2212/2212.00019.md

Title: “Experimental demonstration of superdirective spherical dielectric antenna”

URL Source: https://arxiv.org/html/2212.00019

Markdown Content: Supplementary material for:

“Experimental demonstration of superdirective spherical dielectric antenna”

Roman Gaponenko,1,1{}^{1,}start_FLOATSUPERSCRIPT 1 , * end_FLOATSUPERSCRIPT Mikhail S. Sidorenko,1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Dmitry Zhirihin,1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Ilia L. Rasskazov,2 2{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT Alexander Moroz,3 3{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT Konstantin Ladutenko,1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT Pavel Belov,1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT and Alexey Shcherbakov 1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT 1 1{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT School of Physics and Engineering, ITMO University, 197101, Saint-Petersburg, Russia

2 2{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT KLA Corporation, 5 Technology Drive, Milpitas, California 95035, USA

3 3{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPT Wave-scattering.com

• Corresponding author: roman.gaponenko@metalab.ifmo.ru

I Preparing for measurements

FigureS1(a) is a photograph of the fabrication process of a spherical dielectric antenna using Free Flowing Dielectric Powder ECCOSTOCK HiK. It has has the real part of permittivity ε 1′≃12.2 similar-to-or-equals subscript superscript 𝜀′1 12.2\varepsilon^{\prime}{1}\simeq 12.2 italic_ε start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ≃ 12.2 and the loss tangent tan⁡δ 1≃0.0007 similar-to-or-equals subscript 𝛿 1 0.0007\tan\delta{1}\simeq 0.0007 roman_tan italic_δ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ≃ 0.0007. The powder was poured into a plastic shell made of acrylic with a thickness of ∼1.1 similar-to absent 1.1\sim 1.1∼ 1.1 mm, the outer radius of which is R 2=40 subscript 𝑅 2 40 R_{2}=40 italic_R start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 40 mm, the real part of permittivity ε 2′≃1.7 similar-to-or-equals subscript superscript 𝜀′2 1.7\varepsilon^{\prime}{2}\simeq 1.7 italic_ε start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ≃ 1.7 and the loss tangent tan⁡δ 2≃0.02 similar-to-or-equals subscript 𝛿 2 0.02\tan\delta{2}\simeq 0.02 roman_tan italic_δ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ≃ 0.02. To achieve a homogeneous structure of the powder, it was compacted using vibrations. After the installation and antenna alignment process, the foam pedestal (on a rotary positioner) was rotated in increments of 1∘superscript 1 1^{\circ}1 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT along the θ 𝜃\theta italic_θ angle, with the measurement of S-parameters at each step. FigureS1(b) is a photograph of an anechoic chamber, where the antenna under test is installed on the left on the special foam pedestal, and a horn antenna is on the right on the triaxial positioner. The secant plane ϕ=0∘italic-ϕ superscript 0\phi=0^{\circ}italic_ϕ = 0 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT includes the arms of the dipole and the center of the sphere. To take measurements in the ϕ=90∘italic-ϕ superscript 90\phi=90^{\circ}italic_ϕ = 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT plane (which is perpendicular to the dipole arms), the receiving and transmitting antennas were preliminarily rotated by 90∘superscript 90 90^{\circ}90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT around the axis on which both of these antennas are located. After that, a similar measurement of S-parameters was performed along the θ 𝜃\theta italic_θ angle for the plane ϕ=90∘italic-ϕ superscript 90\phi=90^{\circ}italic_ϕ = 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT.

Figure S1: Preparing for measurements. (a) Antenna fabrication process and (b) a full-view of the measurement setup.

II Experimental data

II.1 Dielectric sphere excited by an external dipole

Figure S2: Measured S-parameters for the dielectric spherical antenna excited by an external dipole. Antenna construction is described in Section III A of the main text of the article.

Figure S3: Calculated S-parameters for the dielectric spherical antenna excited by an external dipole. Antenna construction is described in Section III A of the main text of the article.

II.2 Dielectric sphere excited by an internal dipole

Figure S4: Measured S-parameters for the dielectric spherical antenna excited by an internal dipole. Antenna construction is described in Section III B of the main text of the article.

Figure S5: Calculated S-parameters for the dielectric spherical antenna excited by an internal dipole. Antenna construction is described in Section III B of the main text of the article.

III Antenna efficiency

III.1 Dielectric sphere excited by an external dipole

Figure S6: Spectra of the directivity (𝒟 𝒟\mathcal{D}caligraphic_D) in the forward direction (along the z 𝑧 z italic_z-axis) and efficiency in the range 2.4−2.5 2.4 2.5 2.4-2.5 2.4 - 2.5 GHz obtained (a) numerically and (b) experimentally. Antenna construction is described in Section III A of the main text. The left panel shows the results of the numerical calculation performed in the CST Studio Suite for the case of a full-size dipole oriented tangentially and located at a distance of r d=40.5 subscript 𝑟 𝑑 40.5 r_{d}=40.5 italic_r start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT = 40.5 from the center of the spherical resonator with the radius of 40 40 40 40 mm. The right panel shows the experimentally measured results.

