mirror of
https://github.com/edoverg/modeconverter.git
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447 lines
16 KiB
Python
447 lines
16 KiB
Python
#from jax import numpy as npa, grad
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#from jax.numpy.fft import fft2, ifft2, fftshift, ifftshift
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from typing import List, Tuple, Union
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from autograd import numpy as npa, tensor_jacobian_product, grad as gd
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import time
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import numpy as np
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import matplotlib.pyplot as plt
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import nlopt
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from scipy.special import jv, kv
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ArrayLikeType = Union[List, Tuple, np.ndarray]
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wavelength = 1.55e-6
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k0 = 2 * np.pi / wavelength
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opt_max_eval = 250
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size_x = 1024 * wavelength
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size_y = 1024 * wavelength
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res_x = 3 / 1e-6 #number of pixels per unit-length
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res_y = res_x
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ds = 1 / res_x
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Nx = int(round(res_x * size_x)) + 1
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Ny = int(round(res_y * size_y)) + 1
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print("Nx: ", Nx)
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S = Nx * Ny
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norm_phase_min = 0
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norm_phase_max = 1
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phase_min = 0
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phase_max = 2 * np.pi
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xs = np.linspace(-size_x/2, size_x/2, Nx)
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ys = np.linspace(-size_y/2, size_y/2, Ny)
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X, Y = npa.meshgrid(xs, ys)
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rho = npa.sqrt(X**2 + Y**2)
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sampling_period = xs[1] - xs[0]
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d1 = 4000e-6 #propagation distance
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d2 = 1000e-6 #propagation distance
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d = [d1, d2] #d = [d1,d2] d1:distance MS1-MS2, d2: distance MS2-target
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def phase_given_w(w):
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'''Returns the phase shift given the design parameters w.
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Args:
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w: design parameters (flattened)
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Returns:
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The phase shift corresponding to the geometrical parameters w (flattened)'''
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#for simplicity, we linearly map w (0,1) to a phase shift (0, 2pi)
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return 2 * npa.pi * (w)
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def get_pattern() -> np.ndarray:
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'''Returns the flattened target fiber mode pattern'''
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pattern_name = 'LP11_field_distribution.txt'
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pattern = np.loadtxt('misc/' + pattern_name, dtype=complex)
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return pattern.flatten()
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def get_fiber_mode_pattern():
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'''Returns the flattened target fiber mode pattern'''
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lda = 1.55e-6
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n_co = 1.4630
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n_cl = 1.4585
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a = 6e-6
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#find the v parameter range that corresponds to the 1550 nm wavelength
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#v_1550 = 2 * np.pi * a / lda * np.sqrt(n_co**2 - n_cl**2)
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v_1550 = 4.5
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b = np.linspace(1e-3, 1-1e-3, 400000)
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V_list = np.linspace(2, 5.1, 20)
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V_obs = v_1550
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#b, V = np.meshgrid(b_list, V_list)
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n_list = [0,1,2]
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b_solutions_at_V_obs = []
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for n in n_list:
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b_solutions = []
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for V in V_list:
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LHS = np.sqrt(1-b) * jv(n+1, V * np.sqrt(1-b)) / jv(n, V * np.sqrt(1-b))
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RHS = np.sqrt(b) * kv(n+1, V * np.sqrt(b)) / kv(n, V * np.sqrt(b))
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intersection_index = np.argmax(np.where(np.isclose(LHS, RHS, atol=0.000001),1,0).flatten())
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b_solutions.append(b[intersection_index])
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LHS = np.sqrt(1-b) * jv(n+1, V_obs * np.sqrt(1-b)) / jv(n, V_obs * np.sqrt(1-b))
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RHS = np.sqrt(b) * kv(n+1, V_obs * np.sqrt(b)) / kv(n, V_obs * np.sqrt(b))
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b_solutions_at_V_obs.append(b[np.argmax(np.where(np.isclose(LHS, RHS, atol=0.00001),1,0).flatten())])
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n_mode_sel = 2
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b_mode_sel = b_solutions_at_V_obs[n_mode_sel]
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k_co = 2 * np.pi / lda * n_co
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k_cl = 2 * np.pi / lda * n_cl
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beta = np.sqrt(b_mode_sel * (k_co**2 - k_cl**2) + k_cl**2)
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chi_co = v_1550 * np.sqrt(1 - b_mode_sel) / a
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chi_cl = v_1550 * np.sqrt(b_mode_sel) / a
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E_field = np.zeros_like(X, dtype=complex)
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for i in range(Nx):
