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import numpy as np |
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laplacian_factor = None |
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index_factor = None |
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def compute_dE_dz(E_slice, n_r2_slice, dx, n0, sigma_x, k0): |
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""" |
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Compute the derivative dE/dz using the BPM equation: |
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∂E/∂z = (i/(2 k0 n0)) (∂^2 E/∂x^2) + i (k0/(2 n0)) [n_r^2 - n0^2] E - sigma(x) E |
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""" |
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laplacian_E = (np.roll(E_slice, 1, axis=0) - 2 * E_slice + np.roll(E_slice, -1, axis=0)) / dx**2 |
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laplacian_term = (1j / (2 * k0 * n0)) * laplacian_E |
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index_term = 1j * (k0 / (2 * n0)) * (n_r2_slice - n0**2) * E_slice |
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damping_term = - sigma_x * E_slice |
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return laplacian_term + index_term + damping_term |
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def run_bpm(E, n_r2, x, z, dx, dz, n0, sigma_x, wavelength): |
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""" |
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Run the BPM propagation using an RK4 integrator. |
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Parameters: |
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E: initial field (2D array, shape (len(x), len(z)); only E[:,0] is used) |
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n_r2: refractive index squared distribution (2D array, shape (len(x), len(z))) |
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x, z: transverse and propagation coordinates |
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dx, dz: grid spacings in x and z |
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n0: background refractive index |
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sigma_x: 1D array for PML damping in x |
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wavelength: wavelength in um |
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Returns: |
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E: propagated field (2D array) |
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""" |
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k0 = 2 * np.pi / wavelength |
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Nz = len(z) |
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for zi in range(1, Nz): |
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E_prev = E[:, zi-1] |
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n_r2_slice = n_r2[:, zi-1] |
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k1 = dz * compute_dE_dz(E_prev, n_r2_slice, dx, n0, sigma_x, k0) |
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k2 = dz * compute_dE_dz(E_prev + k1/2, n_r2_slice, dx, n0, sigma_x, k0) |
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k3 = dz * compute_dE_dz(E_prev + k2/2, n_r2_slice, dx, n0, sigma_x, k0) |
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k4 = dz * compute_dE_dz(E_prev + k3, n_r2_slice, dx, n0, sigma_x, k0) |
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E[:, zi] = E_prev + (k1 + 2*k2 + 2*k3 + k4) / 6 |
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return E |
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