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repository update. Added metaprop_fibermode_doublet_sym.py which implements a constrained optimization enforcing mirror symmetry about the x and y axes. Mirror symmetry can be exploited in this problem since the target mode has such symmetry. Each metasurface has effectively a quarter of the degrees of freedom compared to the unconstrained problem.
This commit is contained in:
Edoardo Vergerio
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import time
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import multiprocessing
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import pyfftw
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#pyFFTW setup
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n_cpu = multiprocessing.cpu_count()
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pyfftw.config.NUM_THREADS = n_cpu
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pyfftw.interfaces.cache.enable()
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pyfftw.config.PLANNER_EFFORT = 'FFTW_MEASURE'
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import nlopt
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import numpy as np
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import matplotlib.pyplot as plt
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import matplotlib.patches as patches
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#set the global font size for all plots
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plt.rcParams.update({'font.size': 14})
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from scipy.special import jv, kv
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##############################
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#physics and simulation domain
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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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unit_cell_pitch = 400e-9 #equivalent to spatial sampling
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Nx = 2048 #pixels per dimension
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Ny = Nx
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S = Nx * Ny
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size_x = unit_cell_pitch * Nx #actual physical size
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size_y = unit_cell_pitch * Ny
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xs = np.linspace(-size_x/2, size_x/2 - size_x / Nx, Nx)
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ys = np.linspace(-size_y/2, size_y/2 - size_y / Ny, Ny)
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X, Y = np.meshgrid(xs, ys)
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rho = np.sqrt(X**2 + Y**2)
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sampling_period = xs[1] - xs[0]
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d0 = 345e-6 #propagation distance: source - MS1
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d1 = 500e-6 #propagation distance: MS1 - MS2
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d2 = 300e-6 #propagation distance: MS2 - target
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d = [d1, d2] #d = [d1,d2] d1:distance MS1-MS2, d2: distance MS2-target
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phase_min = 0
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phase_max = 2 * np.pi
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##############################
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##############################
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#optimization algorithm
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epigraph_tolerance = np.array([1e-4]*2)
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#epigraph_tolerance = np.array([1e-4])
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##############################
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##############################
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#Source
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beam_waist = 9e-6
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source_spacing = 300e-6
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##############################
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##############################
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#plan pyfftw objects for forward and inverse FFTs
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fft_input_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
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fft_output_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
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ifft_input_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
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ifft_output_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
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fft_operator = pyfftw.FFTW(fft_input_array, fft_output_array, axes=(0,1), direction='FFTW_FORWARD', threads=n_cpu, flags=('FFTW_MEASURE','FFTW_DESTROY_INPUT',))
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ifft_operator = pyfftw.FFTW(ifft_input_array, ifft_output_array, axes=(0,1), direction='FFTW_BACKWARD', threads=n_cpu, flags=('FFTW_MEASURE','FFTW_DESTROY_INPUT',))
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##############################
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##############################
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#setting up spatial frequencies
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ks = 2 * np.pi / sampling_period
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kappas = np.arange(-Nx//2, Nx//2) * ks / Nx
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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_0 = k0 * d0 * np.sqrt(1 - (wavelength * nu_parallel) ** 2 + 0*1j)
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P_0 = np.exp(1j * phase_factor_0)
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P_0_nat = np.fft.ifftshift(P_0)
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phase_factor_1 = k0 * d1 * np.sqrt(1 - (wavelength * nu_parallel) ** 2 + 0*1j)
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P_1 = np.exp(1j * phase_factor_1)
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P_1_nat = np.fft.ifftshift(P_1)
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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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P_2_nat = np.fft.ifftshift(P_2)
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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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P_1_dagger_nat = np.fft.ifftshift(P_1).T.conj()
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P_2_dagger_nat = np.fft.ifftshift(P_2).T.conj()
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##############################
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##############################
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#Plot zoom parameters [um]
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zoom_x = 60
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zoom_y = 60
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zoom_core_diameter = 2 * 6
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full_view_x = size_x * 1e6 / 2
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full_view_y = size_y * 1e6 / 2
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##############################
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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 * np.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(mode_list:list)->list:
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'''Returns the fiber mode pattern for the selected n index.