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for j in range(Ny):
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r = np.sqrt(X[i,j]**2 + Y[i,j]**2)
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phi = np.arctan2(Y[i,j], X[i,j])
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if r < a:#inside core
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E_field[i,j] = jv(n_mode_sel,chi_co * r) / jv(n_mode_sel, chi_co * a) * np.cos(n_mode_sel * phi)
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else:#outside core
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E_field[i,j] = kv(n_mode_sel, chi_cl * r) / kv(n_mode_sel, chi_cl * a) * np.cos(n_mode_sel * phi)
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return E_field.flatten()
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###########################
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#initialize input field
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beam_waist = 70e-6
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gaussian_field = npa.exp(-rho**2 / (beam_waist)**2) #Gaussian input field, flattened
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input_field = (gaussian_field / np.sqrt(np.sum(np.abs(gaussian_field)**2))).flatten() #normalize the input field to have power = 1
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###########################
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###########################
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#initialize target field
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target_Efield = get_fiber_mode_pattern() / npa.sqrt(npa.sum(npa.abs(get_fiber_mode_pattern())**2)) #normalized target field (intensity = 1)
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###########################
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###########################
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#initialize the phase masks
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w_norm = np.zeros((2*S)) #concatenated normalized parameters for both masks
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X, Y = npa.meshgrid(np.linspace(-size_x/2, size_x/2, Nx), np.linspace(-size_y/2, size_y/2, Ny))
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rho = npa.sqrt(X**2 + Y**2)
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circular_mask_1 = npa.where(rho.flatten() < 10*6e-6, 0.5, 0)
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w_norm[:S] += circular_mask_1
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target_pattern_phase = (np.angle(target_Efield) + 2 * np.pi) % (2 * np.pi) #make sure the phase is between 0 and 2pi
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w_norm[S:] += target_pattern_phase / (2 * np.pi) #normalize the target phase to be between 0 and 1
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###########################
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def forward_propagate(phase_mask:np.ndarray) -> Tuple[List[np.ndarray], List[np.ndarray]]:
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'''Propagates the input field through the system with the given phase mask.
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Args:
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phase_mask: the concatenated phase mask of the system. Masks are flattened and in order. Any mask has always S elements.
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Returns:
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The output field after propagation (flattened) and the propagation matrices P used in the forward propagation.
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'''
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print("Starting propagating...")
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start_time = time.time()
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phase_mask_1 = phase_mask[:S]
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phase_mask_2 = phase_mask[S:]
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d1 = d[0]
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d2 = d[1]
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field_after_mask_1 = input_field * np.exp(1j * phase_mask_1)
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field_after_mask_1_2d = field_after_mask_1.reshape((Nx, Ny))
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field_fft_1 = np.fft.fftshift(np.fft.fft2(field_after_mask_1_2d))
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ks = 2 * np.pi / sampling_period
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kappas = np.arange(-field_fft_1.shape[0]//2, field_fft_1.shape[0]//2) * ks / field_fft_1.shape[0]
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KX, KY = np.meshgrid(kappas, kappas)
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K_parallel = np.sqrt(KX**2 + KY**2)
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nu_parallel = K_parallel / (2 * np.pi)
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phase_factor = k0 * d1 * np.sqrt(1 - (wavelength * nu_parallel) ** 2 + 0*1j)
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P_1 = np.exp(1j * phase_factor)
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fft_field_propagated_1 = np.multiply(field_fft_1,P_1) #element wise product
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output_field_1_2d = np.fft.ifft2(np.fft.ifftshift(fft_field_propagated_1))
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output_field_1 = output_field_1_2d.flatten()
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field_after_mask_2 = output_field_1 * np.exp(1j * phase_mask_2)
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field_after_mask_2_2d = field_after_mask_2.reshape((Nx, Ny))
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field_fft_2 = np.fft.fftshift(np.fft.fft2(field_after_mask_2_2d))
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phase_factor_2 = k0 * d2 * np.sqrt(1 - (wavelength * nu_parallel) ** 2 + 0*1j)
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P_2 = np.exp(1j * phase_factor_2)
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fft_field_propagated_2 = np.multiply(field_fft_2,P_2) #element wise product
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output_field_2_2d = np.fft.ifft2(np.fft.ifftshift(fft_field_propagated_2))
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output_field_2 = output_field_2_2d.flatten()
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end_time = time.time()
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print("Propagation finished in {:.6f} seconds.".format(end_time - start_time))
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output_fields = [output_field_1, output_field_2]
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propagation_matrices = [P_1, P_2]
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return output_fields, propagation_matrices
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def adjoint_propagate(output_fields,propagation_matrices,phase_mask):
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'''Backpropagates the output field using the adjoint of the propagation matrix P.
