modeconverter/metaprop_fibermode_doublet_ego.py

import time
import multiprocessing

import pyfftw
#pyFFTW setup
n_cpu = multiprocessing.cpu_count()
pyfftw.config.NUM_THREADS = n_cpu
pyfftw.interfaces.cache.enable()
pyfftw.config.PLANNER_EFFORT = 'FFTW_MEASURE'

import nlopt

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
#set the global font size for all plots
plt.rcParams.update({'font.size': 14})

from scipy.special import jv, kv

from smt.applications.ego import EGO, KRG
from smt.sampling_methods import LHS
from smt.design_space import (
    DesignSpace,
) 


import os
results_folder = "results_ego"
if not os.path.exists(results_folder):
    os.makedirs(results_folder)

##############################
#physics and simulation domain
wavelength = 1.55e-6
n0 = 1.45
n1 = 1.0
n2 = 1.45

lda0 = wavelength / n0
lda1 = wavelength / n1
lda2 = wavelength / n2

k0 = 2 * np.pi / lda0
k1 = 2 * np.pi / lda1
k2 = 2 * np.pi / lda2

opt_max_eval = 150

unit_cell_pitch = 700e-9 #equivalent to spatial sampling

Nx = 1024 #pixels per dimension
Ny = Nx
S = Nx * Ny

size_x = unit_cell_pitch * Nx #actual physical size
size_y = unit_cell_pitch * Ny

xs = np.linspace(-size_x/2, size_x/2 - size_x / Nx, Nx)
ys = np.linspace(-size_y/2, size_y/2 - size_y / Ny, Ny)

X, Y = np.meshgrid(xs, ys)
rho = np.sqrt(X**2 + Y**2)

sampling_period = xs[1] - xs[0]

d0 = 0 #propagation distance: source - MS1
d1 = 0 #propagation distance: MS1 - MS2
d2 = d0 #propagation distance: MS2 - target
d = np.zeros((3,))

phase_min = 0
phase_max = 2 * np.pi
##############################

##############################
#Source
beam_waist = 5.2e-6
#output fibre
output_fiber_core_diameter = 19e-6
##############################

##############################
#plan pyfftw objects for forward and inverse FFTs
fft_input_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
fft_output_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
ifft_input_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)
ifft_output_array = pyfftw.empty_aligned((Nx, Ny), dtype='complex128', n=16)

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',))
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',))
##############################

##############################
#setting up spatial frequencies
ks = 2 * np.pi / sampling_period
kappas = np.arange(-Nx//2, Nx//2) * ks / Nx
KX, KY = np.meshgrid(kappas, kappas)
K_parallel = np.sqrt(KX**2 + KY**2)
nu_parallel = K_parallel / (2 * np.pi)

phase_factor_0 = k0 * d[0] * np.sqrt(1 - (lda0 * nu_parallel) ** 2 + 0*1j)
P_0 = np.exp(1j * phase_factor_0)
P_0_nat = np.fft.ifftshift(P_0)
phase_factor_1 = k1 * d[1] * np.sqrt(1 - (lda1 * nu_parallel) ** 2 + 0*1j)
P_1 = np.exp(1j * phase_factor_1)
P_1_nat = np.fft.ifftshift(P_1)
phase_factor_2 = k2 * d[2] * np.sqrt(1 - (lda2 * nu_parallel) ** 2 + 0*1j)
P_2 = np.exp(1j * phase_factor_2)
P_2_nat = np.fft.ifftshift(P_2)

P_1_dagger = P_1.T.conj()
P_2_dagger = P_2.T.conj()
P_1_dagger_nat = np.fft.ifftshift(P_1).T.conj()
P_2_dagger_nat = np.fft.ifftshift(P_2).T.conj()
##############################

