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https://github.com/edoverg/modeconverter.git
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added metaprop_fibermode_doublet_epigraph which implements the epigraph formulation of the problem to handle multiplexing
This commit is contained in:
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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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#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 = 500e-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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##############################
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##############################
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#Source
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beam_waist = 9e-6
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source_spacing = 150e-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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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(n_mode_sel):
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'''Returns the target fiber mode pattern'''
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print("Computing target fiber mode pattern for LP %d1" % n_mode_sel)
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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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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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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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return E_field
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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 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,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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plt.plot(x_axis[i], y_axis[i])
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plt.xlabel("x [um]")
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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 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
|
||||||
|
|
||||||
|
#initialize input field 2 (propagated source 2 field)
|
||||||
|
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]
|
||||||
|
###########################
|
||||||
|
|
||||||
|
###########################
|
||||||
|
#initialize target field
|
||||||
|
target_mode_indices = [1,2]
|
||||||
|
fiber_mode_pattern_1 = get_fiber_mode_pattern(target_mode_indices[0])
|
||||||
|
fiber_mode_pattern_2 = get_fiber_mode_pattern(target_mode_indices[1])
|
||||||
|
|
||||||
|
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]
|
||||||
|
###########################
|
||||||
|
|
||||||
|
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[:,:] = (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] = 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[:,:] = (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] = 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.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[:,:] = ifft_operator.output_array * Phi_2_dagger
|
||||||
|
|
||||||
|
grad_C_phi_2 = 2 * np.real(-1j * intermediate_fields[0].T.conj() * 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.T.conj() * 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 = [None, None]
|
||||||
|
gradients = [None, None]
|
||||||
|
|
||||||
|
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[i] = C
|
||||||
|
gradients[i] = 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)
|
||||||
|
|
||||||
|
|
||||||
|
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)
|
||||||
|
|
||||||
|
if gradient.size > 0:
|
||||||
|
gradient[:,0] = -1
|
||||||
|
gradient[:,1:] = grad * (2*np.pi)
|
||||||
|
|
||||||
|
#we take the negative of obj_val because we are minimizing the epigraph
|
||||||
|
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)
|
||||||
|
|
||||||
|
plt.figure()
|
||||||
|
plt.plot(opt_history)
|
||||||
|
plt.xlabel('Iteration')
|
||||||
|
plt.ylabel('Epigraph Value')
|
||||||
|
plt.title('Optimization History')
|
||||||
|
plt.tight_layout()
|
||||||
|
plt.savefig("results/modeconv1_optimization_history.pdf")
|
||||||
|
plt.close()
|
||||||
|
|
||||||
|
return epigraph
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
###########################
|
||||||
|
#initialize the normalized phase masks and global phase mask
|
||||||
|
w_norm = np.zeros((2*S)) #concatenated normalized parameters for both 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
|
||||||
|
|
||||||
|
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-7)
|
||||||
|
solver.set_param("verbosity",1)
|
||||||
|
|
||||||
|
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_2Dplot_of(verify_out_field_1, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_source1_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
make_2Dplot_of(verify_out_field_1, choose_quantity="phase", save_name="modeconv1_optimized_output_field_source1_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
make_2Dplot_of(verify_out_field_2, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_source2_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
make_2Dplot_of(verify_out_field_2, choose_quantity="phase", save_name="modeconv1_optimized_output_field_source2_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
make_2Dplot_of(verify_out_field_all, choose_quantity="amplitude", save_name="modeconv1_optimized_output_field_allSource_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
make_2Dplot_of(verify_out_field_all, choose_quantity="phase", save_name="modeconv1_optimized_output_field_allSource_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
|
||||||
|
|
||||||
|
#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]).reshape((Nx, Ny))
|
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|
phase_mask_2 = phase_given_w(epigraph_and_weights[S:]).reshape((Nx, Ny))
|
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|
phase_mask_zoom = 150
|
||||||
|
# Plot: Phase masks
|
||||||
|
make_2Dplot_of(phase_mask_1, choose_quantity="phase_mask", save_name="phase_mask_1", plot_zoom_x=phase_mask_zoom, plot_zoom_y=phase_mask_zoom)
|
||||||
|
make_2Dplot_of(phase_mask_2, choose_quantity="phase_mask", save_name="phase_mask_2", plot_zoom_x=phase_mask_zoom, plot_zoom_y=phase_mask_zoom)
|
||||||
|
|
||||||
|
#save the phase masks for later use
|
||||||
|
saveMasks = True
|
||||||
|
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