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Args:
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mode_list: the list of the selected fiber mode indices
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Returns:
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The fiber mode patterns corresponding to the selected indices returned
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as a list of 2D arrays with the same order as the input mode_list
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'''
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#check if the modes in mode_list have already been compute by checking
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#the saved files in the 'results' folder. If they have, load them from the files. If not, compute them and save them to the files.
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print("Computing fiber patterns for mode indices: ", mode_list)
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lda = 1.55e-6
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n_co = 1.4630 #core refractive index
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n_cl = 1.4585 #cladding refractive index
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a = 6e-6 #fiber core radius
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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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b_solutions_at_V_obs = []
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for n in mode_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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output_patterns = []
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for enum_index,n_mode_sel in enumerate(mode_list):
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b_mode_sel = b_solutions_at_V_obs[enum_index]
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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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if r < 10*a:
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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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output_patterns.append(E_field)
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return output_patterns
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def get_source_field(beam_waist,center_x=0,center_y=0,):
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'''Returns a normalized Gaussian source field for a given beam waist. Normalization consists in scaling
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the field such that its integrated intensity is 1.
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Args:
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beam_waist: the waist of the Gaussian beam (in meters)
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center_x: the x-coordinate of the center of the Gaussian beam (in meters)
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center_y: the y-coordinate of the center of the Gaussian beam (in meters)
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Returns:
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The normalized Gaussian source field
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'''
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if center_x != 0 or center_y != 0:
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X_shifted, Y_shifted = shift_spatial_grid(center_x, center_y)
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rho = np.sqrt(X_shifted**2 + Y_shifted**2)
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else:
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rho = np.sqrt(X**2 + Y**2)
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gaussian_field = np.exp(-(rho)**2 / (beam_waist)**2) #Gaussian input field, flattened
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gaussian_field_normalized = (gaussian_field / np.sqrt(np.sum(np.abs(gaussian_field)**2))) #normalize the input field to have power = 1
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return gaussian_field_normalized
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def propagate_source(source_to_propagate):
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'''Returns the propagated source field (flattened) just before metasurface 1 (MS1). This involves propagating the
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source for a distance d0: from its plane of definition up to MS1.'''
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fft_input_array[:,:] = source_to_propagate.reshape((Nx, Ny))
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fft_operator()
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ifft_input_array[:,:] = fft_operator.output_array * P_0_nat
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ifft_operator()
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propagated_source_field = ifft_operator.output_array.flatten()
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return propagated_source_field
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def make_1Dplot_of(x_axis,y_axis,legend_labels,plot_zoom_x=zoom_x,save_name="plot_1D",) -> None:
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'''Makes a 1D plot of the given data and saves it to a PDF file.
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Args:
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x_axis: list of x-axis data (list of 1D arrays)
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y_axis: list of y-axis data (list of 1D arrays)
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plot_zoom_x: zoom level for the x-axis (in micrometers)
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save_name: name of the file to save the plot (without extension)
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Returns:
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None
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'''
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if len(x_axis) != len(y_axis):
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raise ValueError("Lists x_axis and y_axis must have the same length.")
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plt.figure()
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for i in range(len(x_axis)):
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if len(legend_labels) != len(x_axis):
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raise ValueError("Length of legend_labels must match the number of plots.")
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else:
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plt.plot(x_axis[i], y_axis[i], label=legend_labels[i])
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plt.legend()
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plt.tight_layout()
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plt.savefig("results/" + save_name + ".pdf")
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plt.xlim(-plot_zoom_x, plot_zoom_x)
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plt.close()
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def make_2Dplot_of(given_field,choose_quantity="amplitude",save_name="plot",plot_zoom_x=zoom_x,plot_zoom_y=zoom_y) -> None:
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'''Makes a plot of the given 2D field in a zoomed region.
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Saves the plot with the chosen filename to a PDF file.