##############################
#Plot zoom parameters [um]
zoom_x = 150
zoom_y = 150
zoom_output_fiber_radius = 63
full_view_x = size_x * 1e6 / 2
full_view_y = size_y * 1e6 / 2
##############################

def phase_given_w(w):
    '''Returns the phase shift given the design parameters w.
    Args:
        w: design parameters (flattened)
    Returns:
        The phase shift corresponding to the geometrical parameters w (flattened)'''
    #for simplicity, we linearly map w (0,1) to a phase shift (0, 2pi)
    return 2 * np.pi * (w)

def get_pattern() -> np.ndarray:
    '''Returns the flattened target fiber mode pattern'''
    pattern_name = 'LP11_field_distribution.txt'
    pattern = np.loadtxt('misc/' + pattern_name, dtype=complex)

    return pattern.flatten()

def get_fiber_mode_pattern(mode_list:list)->list:
    '''Returns the fiber mode pattern for the selected n index.
    Args:
        mode_list: the list of the selected fiber mode indices
    Returns:
        The fiber mode patterns corresponding to the selected indices returned 
        as a list of 2D arrays with the same order as the input mode_list
    '''
    #check if the modes in mode_list have already been compute by checking
    #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.
    fiber_modes_input_folder = "fiber_modes"
    output_patterns = []
    try:
        for enum_index, n in enumerate(mode_list):
            #try to load mode index n
            try:
                pattern_file = fiber_modes_input_folder + f"/LP{n}1_field_distribution_{Nx}.npy"
                pattern = np.load(pattern_file)
                output_patterns.append(pattern)
                print("Loaded fiber patterns for mode index: ", n)
            #if mode index n was not found, compute it
            except FileNotFoundError:
                if not os.path.exists(fiber_modes_input_folder):
                        os.makedirs(fiber_modes_input_folder)

                print("Computing fiber patterns for mode index: ", n)
                lda = 1.55e-6

                n_co = 1.4630 #core refractive index
                n_cl = 1.4585 #cladding refractive index

                fiber_core_diameter = output_fiber_core_diameter # [m]
                a = fiber_core_diameter / 2 #fiber core radius

                #find the v parameter range that corresponds to the 1550 nm wavelength
                #v_1550 = 2 * np.pi * a / lda * np.sqrt(n_co**2 - n_cl**2)
                v_1550 = 4.5

                b = np.linspace(1e-3, 1-1e-3, 400000)
                V_list = np.linspace(2, 5.1, 20)
                V_obs = v_1550
                #b, V = np.meshgrid(b_list, V_list)

                b_solutions_at_V_obs = []
                b_solutions = []    
                for V in V_list:
                    LHS = np.sqrt(1-b) * jv(n+1, V * np.sqrt(1-b)) / jv(n, V * np.sqrt(1-b))
                    RHS = np.sqrt(b) * kv(n+1, V * np.sqrt(b)) / kv(n, V * np.sqrt(b))

                    intersection_index = np.argmax(np.where(np.isclose(LHS, RHS, atol=0.000001),1,0).flatten())

                    b_solutions.append(b[intersection_index])

                LHS = np.sqrt(1-b) * jv(n+1, V_obs * np.sqrt(1-b)) / jv(n, V_obs * np.sqrt(1-b))
                RHS = np.sqrt(b) * kv(n+1, V_obs * np.sqrt(b)) / kv(n, V_obs * np.sqrt(b))
                b_solutions_at_V_obs.append(b[np.argmax(np.where(np.isclose(LHS, RHS, atol=0.00001),1,0).flatten())])

                b_mode_sel = b_solutions_at_V_obs[0]

                k_co = 2 * np.pi / lda * n_co
                k_cl = 2 * np.pi / lda * n_cl

                beta = np.sqrt(b_mode_sel * (k_co**2 - k_cl**2) + k_cl**2)

                chi_co = v_1550 * np.sqrt(1 - b_mode_sel) / a
                chi_cl = v_1550 * np.sqrt(b_mode_sel) / a

