when a snake has its eyes closed, it can still see through its eyelids.",
"_id": "5bac47b037bd5c7bf91b293e"
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{
"category": "animal",
"title": "A cockroach will live nine days without it’s head, before it starves to death.",
"_id": "5ba9a4b037bd5c7bf91b2930"
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{
"category": "animal",
"title": "Well, there are 3,000 kinds of lice. Yes, it is the lice we are prone to get due to lack of hair hygiene. ",
"_id": "5b948cb0846f05473619b9f5"
},
{
"category": "animal",
"title": "A pregnant goldfish is called a twit.",
"_id": "5b7e2330a025fb2f3f91e3c6"
},
{
"category": "animal",
"title": "Ever wonder where the phrase “It’s raining cats and dogs” comes from? In the 17th century many homeless cats and dogs would drown and float down the streets of England, making it look like it literally rained cats and dogs.",
"_id": "592281cf9c69979539589719"
},
{
"category": "animal",
"title": "The bloodhound is the only animal whose evidence is admissible in court.",
"_id": "592281609c69979539589717"
},
{
"category": "animal",
"title": "In 1386, a pig in France was executed by public hanging for murder of a child.",
"_id": "592183199c69979539589709"
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{
"category": "animal",
"title": "If all the females in a group of clownfish die a male will change its gender in order to keep its group alive.",
"_id": "58e4fa009c699795395895fa"
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{
"category": "animal",
"title": "A Pineapple is actually a bunch of small berries fused together into a single mass",
"_id": "58bf3a4f9c69979539589568"
},
{
"category": "animal",
"title": "Cows Have Four Different Stomachs.",
"_id": "58bd885ed25f996713186f0b"
},
{
"category": "animal",
"title": "Palm trees are part of the grass family.",
"_id": "58bd87aed25f996713186f0a"
},
{
"category": "animal",
"title": "Rats can chew through wood, cement, brick, lead, cinder blocks and aluminum.",
"_id": "58a1091d1344c5dc07f371e4"
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{
"category": "animal",
"title": "The Chinese soft-shelled turtle urinates through its mouth ",
"_id": "587468a08720e061098c441d"
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{
"category": "animal",
"title": "The leg muscle of a locust are about 1000 times more powerful than an equal weight of a humans.",
"_id": "585ca425aedebe8e6bc408e2"
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{
"category": "animal",
"title": "The penguin is the only bird who can swim, but not fly.",
"_id": "585ca31faedebe8e6bc408df"
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{
"category": "animal",
"title": "A mole can dig a tunnel 300 feet (91.44 meters) long in just one night.",
"_id": "585ca28aaedebe8e6bc408dc"
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{
"category": "animal",
"title": "Some species of earthworm can have as many as 10 hearts.",
"_id": "585c9d39aedebe8e6bc408d6"
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{
"category": "animal",
"title": "A group of cats is called a clowder",
"_id": "583ca1522fd3b38305b6381c"
},
{
"category": "animal",
"title": "Ants can accidentally misinterpret the chemical trails left by other ants and start walking in circles. If too many members of the colony join in, it can kill the whole colony in what is sometimes known as the 'Death Spiral'",
"_id": "5808ed79b92d09cb1922b335"
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{
"category": "animal",
"title": "Dolphins have a super sense called electroreception. They can sense electrical impulses given off by all living things. Dolphins use this to search for fish hiding in the mud.",
"_id": "57b4fbfd2165d1ab1080104f"
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{
"category": "animal",
"title": "Some moths never eat anything as adults because they don't have mouths. They must live on the energy they stored as caterpillars.",
"_id": "57992997f115a9e604a5e5c6"
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{
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"title": "Elephants use the skin folds on their backs to crush mosquitos.",
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{
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"title": "A cockroach will live nine days without it’s head, before it starves to death.",
"_id": "572bcb8b0cf046574a3dc256"
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{
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"title": "Insects such as bees, mosquitoes and cicadas make noise by rapidly moving their wings.",