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Args:
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given_field: the 2D field to be plotted (flattened)
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choose_quantity: either "amplitude" or "phase" to select quantity to plot
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save_name: name of the file to save the plot (without extension)
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plot_zoom_x: zoom level for the x-axis (in micrometers)
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plot_zoom_y: zoom level for the y-axis (in micrometers)
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Returns:
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None'''
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given_field_2d = given_field.reshape((Nx, Ny)) #assure the field is 2D before plotting
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plt.figure()
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if choose_quantity == "amplitude":
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plt.imshow(np.abs(given_field_2d), extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2))
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elif choose_quantity == "phase":
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plt.imshow((np.angle(given_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), cmap='hsv', vmin=0, vmax=2*np.pi)
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elif choose_quantity == "phase_mask":
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plt.imshow((given_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), cmap='hsv', vmin=0, vmax=2*np.pi)
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else:
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raise ValueError("choose_quantity must be either 'amplitude' or 'phase'")
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plt.xlim(-plot_zoom_x, plot_zoom_x)
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plt.ylim(-plot_zoom_y, plot_zoom_y)
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plt.xlabel("x [um]")
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plt.ylabel("y [um]")
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plt.colorbar()
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plt.tight_layout()
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plt.savefig("results/" + save_name + ".pdf")
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plt.close()
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def make_polarPlot_of(given_field,choose_quantity="amplitude",save_name="polar_plot",plot_zoom_r=zoom_x) -> None:
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'''Makes a polar plot of the given 2D field in a zoomed region.
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Saves the plot with the chosen filename to a PDF file.
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Args:
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given_field: the 2D field to be plotted (flattened)
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choose_quantity: either "amplitude" or "phase" to select quantity to plot
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save_name: name of the file to save the plot (without extension)
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plot_zoom_r: zoom level for the radial axis (in micrometers)
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Returns:
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None
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'''
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_, ax = plt.subplots(figsize=(6, 6))
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if choose_quantity == "amplitude":
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given_field_2d = np.abs(given_field.reshape((Nx, Ny))) #assure the field is 2D before plotting
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im = ax.imshow(given_field_2d,origin='lower')
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elif choose_quantity == "phase":
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given_field_2d = (np.angle(given_field.reshape((Nx, Ny))) + 2*np.pi) % (2*np.pi)#assure the field is 2D before plotting
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im = ax.imshow(given_field_2d, cmap='hsv', vmin=0, vmax=2*np.pi)
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else:
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raise ValueError("choose_quantity must be either 'amplitude' or 'phase'")
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center_x, center_y = Nx//2, Ny//2
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radius = plot_zoom_r * 1e-6 / (size_x/2) * (Nx/2) #convert zoom in um to pixels
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circle = patches.Circle((center_x, center_y), radius, transform=ax.transData)
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im.set_clip_path(circle)
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ax.set_xlim(center_x - radius, center_x + radius)
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ax.set_ylim(center_y - radius, center_y + radius)
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ax.axis('off')
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cbar = plt.colorbar(im, ax=ax)
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plt.savefig("results/" + save_name + ".pdf")
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def shift_spatial_grid(shift_amount_x,shift_amount_y):
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'''Shifts the spatial grid by a given amount. This is useful for centering the source field on the metasurface.
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Args:
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shift_amount_x: amount to shift the grid in x direction (in meters)
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shift_amount_y: amount to shift the grid in y direction (in meters)
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Returns:
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the shifted spatial grid (X, Y)'''
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Xp = X + shift_amount_x
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Yp = Y + shift_amount_y
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return Xp, Yp
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def shift_grid(array_to_shift,shift_amount_x,shift_amount_y):
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'''Shifts a given 2D array by a given amount.