                E_field = np.zeros_like(X, dtype=complex)

                for i in range(Nx):
                    for j in range(Ny):
                        r = np.sqrt(X[i,j]**2 + Y[i,j]**2)
                        if r < 10*a:
                            phi = np.arctan2(Y[i,j], X[i,j])
                            if r < a:#inside core
                                E_field[i,j] = jv(n,chi_co * r) / jv(n, chi_co * a) * np.cos(n * phi)
                            else:#outside core
                                E_field[i,j] = kv(n, chi_cl * r) / kv(n, chi_cl * a) * np.cos(n * phi)
                #save the computed pattern to a file for future use
                pattern_file = fiber_modes_input_folder + f"/LP{n}1_field_distribution_{Nx}.npy"
                np.save(pattern_file, E_field)
                output_patterns.append(E_field)
        return output_patterns
    except:
        raise(Exception("Error in computing fiber patterns"))

def shift_spatial_grid(shift_amount_x,shift_amount_y):
    '''Shifts the simulation spatial grid by a given physical (true space) amount. 
    Args:
        shift_amount_x: amount to shift the grid in x direction (in meters)
        shift_amount_y: amount to shift the grid in y direction (in meters)
    Returns:
        the shifted spatial grid (X, Y)'''
    Xp = X + shift_amount_x
    Yp = Y + shift_amount_y
    return Xp, Yp

def get_source_field(beam_waist,center_x=0,center_y=0,):
    '''Returns a 2D normalized Gaussian source field for a given beam waist and centered at the specified (x,y) coordinates. 
    Normalization consists in scaling the field such that its integrated intensity is 1.
    
    Args:
        beam_waist: the waist of the Gaussian beam (in meters)
        center_x: the x-coordinate of the center of the Gaussian beam (in meters)
        center_y: the y-coordinate of the center of the Gaussian beam (in meters)
    Returns:
        The 2D normalized Gaussian source field.
    '''

    if center_x != 0 or center_y != 0:
        X_shifted, Y_shifted = shift_spatial_grid(center_x, center_y)
        rho = np.sqrt(X_shifted**2 + Y_shifted**2)
    else:
        rho = np.sqrt(X**2 + Y**2)

    gaussian_field = np.exp(-(rho)**2 / (beam_waist)**2) #Gaussian input field, flattened
    gaussian_field_normalized = (gaussian_field / np.sqrt(np.sum(np.abs(gaussian_field)**2))) #normalize the input field to have power = 1
    
    return gaussian_field_normalized

def propagate_source(source_to_propagate):
    '''Returns the propagated source field (flattened) just before metasurface 1 (MS1). 
    This involves propagating the source for a distance d0: from its plane of definition up to MS1.
    Args:
        source_to_propagate: the source field to be propagated (flattened)
    Returns:
        The propagated source field (flattened) just before MS1.
    '''
    
    fft_input_array[:,:] = np.fft.ifftshift(source_to_propagate.reshape((Nx, Ny)))
    fft_operator()
    ifft_input_array[:,:] = fft_operator.output_array * P_0_nat
    ifft_operator()
    propagated_source_field = np.fft.fftshift(ifft_operator.output_array).flatten()
    
    return propagated_source_field

def make_1Dplot_of(x_axis,y_axis,plot_zoom_x=zoom_x,save_name="plot_1D",) -> None:
    '''Makes a 1D plot of the given data and saves it to a PDF file.
    Args:
        x_axis: list of x-axis data (list of 1D arrays)
        y_axis: list of y-axis data (list of 1D arrays)
        plot_zoom_x: zoom level for the x-axis (in micrometers)
        save_name: name of the file to save the plot (without extension)
    Returns:
        None
    '''
    if len(x_axis) != len(y_axis):
        raise ValueError("Lists x_axis and y_axis must have the same length.")
    plt.figure()
    for i in range(len(x_axis)):
        plt.plot(x_axis[i], y_axis[i])
    plt.xlabel("x [um]")
    plt.tight_layout()
    plt.xlim(-plot_zoom_x, plot_zoom_x)
    plt.savefig(results_folder + "/" + save_name + ".pdf")
    plt.close()