"_id": "572bcb8b0cf046574a3dc253"
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{
"category": "animal",
"title": "The length of an elephant is the same as the tongue of a blue whale. ",
"_id": "572bcb880cf046574a3dc247"
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{
"category": "animal",
"title": "A crocodile can’t stick it’s tongue out.",
"_id": "572bcb860cf046574a3dc23b"
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{
"category": "animal",
"title": "A rat can last longer without water than a camel.",
"_id": "572bcb800cf046574a3dc21c"
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{
"category": "animal",
"title": "Snails can sleep for 3 years without eating",
"_id": "572bcb7d0cf046574a3dc20c"
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{
"category": "animal",
"title": "You do not need cotton buds to clean a giraffe ears. It can do so with its own 50cm-tongue. ",
"_id": "572bcb760cf046574a3dc1e9"
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{
"category": "animal",
"title": "It’s possible to lead a cow upstairs…but not downstairs.",
"_id": "572bcb750cf046574a3dc1e8"
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{
"category": "animal",
"title": "Want to known the appetite of a South American Giant Anteater? Well it eats over 30,000 ants, per day. ",
"_id": "572bcb720cf046574a3dc1d9"
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{
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{"comment": "3", "idNoticia": "1066", "tags": [], "url": "http://www.valor.com.br/financas/3508466/financial-times-nova-matriz-economica-do-brasil-ouve-anuncio-de-morte ", "autor": " Joe Leahy | Financial Times", "titulo": "Financial Times: Nova matriz econômica do Brasil ouve anúncio de morte", "corpo": "SÃO PAULO - Até pouco tempo atrás, o governo da presidente Dilma Rousseff falava empolgadamente sobre uma \"nova matriz\" de políticas econômicas que renovariam a vacilante história de crescimento do país. Essa estratégia, que consiste em taxas de juro historicamente baixas, uma taxa de câmbio enfraquecida - obtida em parte por meio de controles cambiais - e incentivos fiscais temporários para a indústria, foi concebida para devolver o Brasil a uma taxa de crescimento de 4%. Neste mês, no entanto, a nova matriz econômica pareceu ouvir um anúncio de morte. Pressões inflacionárias persistentes forçaram o Banco Central do Brasil a elevar novamente a taxa básica de juros, que foi de um piso recorde de 7,25% em 2012 para 11% na semana passada, com a possibilidade de novos aumentos. Com o crescimento ainda frágil e a credibilidade do governo em dúvida após o rebaixamento do rating de crédito no mês passado pela Standard & Poor s, a questão que se apresenta aos investidores no Brasil agora é o quão rápido as autoridades podem desembaraçar a nova matriz econômica e voltar para práticas mais ortodoxas, admitindo-se que elas tenham vontade política de fazê-lo. \"Essa coisa toda foi a tentativa de Dilma Rousseff de realmente executar o modelo macroeconômico keynesiano de desenvolvimento, de que os caras da Unicamp falavam todos esses anos, mas que nunca foi posto em prática\", disse o economista Tony Volpon, da Nomura, referindo-se à universidade onde Dilma fez pós-graduação em Economia (mas não concluiu o curso). \"Não deu certo, isso só piorou as coisas, em todos os ângulos que você puder pensar - crescimento, inflação e contas externas.\" A maioria dos economistas acredita que o governo de Dilma Rousseff começou a tropeçar em 2012, após o início da crise da zona do euro. Com a economia global ainda fraca e o Federal Reserve (banco central dos EUA) injetando liquidez nos mercados, o governo começou uma campanha para reduzir as taxas de juros a um patamar sem precedentes para o Brasil. Ao mesmo tempo, lançou medidas heterodoxas de combate à inflação que ameaçavam perturbar a sua estratégia de taxas de juros baixas. A mais proeminente foi forçar extra-oficialmente a Petrobras, a companhia estatal de petróleo, a vender combustível importado a preços subsidiados no Brasil. O governo também interveio para reduzir as tarifas de energia elétrica e as tarifas de transportes públicos na sequência de protestos de rua no ano passado. No entanto, os formuladores das políticas econômicas também introduziram ações contraditórias que estimularam a inflação, como o apoio a uma moeda mais fraca em relação ao dólar e estímulos à indústria e ao consumo por meio de incentivos fiscais temporários. O resultado foi uma situação de baixo crescimento e alta inflação. A economia do Brasil este ano deverá crescer cerca de 2%, mantendo-se em uma das suas mais lentas taxas de expansão desde a