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Args:
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array_to_shift: the 2D array to be shifted
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shift_amount_x: amount to shift the array in x direction (in meters)
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shift_amount_y: amount to shift the array in y direction (in meters)
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Returns:
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the shifted 2D array'''
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pass
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###########################
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#initialize source field
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source_field_1 = get_source_field(beam_waist,center_x=-source_spacing/2,center_y=0)
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source_field_1_2d = source_field_1.reshape((Nx, Ny)) #reshape to 2D for plotting
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source_field_2 = get_source_field(beam_waist,center_x=source_spacing/2,center_y=0)
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source_field_2_2d = source_field_2.reshape((Nx, Ny)) #reshape to 2D for plotting
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#source field integrated intensity
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source_1_power = np.sum(np.abs(source_field_1)**2)
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source_2_power = np.sum(np.abs(source_field_2)**2)
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print("Source 1 field integrated intensity: %.4e" % source_1_power)
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print("Source 2 field integrated intensity: %.4e" % source_2_power)
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#make a plot and save the source field
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make_2Dplot_of(source_field_1_2d, choose_quantity="amplitude", save_name="source_1_field_amplitude", plot_zoom_x=3*zoom_x, plot_zoom_y=3*zoom_y)
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make_2Dplot_of(source_field_1_2d, choose_quantity="phase", save_name="source_1_field_phase", plot_zoom_x=3*zoom_x, plot_zoom_y=3*zoom_y)
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make_2Dplot_of(source_field_2_2d, choose_quantity="amplitude", save_name="source_2_field_amplitude", plot_zoom_x=3*zoom_x, plot_zoom_y=3*zoom_y)
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make_2Dplot_of(source_field_2_2d, choose_quantity="phase", save_name="source_2_field_phase", plot_zoom_x=3*zoom_x, plot_zoom_y=3*zoom_y)
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###########################
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###########################
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#initialize input field 1 (propagated source 1 field)
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input_field_1 = propagate_source(source_field_1)
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input_field_1_2d = input_field_1.reshape((Nx, Ny)) #reshape to 2D for plotting
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#initialize input field 2 (propagated source 2 field)
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input_field_2 = propagate_source(source_field_2)
|
||||
input_field_2_2d = input_field_2.reshape((Nx, Ny)) #reshape to 2D for plotting
|
||||
|
||||
#input field 1 integrated intensity
|
||||
input_field_1_intensity = np.sum(np.abs(input_field_1)**2)
|
||||
print("Input field integrated intensity: %.4e" % input_field_1_intensity)
|
||||
|
||||
#input field 2 integrated intensity
|
||||
input_field_2_intensity = np.sum(np.abs(input_field_2)**2)
|
||||
print("Input field integrated intensity: %.4e" % input_field_2_intensity)
|
||||
|
||||
#make a plot and save the input field
|
||||
make_2Dplot_of(input_field_1_2d, choose_quantity="amplitude", save_name="input_field_1_amplitude", plot_zoom_x=zoom_x*3, plot_zoom_y=zoom_y*3)
|
||||
make_2Dplot_of(input_field_1_2d, choose_quantity="phase", save_name="input_field_1_phase", plot_zoom_x=zoom_x*3, plot_zoom_y=zoom_y*3)
|
||||
make_2Dplot_of(input_field_2_2d, choose_quantity="amplitude", save_name="input_field_2_amplitude", plot_zoom_x=zoom_x*3, plot_zoom_y=zoom_y*3)
|
||||
make_2Dplot_of(input_field_2_2d, choose_quantity="phase", save_name="input_field_2_phase", plot_zoom_x=zoom_x*3, plot_zoom_y=zoom_y*3)
|
||||
|
||||
#list of input fields to be propagated within the optimization loop
|
||||
input_field_list = [input_field_1, input_field_2]
|
||||
#input_field_list = [input_field_1]
|
||||
###########################
|
||||
|
||||
###########################
|
||||
#initialize target field
|
||||
target_mode_indices = [1,2]
|
||||
fiber_mode_pattern_1, fiber_mode_pattern_2 = get_fiber_mode_pattern(target_mode_indices)
|
||||
|
||||
target_Efield_1_2d = fiber_mode_pattern_1 / np.sqrt(np.sum(np.abs(fiber_mode_pattern_1)**2))
|
||||
target_Efield_1 = target_Efield_1_2d.flatten() #normalized target field (intensity = 1)
|
||||
|
||||
target_Efield_2_2d = fiber_mode_pattern_2 / np.sqrt(np.sum(np.abs(fiber_mode_pattern_2)**2))
|
||||
target_Efield_2 = target_Efield_2_2d.flatten() #normalized target field (intensity = 1)
|
||||
|
||||
# Plot: Target fields
|
||||
make_2Dplot_of(target_Efield_1_2d, choose_quantity="amplitude", save_name="target_field_1_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||
make_2Dplot_of(target_Efield_1_2d, choose_quantity="phase", save_name="target_field_1_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||
make_2Dplot_of(target_Efield_2_2d, choose_quantity="amplitude", save_name="target_field_2_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||
make_2Dplot_of(target_Efield_2_2d, choose_quantity="phase", save_name="target_field_2_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||
|
||||
target_field_list = [target_Efield_1, target_Efield_2]
|
||||
#target_field_list = [target_Efield_1]
|
||||
###########################
|
||||
|
||||
def forward_propagate(input_field:np.ndarray,weights:np.ndarray) -> np.ndarray:
|
||||
'''Propagates the input field through the system. Stores results in-place within the intermediate_fields list.