def make_2Dplot_of(given_field,choose_quantity="amplitude",save_name="plot",plot_zoom_x=zoom_x,plot_zoom_y=zoom_y) -> None:
    '''Makes a plot of the given 2D field in a zoomed region. 
    Saves the plot with the chosen filename to a PDF file. 
    Args:
        given_field: the 2D field to be plotted (flattened)
        choose_quantity: either "amplitude" or "phase" to select quantity to plot
        save_name: name of the file to save the plot (without extension)
        plot_zoom_x: zoom level for the x-axis (in micrometers)
        plot_zoom_y: zoom level for the y-axis (in micrometers)
    Returns:
        None'''
    
    given_field_2d = given_field.reshape((Nx, Ny)) #assure the field is 2D before plotting
    plt.figure()
    if choose_quantity == "amplitude":
        plt.imshow(np.abs(given_field_2d), extent=(-size_x*1e6/2, size_x*1e6/2, -size_y*1e6/2, size_y*1e6/2))
    elif choose_quantity == "phase":
        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)
    elif choose_quantity == "phase_mask":
        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)
    else:
        raise ValueError("choose_quantity must be either 'amplitude' or 'phase'")

    plt.xlim(-plot_zoom_x, plot_zoom_x)
    plt.ylim(-plot_zoom_y, plot_zoom_y)
    plt.xlabel("x [um]")
    plt.ylabel("y [um]")
    plt.colorbar()
    plt.tight_layout()
    plt.savefig(results_folder + "/" + save_name + ".pdf")
    plt.close()

def make_polarPlot_of(given_field,choose_quantity="amplitude",save_name="polar_plot",plot_zoom_r=zoom_x) -> None:
    '''Makes a polar plot of the given 2D field in a zoomed region. 
    Saves the plot with the chosen filename to a PDF file. 
    Args:
        given_field: the 2D field to be plotted (flattened)
        choose_quantity: either "amplitude" or "phase" to select quantity to plot
        save_name: name of the file to save the plot (without extension)
        plot_zoom_r: zoom level for the radial axis (in micrometers)
    Returns:
        None
    '''
    fig, ax = plt.subplots(figsize=(6, 6))
    if choose_quantity == "amplitude":
        given_field_2d = np.abs(given_field.reshape((Nx, Ny))) #assure the field is 2D before plotting
        im = ax.imshow(given_field_2d,origin='lower')
    elif choose_quantity == "phase":
        given_field_2d = (np.angle(given_field.reshape((Nx, Ny))) + 2*np.pi) % (2*np.pi)#assure the field is 2D before plotting
        im = ax.imshow(given_field_2d, cmap='hsv', vmin=0, vmax=2*np.pi)
    else:
        raise ValueError("choose_quantity must be either 'amplitude' or 'phase'")
    
    center_x, center_y = Nx//2, Ny//2
    radius = plot_zoom_r * 1e-6 / (size_x/2) * (Nx/2) #convert zoom in um to pixels
    circle = patches.Circle((center_x, center_y), radius, transform=ax.transData)
    im.set_clip_path(circle)
    ax.set_xlim(center_x - radius, center_x + radius)
    ax.set_ylim(center_y - radius, center_y + radius)
    ax.axis('off')
    cbar = plt.colorbar(im, ax=ax)
    plt.savefig(results_folder + "/" + save_name + ".pdf")
###########################
#initialize source field
source_field = get_source_field(beam_waist)
source_field_2d = source_field.reshape((Nx, Ny)) #reshape to 2D for plotting
#source field integrated intensity
source_power = np.sum(np.abs(source_field)**2)
print("Source field integrated intensity: %.4e" % source_power)
#make a plot and save the source field
make_2Dplot_of(source_field_2d, choose_quantity="amplitude", save_name="source_field_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
make_2Dplot_of(source_field_2d, choose_quantity="phase", save_name="source_field_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
###########################

###########################
#initialize input field (propagated source field)
input_field = propagate_source(source_field)
input_field_2d = input_field.reshape((Nx, Ny)) #reshape to 2D for plotting
#save the input field to numpy array
np.save(results_folder + "/input_field.npy", input_field_2d)
#input field integrated intensity
input_field_intensity = np.sum(np.abs(input_field)**2)
print("Input field integrated intensity: %.4e" % input_field_intensity)
#make a plot and save the input field
make_2Dplot_of(input_field_2d, choose_quantity="amplitude", save_name="input_field_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
make_2Dplot_of(input_field_2d, choose_quantity="phase", save_name="input_field_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
###########################