década de 1990. Enquanto isso, a inflação, que deverá atingir 6,3% este ano, está perto do topo da banda do Banco Central, de 4,5% mais ou menos 2 pontos percentuais. \"O crescimento medíocre se tornou a regra, e não a exceção\", disse o Instituto de Finanças Internacionais (IIF), em um relatório no mês passado sobre o Brasil. O problema com as autoridades brasileiras é a obsessão com as questões cíclicas e uma falta de vontade política para resolver os problemas estruturais enraizados do país, afirmou Alberto Ramos, economista do Goldman Sachs. \"O melhor serviço que eles poderiam fazer para a economia é entregar uma inflação baixa e estável\", disse. \"Eles acham que a luta contra a inflação prejudica a economia, mas não combater a inflação prejudica muito mais.\" Entre as questões estruturais mais importantes está a redução da carga tributária, que passou de 27% do Produto Interno Bruto em 1997 para 36% em 2012. Esse patamar supera o do Chile (cerca de 20%) e é maior do que a média da Organização para a Cooperação e Desenvolvimento Econômico (OCDE), um grupo de economias mais desenvolvidas. O argumento é que o Brasil precisa gastar menos, poupar mais e investir muito mais - especialmente o governo. Há sinais silenciosos de que a mensagem está chegando - por exemplo, o ciclo de aperto monetário agressivo do Banco Central. A retórica do governo em face de tais críticas, no entanto, manteve-se desafiadora. Em um discurso esta semana, Dilma disse que a inflação foi mantida dentro da meta oficial por quase 12 anos. O Brasil acumulou US$ 377 bilhões em reservas internacionais e o governo leiloou 18 concessões de infra-estrutura no ano passado. Em última análise, os analistas pensam que não há tanta coisa que Dilma possa fazer com uma eleição em outubro. O governo provavelmente está apostando em suas políticas protecionistas para ganhar tempo suficiente e passar pela eleição. Mais importante, o desemprego permanece baixo. \"Eu acho que a economia deve estar OK, porque eu continuo capaz de ganhar a vida e pagar uma cerveja \", disse Guilherme Breno, um professor em São Paulo.", "data": "2014-04-07 16:20:00"} |
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Provides that the amount remaining shall be allotted in accordance with a formula under which each State receives an amount that bears the same ratio to such total as the average number of individuals in such State who, during the month of January last preceding the beginning of the fiscal year, were registered for employment programs under part A. Authorizes a State to transfer any portion of its allotment for use under the adult and youth training services for the disadvantaged program of the Job Training Partnership Act. Requires a State to use its allotment to maintain its work incentive program for individuals who are required to register for employment programs under part A. Requires a State program to include: (1) a program placing as many such individuals as is possible in employment, which may include intensive job search services and participation in group job search activities; (2) a program utilizing on-the-job training positions; (3) a program of institutional and work experience training for those individuals for whom such training is likely to lead to regular employment; and (4) a program of testing, counseling, and referral that is designed to promote the participation by individuals in activities included in the State program that are most likely to lead to regular employment. Requires a State program, to the extent practicable and where necessary, to include program orientation, basic education, training in communications and employability skills, work experience, institutional training, on-the-job training, job development, and special job placement and followup services required to assist participants in securing and retaining employment and securing posibilities for advancement. Permits payments to any family member participating in employment training for allowances for transportation, child care, and other costs incurred which are related to participation in the training. Prohibits any funds made available under part C from being used to provide public service employment for any individual registered pursuant to a part A employment program for a program established under part C. Directs any State desiring to receive a work incentive block grant under part C to apply to the Secretary. 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}
],
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},
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{
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