|
||||
Returns:
|
||||
the output field computed at the observation plane
|
||||
'''
|
||||
print("Starting propagating...")
|
||||
intermediate_fields = [None, None]
|
||||
start_time = time.time()
|
||||
phase_mask = phase_given_w(weights)
|
||||
fft_input_array[:,:] = np.fft.ifftshift((input_field * np.exp(1j * phase_mask[:S])).reshape((Nx, Ny)))
|
||||
fft_operator()
|
||||
#print("BEFORE")
|
||||
fft_power = np.sum(np.abs(fft_operator.output_array)**2)/S
|
||||
non_propagating_mask = np.where((wavelength * nu_parallel)**2 > 1, 0, 1)
|
||||
non_propagating_mask = np.fft.ifftshift(non_propagating_mask)
|
||||
propagating_power = np.sum(np.abs(fft_operator.output_array * non_propagating_mask)**2)/S
|
||||
#print("FFT power: %.4e, Propagating power: %.4e, Non-propagating power: %.4e" % (fft_power, propagating_power, fft_power - propagating_power))
|
||||
|
||||
#FIRST PROPAGATION
|
||||
ifft_input_array[:,:] = fft_operator.output_array * P_1_nat #element wise product
|
||||
#print("AFTER")
|
||||
|
||||
fft_power = np.sum(np.abs(ifft_operator.input_array)**2)/S
|
||||
non_propagating_mask = np.where((wavelength * nu_parallel)**2 > 1, 0, 1)
|
||||
non_propagating_mask = np.fft.ifftshift(non_propagating_mask)
|
||||
propagating_power = np.sum(np.abs(ifft_operator.input_array * non_propagating_mask)**2)/S
|
||||
#print("FFT power: %.4e, Propagating power: %.4e, Non-propagating power: %.4e" % (fft_power, propagating_power, fft_power - propagating_power))
|
||||
|
||||
ifft_operator()
|
||||
intermediate_fields[0] = np.fft.fftshift(ifft_operator.output_array.copy())
|
||||
#print("Field intensity after first phase mask and propagation: %.4e" % np.sum(np.abs(intermediate_fields[0])**2))
|
||||
|
||||
fft_input_array[:,:] = np.fft.ifftshift((np.fft.fftshift(ifft_operator.output_array) * np.exp(1j * phase_mask[S:].reshape((Nx, Ny)))))
|
||||
fft_operator()
|
||||
|
||||
#SECOND PROPAGATION
|
||||
ifft_input_array[:,:] = fft_operator.output_array * P_2_nat #element wise product
|
||||
ifft_operator()
|
||||
intermediate_fields[1] = np.fft.fftshift(ifft_operator.output_array.copy())
|
||||
|
||||
end_time = time.time()
|
||||
print("Propagation finished in {:.6f} seconds.".format(end_time - start_time))
|
||||
|
||||
make_2Dplot_of(intermediate_fields[0], choose_quantity="amplitude", save_name="intermediate_field_1_amplitude", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
make_2Dplot_of(intermediate_fields[1], choose_quantity="amplitude", save_name="intermediate_field_2_amplitude", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
|
||||
return intermediate_fields
|
||||
|
||||
def adjoint_propagate(input_field_2d,target_Efield_2d,intermediate_fields):
|
||||
'''Backpropagates the output field using the adjoint of the propagation matrix P.
|
||||
Returns:
|
||||
the gradient of the cost function with respect to the phase mask (flattened)
|
||||
'''
|
||||
print("Computing adjoint...")