###########################
#initialize target field
target_mode_indices = [2] 
fiber_mode_pattern = get_fiber_mode_pattern(target_mode_indices)
target_Efield_2d = fiber_mode_pattern / np.sqrt(np.sum(np.abs(fiber_mode_pattern)**2))
target_Efield =  target_Efield_2d.flatten() #normalized target field (intensity = 1)

# Plot: Target field
make_polarPlot_of(target_Efield_2d, choose_quantity="amplitude", save_name="target_field_1_amplitude_polar", plot_zoom_r=zoom_output_fiber_radius)
make_polarPlot_of(target_Efield_2d, choose_quantity="phase", save_name="target_field_1_phase_polar", plot_zoom_r=zoom_output_fiber_radius)
###########################

###########################
#initialize the normalized phase masks and global phase mask
w_norm = np.zeros((2*S)) #concatenated normalized parameters for both masks
X, Y = np.meshgrid(np.linspace(-size_x/2, size_x/2, Nx), np.linspace(-size_y/2, size_y/2, Ny))
rho = np.sqrt(X**2 + Y**2)
circular_mask_1 = np.where(rho.flatten() < output_fiber_core_diameter/3, 1, 0)
#w_norm[:S] += circular_mask_1
target_pattern_phase = (np.angle(target_Efield) + 2 * np.pi) % (2 * np.pi)*circular_mask_1 #make sure the phase is between 0 and 2pi
w_norm[S:] += target_pattern_phase / (2 * np.pi) #normalize the target phase to be between 0 and 1
phase_mask = phase_given_w(w_norm)

#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
norm_phase_max = 1
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)
###########################

intermediate_fields = [None, None]
def forward_propagate() -> None:
    '''Propagates the input field through the system. Stores results in-place within the intermediate_fields list.
    Returns:
        None
    '''
    print("Starting propagating...")
    start_time = time.time()

    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))
    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()
    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()
    #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)
    
    print("Propagation finished in {:.6f} seconds.".format(end_time - start_time))


def adjoint_propagate():
    '''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 _compute_cost():
    forward_propagate()

    output_field = intermediate_fields[-1].flatten()

    #circular_mask = np.where(rho.flatten() < 10*6e-6, 1, 0) 
    C_s = np.abs(np.sum(output_field * np.conj(target_Efield))) ** 2
    C_s = np.real(np.sum(C_s))

    C_t = C_s

    return C_t   

iter_num = [0]
opt_history = []
def cost_fun(x, grad):
    ''' Cost function to be minimized.
    Args:
        x: input normalized parameter field (flattened)
        grad: gradient of the cost function with respect to x, modified in place (flattened)
    Returns:
        The cost function value for the input parameter field x.
    '''
    w_norm[:] = x

    phase_mask[:] = phase_given_w(w_norm)

    C = _compute_cost() 

    opt_history.append(C)
    iter_num[0] += 1
    if iter_num[0] % 10 == 0:
        plt.figure()
        plt.plot(opt_history)
        plt.xlabel('Iteration')
        plt.ylabel('Cost Function Value')
        plt.title('Optimization History')
        plt.tight_layout()
        plt.savefig(results_folder + "/modeconv1_optimization_history.pdf")
        plt.close()

    if grad.size > 0:
        grad[:] = adjoint_propagate() * 2 * np.pi         
    return C

def metaprop():
    #initialize nlopt solver
    solver = nlopt.opt(nlopt.LD_CCSAQ, 2*S)
    
    solver.set_lower_bounds(mask_lower_bounds.flatten())
    solver.set_upper_bounds(mask_upper_bounds.flatten())
    solver.set_max_objective(cost_fun)
    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:
        w_norm[:] = solver.optimize(w_norm)
    print("Optimization completed.")