e c⁢d=𝒢/𝒟 subscript 𝑒 𝑐 𝑑 𝒢 𝒟 e_{cd}=\mathcal{G}/\mathcal{D}italic_e start_POSTSUBSCRIPT italic_c italic_d end_POSTSUBSCRIPT = caligraphic_G / caligraphic_D is the antenna radiation efficiency (dimensionless); 𝒟 𝒟\mathcal{D}caligraphic_D is the antenna directivity;

e r=𝒢 ℛ/𝒢 subscript 𝑒 𝑟 subscript 𝒢 ℛ 𝒢 e_{r}=\mathcal{G}_{\cal R}/\mathcal{G}italic_e start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = caligraphic_G start_POSTSUBSCRIPT caligraphic_R end_POSTSUBSCRIPT / caligraphic_G is the reflection (mismatch) efficiency (dimensionless); 𝒢 𝒢\mathcal{G}caligraphic_G is the antenna gain;

e 0=𝒢 ℛ/𝒟=e r⁢e c⁢d subscript 𝑒 0 subscript 𝒢 ℛ 𝒟 subscript 𝑒 𝑟 subscript 𝑒 𝑐 𝑑 e_{0}=\mathcal{G}{\cal R}/\mathcal{D}=e{r}e_{cd}italic_e start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = caligraphic_G start_POSTSUBSCRIPT caligraphic_R end_POSTSUBSCRIPT / caligraphic_D = italic_e start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT italic_e start_POSTSUBSCRIPT italic_c italic_d end_POSTSUBSCRIPT, is the total efficiency (dimensionless); 𝒢 R subscript 𝒢 𝑅\mathcal{G}_{R}caligraphic_G start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT is the realized gain.

III.2 Dielectric sphere excited by an internal dipole

Figure S7: Spectra of the directivity (𝒟 𝒟\mathcal{D}caligraphic_D) in the forward direction (along the z 𝑧 z italic_z-axis) and efficiency in the range 2.33−2.4 2.33 2.4 2.33-2.4 2.33 - 2.4 GHz obtained (a) numerically and (b) experimentally. Antenna construction is described in Section III B of the main text. The left panel shows the results of the numerical calculation performed in the CST Studio Suite for the case of a full-size dipole oriented tangentially and located at a distance of r d=14.5 subscript 𝑟 𝑑 14.5 r_{d}=14.5 italic_r start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT = 14.5 from the center of the spherical resonator with the radius of 40 40 40 40 mm. The right panel shows the experimentally measured results.

Frequencies where the overall efficiency is >80%absent percent 80>80%> 80 % near the main resonance are marked with green shading. It should be noted that the accuracy of the experimental results could be affected by numerous reasons indicated in Section IV of the main text of the article. If the realized gain measurements are obtained by directly measuring the S-parameters, then the directivity measurements were calculated from the shape of the pattern in only two planes (ϕ=0∘italic-ϕ superscript 0\phi=0^{\circ}italic_ϕ = 0 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT and ϕ=90∘italic-ϕ superscript 90\phi=90^{\circ}italic_ϕ = 90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT). This could lead to some inaccuracies at frequencies outside the main resonances, including the zone near 𝒟≃0 similar-to-or-equals 𝒟 0\mathcal{D}\simeq 0 caligraphic_D ≃ 0 and in the case of the appearance of side lobes outside the mentioned planes. The presented results of numerical optimization were obtained in the process of maximizing the realized gain, and if the goal was to maximize directivity, then for the same sphere and at the same resonances it is possible to obtain 𝒟≃11 similar-to-or-equals 𝒟 11\mathcal{D}\simeq 11 caligraphic_D ≃ 11, but with a low total radiation efficiency.

IV Influence of the plastic shell on the results of the experiment

Figure S8: Antenna characteristics (𝒟 𝒟\mathcal{D}caligraphic_D, 𝒢 𝒢\mathcal{G}caligraphic_G, 𝒢 R subscript 𝒢 𝑅\mathcal{G}{R}caligraphic_G start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT) in the forward direction (along the z 𝑧 z italic_z axis) in the range of 1.4−2.6 1.4 2.6 1.4-2.6 1.4 - 2.6 GHz for the case a full size dipole oriented tangentially and spaced r d=40.5 subscript 𝑟 𝑑 40.5 r{d}=40.5 italic_r start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT = 40.5 from the center of the spherical resonator as shown in the upper left corner. The outer shell of the resonator is made of plastic with an outer radius of 40 40 40 40 mm, a thickness of 1.1 1.1 1.1 1.1 mm, having ε 2′=1.7 subscript superscript 𝜀′2 1.7\varepsilon^{\prime}{2}=1.7 italic_ε start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 1.7 and tan⁡δ 2=0.02 subscript 𝛿 2 0.02\tan\delta{2}=0.02 roman_tan italic_δ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = 0.02. The main body of the spherical resonator with a radius of 38.9 38.9 38.9 38.9 mm is made of a dielectric material with ε 1′=12.2 subscript superscript 𝜀′1 12.2\varepsilon^{\prime}{1}=12.2 italic_ε start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = 12.2 and tan⁡δ 1=0.0007 subscript 𝛿 1 0.0007\tan\delta{1}=0.0007 roman_tan italic_δ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = 0.0007. Other parameters of the considered antenna are described in Section III A. The results were obtained by numerical simulation in the CST Studio Suite for the case with and without a plastic shell.

References