|
||||
start_time = time.time()
|
||||
|
||||
Phi_1_dagger = np.exp(-1j * phase_mask[:S]).reshape((Nx, Ny))
|
||||
Phi_2_dagger = np.exp(-1j * phase_mask[S:]).reshape((Nx, Ny))
|
||||
|
||||
#compute the adjoint source
|
||||
fft_input_array[:,:] = np.fft.ifftshift(np.sum(intermediate_fields[1] * np.conj(target_Efield_2d)) * target_Efield_2d)
|
||||
fft_operator()
|
||||
ifft_input_array[:,:] = fft_operator.output_array * P_2_dagger_nat
|
||||
ifft_operator()
|
||||
fft_input_array[:,:] = np.fft.ifftshift(np.fft.fftshift(ifft_operator.output_array) * Phi_2_dagger)
|
||||
|
||||
grad_C_phi_2 = 2 * np.real(-1j * intermediate_fields[0].conj() * np.fft.fftshift(fft_input_array)).flatten()
|
||||
|
||||
fft_operator()
|
||||
ifft_input_array[:,:] = fft_operator.output_array * P_1_dagger_nat #element wise
|
||||
ifft_operator()
|
||||
|
||||
grad_C_phi_1 = 2 * np.real(-1j * input_field_2d.conj() * np.fft.fftshift(ifft_operator.output_array) * Phi_1_dagger).flatten()
|
||||
|
||||
end_time = time.time()
|
||||
print("Adjoint finished in {:.6f} seconds.".format(end_time - start_time))
|
||||
return np.concatenate((grad_C_phi_1, grad_C_phi_2))
|
||||
|
||||
|
||||
def value_and_grad(weights):
|
||||
values = []
|
||||
gradients = []
|
||||
|
||||
phase_mask[:] = phase_given_w(weights) #update phase mask in place
|
||||
for i, input_field in enumerate(input_field_list):
|
||||
|
||||
intermediate_fields = forward_propagate(input_field, weights)
|
||||
|
||||
circular_mask = np.where(rho.flatten() < 10*6e-6, 1, 0)
|
||||
C_s = np.abs(np.sum(intermediate_fields[-1].flatten() * circular_mask * np.conj(target_field_list[i]))) ** 2
|
||||
C = np.real(np.sum(C_s))
|
||||
|
||||
values.append(-C)
|
||||
gradients.append(
|
||||
adjoint_propagate(
|
||||
input_field_2d = input_field.reshape((Nx, Ny)),
|
||||
target_Efield_2d = target_field_list[i].reshape((Nx, Ny)),
|
||||
intermediate_fields = intermediate_fields)
|
||||
)
|
||||
|
||||
return np.array(values), np.array(gradients)
|
||||
|
||||
obj_values1 = []
|
||||
obj_values2 = []
|
||||
def epigraph_constraint(result,epigraph_and_weights,gradient)->None:
|
||||
'''Constraint function for the epigraph formulation
|
||||
Args:
|
||||
result: 1D array, modified in place, with the results of this constraint
|
||||
evaluation
|
||||
epigraph_and_weights: 1D array of epigraph (first element) and
|
||||
design weights (remaining elements)
|
||||
gradient: gradients, modified in place, of the constraint function with respect to the design weights
|
||||
'''
|
||||
epigraph = epigraph_and_weights[0]
|
||||
weights = epigraph_and_weights[1:]
|
||||
|
||||
obj_val, grad = value_and_grad(weights)
|
||||
obj_values1.append(obj_val[0])
|
||||
obj_values2.append(obj_val[1])
|
||||
|
||||
if gradient.size > 0:
|
||||
gradient[:,0] = -1
|
||||
gradient[:,1:] = - grad * (2*np.pi)
|
||||
|
||||
#result of the evaluation of this constraint function
|
||||
result[:] = np.real(obj_val) - epigraph
|
||||
|
||||
opt_history = []
|
||||
def obj_fun(epigraph_and_weights, grad):
|
||||
'''Objective function for the epigraph formulation
|
||||
Args:
|
||||
epigraph_and_weights: 1D array of epigraph (first element) and
|
||||
design weights (remaining elements)
|
||||
grad: gradient of the objective function with respect to the design weights, modified in place
|
||||
Returns:
|
||||
The scalar epigraph variable (the objective function)
|
||||
'''
|
||||
|
||||
epigraph = epigraph_and_weights[0]
|
||||
|
||||
if grad.size > 0:
|
||||
grad[0] = 1
|
||||
grad[1:] = 0
|
||||
|
||||
opt_history.append(epigraph)
|
||||
#make a 1d plot of the optimization history together with the objective values
|
||||