    #verify the results
    phase_mask = phase_given_w(w_norm)
    forward_propagate()
    field_input_ms2 = intermediate_fields[0]
    output_field = intermediate_fields[-1]
    
    input_power = np.sum(np.abs(input_field)**2)
    output_power = np.sum(np.abs(output_field)**2)

    print("Norm. input power: %.4e" % input_power)
    print("Norm. output power: %.4e" % output_power)

    #save the output field for later use
    save_output_field = True
    if save_output_field:
        np.save(results_folder + "/intermediate_field_0.npy", intermediate_fields[0].reshape((Nx, Ny)))
        np.save(results_folder + "/optimized_output_field.npy", output_field.reshape((Nx, Ny)))
    # Plot results in individual PDF figures
    
    # Reshape fields to 2D for visualization
    output_field_2d = output_field.reshape((Nx, Ny))
    phase_mask_1 = phase_given_w(w_norm[:S]).reshape((Nx, Ny))
    phase_mask_2 = phase_given_w(w_norm[S:]).reshape((Nx, Ny))

    phase_mask_zoom = 150
    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)

    # Plot: Output field amplitude and phase
    make_polarPlot_of(output_field_2d, choose_quantity="amplitude", save_name="optimized_output_field_amplitude", plot_zoom_r=zoom_output_fiber_radius)
    make_polarPlot_of(output_field_2d, choose_quantity="phase", save_name="optimized_output_field_phase", plot_zoom_r=zoom_output_fiber_radius)
    
    slice_y_index = Ny//2
    slice_x = xs * 1e6
    slice_target = target_Efield.reshape((Nx, Ny))[slice_y_index,:]
    slice_output = output_field.reshape((Nx, Ny))[slice_y_index,:]
    make_1Dplot_of([slice_x, slice_x], [np.abs(slice_target), np.abs(slice_output)], plot_zoom_x=1e6*output_fiber_core_diameter, save_name="modeconv_output_vs_target_amplitude")
    make_1Dplot_of([slice_x, slice_x], [(np.angle(slice_target)+2*np.pi)%(2*np.pi), (np.angle(slice_output)+2*np.pi)%(2*np.pi)], plot_zoom_x=1e6*output_fiber_core_diameter, save_name="modeconv_output_vs_target_phase")

    #save the phase masks for later use
    savePhase_masks = True
    if savePhase_masks:
        np.save(results_folder + "/optimized_phase_mask_1.npy", phase_mask_1)
        np.save(results_folder + "/optimized_phase_mask_2.npy", phase_mask_2)

    last_optimum_value = solver.last_optimum_value()
    print("Last optimum value: %.4e" % last_optimum_value)
    print(f"All plots saved to {results_folder}/ folder.")
    return last_optimum_value

def update_phase_factors():
    phase_factor_0[:] = k0 * d[0] * np.sqrt(1 - (lda0 * nu_parallel) ** 2 + 0*1j)
    P_0[:] = np.exp(1j * phase_factor_0)
    P_0_nat[:] = np.fft.ifftshift(P_0)
    phase_factor_1[:] = k1 * d[1] * np.sqrt(1 - (lda1 * nu_parallel) ** 2 + 0*1j)
    P_1[:] = np.exp(1j * phase_factor_1)
    P_1_nat[:] = np.fft.ifftshift(P_1)
    phase_factor_2[:] = k2 * d[2] * np.sqrt(1 - (lda2 * nu_parallel) ** 2 + 0*1j)
    P_2[:] = np.exp(1j * phase_factor_2)
    P_2_nat[:] = np.fft.ifftshift(P_2)