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Args:
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output_field: the output field to be backpropagated (flattened)
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P: the propagation matrix used in the forward propagation
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phase_mask: the phase mask used in the forward propagation (flattened)
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Returns:
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The backpropagated field (flattened)
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'''
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print("Computing adjoint...")
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start_time = time.time()
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phase_mask_1 = phase_mask[:S]
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phase_mask_2 = phase_mask[S:]
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output_field_1 = output_fields[0]
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input_field_2 = output_field_1
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output_field_2 = output_fields[1]
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P_1 = propagation_matrices[0]
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P_2 = propagation_matrices[1]
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P_1_dagger = P_1.T.conj()
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P_2_dagger = P_2.T.conj()
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Phi_1 = np.exp(1j * phase_mask_1)
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Phi_2 = np.exp(1j * phase_mask_2)
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Phi_1_dagger = np.exp(-1j * phase_mask_1)
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Phi_2_dagger = np.exp(-1j * phase_mask_2)
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#compute the adjoint source
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adjoint_field = npa.sum(output_field_2 * npa.conj(target_Efield)) * target_Efield
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adjoint_field_2d = adjoint_field.reshape((Nx, Ny))
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adjoint_field_fft = npa.fft.fftshift(npa.fft.fft2(adjoint_field_2d))
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pd2 = adjoint_field_fft * P_2_dagger #element wise
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adjoint_field_2_propagated_2d = npa.fft.ifft2(npa.fft.ifftshift(pd2))
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adjoint_field_2_propagated = adjoint_field_2_propagated_2d.flatten() * Phi_2_dagger
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adjoint_field_2_propagated_2d = adjoint_field_2_propagated.reshape((Nx, Ny))
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adjoint_field_2_propagated_fft = npa.fft.fftshift(npa.fft.fft2(adjoint_field_2_propagated_2d))
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pd1 = adjoint_field_2_propagated_fft * P_1_dagger #element wise
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adjoint_field_1_propagated_2d = npa.fft.ifft2(npa.fft.ifftshift(pd1))
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adjoint_field_1_propagated = adjoint_field_1_propagated_2d.flatten() * Phi_1_dagger
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grad_C_phi_1 = 2 * np.real(-1j * input_field.reshape((Nx,Ny)).T.conj().flatten() * adjoint_field_1_propagated)
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grad_C_phi_2 = 2 * np.real(-1j * output_field_1.reshape((Nx,Ny)).T.conj().flatten() * adjoint_field_2_propagated)
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grads = np.concatenate((grad_C_phi_1, grad_C_phi_2))
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end_time = time.time()
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print("Adjoint finished in {:.6f} seconds.".format(end_time - start_time))
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return grads
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def _compute_cost(phase_mask):
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output_fields, propagation_matrices = forward_propagate(phase_mask)
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output_field = output_fields[-1]
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circular_mask = npa.where(rho.flatten() < 10*6e-6, 1, 0)
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C_s = npa.abs(npa.sum(output_field*circular_mask * npa.conj(target_Efield))) ** 2
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C_s = npa.real(npa.sum(C_s))
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C_t = C_s
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return C_t, output_fields, propagation_matrices
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opt_history = []
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def cost_fun(x, grad):
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''' Cost function to be minimized.
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Args:
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x: input normalized parameter field (flattened)
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grad: gradient of the cost function with respect to x, modified in place (flattened)
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Returns:
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The cost function value for the input parameter field x.
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'''
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w_norm[:] = x
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phase_mask = phase_given_w(w_norm)
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C, output_fields, propagation_matrices = _compute_cost(phase_mask)
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opt_history.append(C)
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plt.figure()
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plt.plot(opt_history)
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plt.xlabel('Iteration')
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plt.ylabel('Cost Function Value')
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plt.title('Optimization History')
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plt.tight_layout()
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plt.savefig("results/modeconv1_optimization_history.pdf")
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plt.close()
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if grad.size > 0:
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grad[:] = adjoint_propagate(output_fields,propagation_matrices,phase_mask) * 2 * np.pi
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return C
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if __name__ == "__main__":
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#initialize nlopt solver
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solver = nlopt.opt(nlopt.LD_CCSAQ, 2*S)
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solver.set_lower_bounds(norm_phase_min)
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solver.set_upper_bounds(norm_phase_max)
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solver.set_max_objective(cost_fun)
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solver.set_maxeval(opt_max_eval)
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solver.set_param("dual_ftol_rel", 1e-7)
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solver.set_param("verbosity",1)
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print("Starting optimization...")
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start = True
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if start:
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w_norm[:] = solver.optimize(w_norm)
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print("Optimization completed.")