make_1Dplot_of(x_axis=[np.arange(len(obj_values1)), np.arange(len(obj_values2)), np.arange(len(opt_history))], y_axis=[obj_values1, obj_values2, opt_history], legend_labels=["ob1","ob2","t"], save_name="optimization_history", plot_zoom_x=len(opt_history))
|
||||
|
||||
return epigraph
|
||||
|
||||
def initialize_masks():
|
||||
X1,Y1 = shift_spatial_grid(-source_spacing/2,0)
|
||||
rho1 = np.sqrt(X1**2 + Y1**2)
|
||||
circular_mask_1 = np.where(rho1.flatten() < 10*6e-6, 1, 0)
|
||||
|
||||
X2,Y2 = shift_spatial_grid(source_spacing/2,0)
|
||||
rho2 = np.sqrt(X2**2 + Y2**2)
|
||||
circular_mask_2 = np.where(rho2.flatten() < 10*6e-6, 1, 0)
|
||||
|
||||
target_pattern_1_norm_phase = (np.angle(target_Efield_1) + 2 * np.pi) % (2 * np.pi) / (2*np.pi)
|
||||
target_pattern_1_norm_phase = np.roll(target_pattern_1_norm_phase, shift=int(source_spacing/sampling_period/2), axis=0)
|
||||
|
||||
target_pattern_2_norm_phase = (np.angle(target_Efield_2) + 2 * np.pi) % (2 * np.pi) / (2*np.pi)
|
||||
target_pattern_2_norm_phase = np.roll(target_pattern_2_norm_phase, shift=-int(source_spacing/sampling_period/2), axis=0)
|
||||
#on metasurface 1, set initial guess on normalized phase elements
|
||||
w_norm[:S] += circular_mask_1 * target_pattern_1_norm_phase + circular_mask_2 * target_pattern_2_norm_phase
|
||||
#on metasurface 2, generate random initial guess for normalized phase elements
|
||||
#w_norm[S:] += np.random.rand(S) * circular_mask_1 + np.random.rand(S) * circular_mask_2
|
||||
|
||||
if __name__ == "__main__":
|
||||
###########################
|
||||
#initialize the normalized phase masks and global phase mask
|
||||
w_norm = np.zeros((2*S)) #concatenated normalized parameters for both masks
|
||||
initialize_masks()
|
||||
phase_mask = phase_given_w(w_norm)
|
||||
|
||||
#make an initial plot of the phase masks
|
||||
make_2Dplot_of(phase_mask[:S].reshape((Nx, Ny)), choose_quantity="phase_mask", save_name="initial_phase_mask_1", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
make_2Dplot_of(phase_mask[S:].reshape((Nx, Ny)), choose_quantity="phase_mask", save_name="initial_phase_mask_2", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
|
||||
#define bounding box for the optimization. The outer mask is fixed to zero phase, while the inner mask can vary between 0 and 2pi phase.
|
||||
#the bounding box is the outer shell of a square with thickness 100 um
|
||||
norm_phase_min = 0.0
|
||||
norm_phase_max = 1.0
|
||||
mask_buffer = 100e-6
|
||||
mask_upper_bounds = norm_phase_max * np.where((np.abs(X.flatten()) > size_x/2 - mask_buffer) | (np.abs(Y.flatten()) > size_y/2 - mask_buffer), 0, 1)
|
||||
mask_upper_bounds = np.concatenate((mask_upper_bounds, mask_upper_bounds),axis=0)
|
||||
mask_lower_bounds = np.zeros_like(mask_upper_bounds)
|
||||
|
||||
|
||||
epigraph_and_weights = np.insert(w_norm,0,0) #initialize epigraph variable to 0
|
||||
print("#####Shape of epigraph_and_weights: ", epigraph_and_weights.shape)
|
||||
###########################
|
||||
|
||||
#initialize nlopt solver
|
||||
solver = nlopt.opt(nlopt.LD_CCSAQ, 2*S + 1) #weights (2S) + epigraph (1)
|
||||
epigraph_and_weights_lower_bounds = np.insert(mask_lower_bounds.flatten(),0,-np.inf)
|
||||
epigraph_and_weights_upper_bounds = np.insert(mask_upper_bounds.flatten(),0,+np.inf)
|
||||
solver.set_lower_bounds(epigraph_and_weights_lower_bounds)
|
||||
solver.set_upper_bounds(epigraph_and_weights_upper_bounds)
|
||||
solver.set_min_objective(obj_fun)
|
||||
solver.add_inequality_mconstraint(
|
||||
lambda result_, epigraph_and_weights_, grad_: epigraph_constraint(
|
||||
result_,
|
||||
epigraph_and_weights_,
|
||||
grad_,
|
||||
),
|
||||
epigraph_tolerance,
|
||||
)
|
||||
solver.set_maxeval(opt_max_eval)
|
||||
solver.set_param("dual_ftol_rel", 1e-5)
|
||||
solver.set_param("verbosity", 1)
|
||||
solver.set_param("inner_maxeval", 10)
|
||||
|
||||
print("Starting optimization...")