    P_1_dagger[:] = P_1.T.conj()
    P_2_dagger[:] = P_2.T.conj()
    P_1_dagger_nat[:] = np.fft.ifftshift(P_1).T.conj()
    P_2_dagger_nat[:] = np.fft.ifftshift(P_2).T.conj()

def update_input_fields():
    input_field[:] = propagate_source(source_field)
    input_field_2d[:] = input_field.reshape((Nx, Ny)) #reshape to 2D for plotting
    #save the input field to numpy array
    #np.save("results/input_field.npy", input_field_2d)
    #input field integrated intensity
    input_field_intensity = np.sum(np.abs(input_field)**2)
    print("Input field integrated intensity: %.4e" % input_field_intensity)
    #make a plot and save the input field
    make_2Dplot_of(input_field_2d, choose_quantity="amplitude", save_name="input_field_amplitude", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)
    make_2Dplot_of(input_field_2d, choose_quantity="phase", save_name="input_field_phase", plot_zoom_x=zoom_x, plot_zoom_y=zoom_y)

def initialize_phase_masks():
    #initialize the normalized phase masks and global phase mask
    w_norm[:] = np.zeros((2*S)) #concatenated normalized parameters for both masks
    X, Y = np.meshgrid(np.linspace(-size_x/2, size_x/2, Nx), np.linspace(-size_y/2, size_y/2, Ny))
    rho = np.sqrt(X**2 + Y**2)
    circular_mask_1 = np.where(rho.flatten() < output_fiber_core_diameter/3, 1, 0)
    #w_norm[:S] += circular_mask_1
    target_pattern_phase = (np.angle(target_Efield) + 2 * np.pi) % (2 * np.pi)*circular_mask_1 #make sure the phase is between 0 and 2pi
    w_norm[S:] += target_pattern_phase / (2 * np.pi) #normalize the target phase to be between 0 and 1
    phase_mask[:] = phase_given_w(w_norm)

def reset_globals():
    opt_history[:] = []
    w_norm[:] = np.zeros((2*S))
    phase_mask[:] = phase_given_w(w_norm)
    d[:] = np.zeros((3,))

def metaprop_update(x):
    '''Objective function called from EGO loop. Given a set of input design parameters x,
    it updates the system and calls the inner adjoint-based optimization.
    Changing the system distance parameters requires updating the following terms:
    1) propagation matrices
    2) input field'''

    if not os.path.exists(f'{results_folder}/metaprop_results.txt'):
        with open(f'{results_folder}/metaprop_results.txt', 'w') as f:
            f.write("d1 [m] d2 [m] d3 [m] ob1 ob2 t\n")
    
    m, n = x.shape
    C = np.zeros((m,1))
    for i in range(m):
        for j in range(n):
            d[j] = 1e-6*np.round(x[i,j]) #update the global propagation distances with the new design parameters

        d[-1] = d[0]
        assert np.all(d), "Propagation distances must be real-positive."
        print("Current propagation distances: ", d)
        update_phase_factors() #update the phase factors for the new propagation distances
        update_input_fields()
        initialize_phase_masks()
        print("USING D=",d)
        last_optimum_value = metaprop() #solve the inner optimization problem for the given design parameters

        #save all the partial results for a specific set of design parameters x to a text file
        #in append mode, so that we can keep track of the optimization history
        with open(f'{results_folder}/metaprop_results.txt', 'a') as f:
            f.write(f"{d[0]:.6e} {d[1]:.6e} {d[2]:.6e} {last_optimum_value:.6e}\n")

        print("Current cost function value: ", opt_history[-1])
        C[i] = -last_optimum_value #remember ego does minimization

        reset_globals()   
    return C

def run_ego():
    ##############################
    #EGO setup
    ##############################
    n_ego_iter = 30
    xlimits = np.array([[100,700], [100,700]])
    seed = 777
    design_space = DesignSpace(xlimits, seed=seed)
    criterion = 'EI'
    ndoe = 20

    #build DOE
    sampling = LHS(xlimits=xlimits, seed=seed)
    xdoe = sampling(ndoe)

    sm = KRG(design_space=design_space, n_start=25, print_global=False)
    ego = EGO(
        n_iter=n_ego_iter,
        criterion=criterion,
        xdoe=xdoe,
        surrogate=sm,
        n_start=25,
    )

    x_opt, y_opt, ind_best, x_data, y_data = ego.optimize(fun=metaprop_update)
    #save the optimization results to a text file    
    np.savetxt(f'{results_folder}/ego_opt_results.txt', np.hstack((x_opt,y_opt)))

if __name__ == "__main__":
    run_ego()