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#verify the results
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phase_mask = phase_given_w(w_norm)
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output_fields, _ = forward_propagate(phase_mask)
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output_field = output_fields[-1]
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input_power = np.sum(np.abs(input_field)**2)
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output_power = np.sum(np.abs(output_field)**2)
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print("Norm. input power: %.4e" % input_power)
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print("Norm. output power: %.4e" % output_power)
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#save the output field for later use
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np.savetxt("results/modeconv1_optimized_output_field.txt", output_field.reshape((Nx, Ny)))
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# Plot results in individual PDF figures
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# Reshape fields to 2D for visualization
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output_field_2d = output_field.reshape((Nx, Ny))
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target_field_2d = target_Efield.reshape((Nx, Ny))
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phase_mask_1 = phase_given_w(w_norm[:S]).reshape((Nx, Ny))
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phase_mask_2 = phase_given_w(w_norm[S:]).reshape((Nx, Ny))
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a = 6e-6
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d = 10 * a * 1e6
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# Plot 1: Output field amplitude
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow(np.abs(output_field_2d),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='viridis')
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ax.set_title('Output Field Amplitude')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_xlim(-d, d)
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ax.set_ylim(-d, d)
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/output_field_amplitude.pdf")
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plt.close()
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# Plot 2: Output field phase
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow((np.angle(output_field_2d)+2*np.pi)%(2*np.pi),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='hsv')
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ax.set_title('Output Field Phase')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_xlim(-d, d)
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ax.set_ylim(-d, d)
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/output_field_phase.pdf")
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plt.close()
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# Plot 3: Target field amplitude
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow(np.abs(target_field_2d),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='viridis')
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ax.set_title('Target Field Amplitude')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_xlim(-d, d)
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ax.set_ylim(-d, d)
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/target_field_amplitude.pdf")
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plt.close()
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# Plot 4: Target field phase
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow((np.angle(target_field_2d)+2*np.pi)%(2*np.pi),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='hsv')
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ax.set_title('Target Field Phase')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_xlim(-d, d)
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ax.set_ylim(-d, d)
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/target_field_phase.pdf")
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plt.close()
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# Plot 5: Phase mask 1
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow((phase_mask_1+2*np.pi)%(2*np.pi),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='viridis')
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ax.set_title('Phase Mask 1')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/phase_mask_1.pdf")
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plt.close()
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# Plot 6: Phase mask 2
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fig, ax = plt.subplots(figsize=(10, 8))
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im = ax.imshow((phase_mask_2+2*np.pi)%(2*np.pi),extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2), origin='lower', cmap='viridis')
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ax.set_title('Phase Mask 2')
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_aspect('equal')
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plt.colorbar(im, ax=ax)
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plt.tight_layout()
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plt.savefig("results/phase_mask_2.pdf")
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plt.close()
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# Plot 7: Cuts along y=0 axis - Amplitude comparison
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y_center_idx = Ny // 2
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output_amplitude_cut = np.abs(output_field_2d[y_center_idx, :])
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target_amplitude_cut = np.abs(target_field_2d[y_center_idx, :])
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fig, ax = plt.subplots(figsize=(12, 6))
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ax.plot(xs*1e6, output_amplitude_cut, label='Output Field', linewidth=2)
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ax.plot(xs*1e6, target_amplitude_cut, label='Target Field', linewidth=2)
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ax.set_xlabel('x (m)')
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ax.set_xlim(-d,d)
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ax.set_ylabel('Amplitude')
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ax.set_title('Field Amplitude along y=0 axis')
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ax.legend()
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig("results/amplitude_cut_comparison.pdf")
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plt.close()
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# Plot 8: Cuts along y=0 axis - Phase comparison
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output_phase_cut = (np.angle(output_field_2d[y_center_idx, :]) + 2*np.pi) % (2*np.pi)
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target_phase_cut = (np.angle(target_field_2d[y_center_idx, :]) + 2*np.pi) % (2*np.pi)
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fig, ax = plt.subplots(figsize=(12, 6))
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ax.plot(xs*1e6, output_phase_cut, label='Output Field', linewidth=2)
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ax.plot(xs*1e6, target_phase_cut, label='Target Field', linewidth=2)
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ax.set_xlabel('x (m)')
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ax.set_ylabel('Phase (rad)')
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ax.set_xlim(-d,d)
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ax.set_title('Field Phase along y=0 axis')
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ax.legend()
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ax.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig("results/phase_cut_comparison.pdf")
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plt.close()
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#save the phase masks for later use
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np.savetxt("results/optimized_phase_mask_1.txt", phase_mask_1)
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np.savetxt("results/optimized_phase_mask_2.txt", phase_mask_2)
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print("All plots saved to results/ folder.")
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