|
||||
start = True
|
||||
if start:
|
||||
epigraph_and_weights[:] = solver.optimize(epigraph_and_weights)
|
||||
print("Optimization completed.")
|
||||
|
||||
#verify the results
|
||||
opt_weights = epigraph_and_weights[1:]
|
||||
verify_out_field_1 = forward_propagate(input_field_list[0], opt_weights)[-1]
|
||||
verify_out_field_2 = forward_propagate(input_field_list[1], opt_weights)[-1]
|
||||
all_source_on_field = input_field_list[0] + input_field_list[1]
|
||||
verify_out_field_all = forward_propagate(all_source_on_field, opt_weights)[-1]
|
||||
|
||||
make_polarPlot_of(verify_out_field_1, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_source1_amplitude", plot_zoom_r=zoom_core_diameter)
|
||||
make_polarPlot_of(verify_out_field_1, choose_quantity="phase", save_name="modeconv1_optimized_output_field_source1_phase", plot_zoom_r=zoom_core_diameter)
|
||||
make_polarPlot_of(verify_out_field_2, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_source2_amplitude", plot_zoom_r=zoom_core_diameter)
|
||||
make_polarPlot_of(verify_out_field_2, choose_quantity="phase", save_name="modeconv1_optimized_output_field_source2_phase", plot_zoom_r=zoom_core_diameter)
|
||||
make_polarPlot_of(verify_out_field_all, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_allSource_amplitude", plot_zoom_r=zoom_core_diameter)
|
||||
make_polarPlot_of(verify_out_field_all, choose_quantity="phase", save_name="modeconv1_optimized_output_field_allSource_phase", plot_zoom_r=zoom_core_diameter)
|
||||
|
||||
#save the output fields for later use
|
||||
saveFields = False
|
||||
if saveFields:
|
||||
np.savetxt("results/modeconv1_optimized_output_field_source1.txt", verify_out_field_1.reshape((Nx, Ny)))
|
||||
np.savetxt("results/modeconv1_optimized_output_field_source2.txt", verify_out_field_2.reshape((Nx, Ny)))
|
||||
np.savetxt("results/modeconv1_optimized_output_field_allSource.txt", verify_out_field_all.reshape((Nx, Ny)))
|
||||
|
||||
# Reshape fields to 2D for visualization
|
||||
phase_mask_1 = phase_given_w(epigraph_and_weights[1:S+1]).reshape((Nx, Ny))
|
||||
phase_mask_2 = phase_given_w(epigraph_and_weights[S+1:]).reshape((Nx, Ny))
|
||||
# Plot: Phase masks
|
||||
make_2Dplot_of(phase_mask_1, choose_quantity="phase_mask", save_name="phase_mask_1", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
make_2Dplot_of(phase_mask_2, choose_quantity="phase_mask", save_name="phase_mask_2", plot_zoom_x=full_view_x, plot_zoom_y=full_view_y)
|
||||
|
||||
#save the phase masks for later use
|
||||
saveMasks = False
|
||||
if saveMasks:
|
||||
np.savetxt("results/optimized_phase_mask_1.txt", phase_mask_1)
|
||||
np.savetxt("results/optimized_phase_mask_2.txt", phase_mask_2)
|
||||
|
||||
print("All plots saved to results/ folder.")
|
||||
Reference in New Issue
Block a user