diff --git a/metaprop_fibermode_doublet_ego_sym.py b/metaprop_fibermode_doublet_ego_sym.py
new file mode 100644
index 0000000..3196418
--- /dev/null
+++ b/metaprop_fibermode_doublet_ego_sym.py
@@ -0,0 +1,794 @@
+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_symm_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 = 1025 #pixels per dimension
+Ny = Nx
+nx = (Nx - 1) // 2 #indices without axes (= #512)
+ny = (Ny - 1) // 2
+dof = 2*((nx + 1)**2) #number of degrees of freedom per metasurface
+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
+#fibre cladding diameter
+fibre_cladding_diameter = 125e-6 #[um]
+max_available_diameter = 122e-6 #this is the metasurface maximum diameter (must be smaller than cladding)
+##############################
+
+##############################
+#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")
+
+def symmetrize(w):
+    '''
+    Takes an input array, which must be full in size, turns it into a 2D array, and symmetrizes it along the x and y axes.
+    Returns the first quadrant of shape (nx,ny), including the zero axis, flattened
+    '''
+    try:
+        w_2d = w.reshape((Nx, Ny))
+    except:
+        raise ValueError(f"Input array w cannot be reshaped to ({Nx}, {Ny}). Current shape: {w.shape}")
+
+    w_symm = np.zeros((nx+1, ny+1))
+    w_symm[:,:] = w_2d[:nx+1, :ny+1]
+
+    return w_symm.flatten()
+
+def expand_symmetrize(w_symm):
+    '''
+    Takes a array of shape (nx+1, ny+1), representing the first quadrant, including zero axes, and 
+    expands it to a full 2D array of shape (Nx, Ny) by mirroring, flattened.
+    '''
+
+    w_symm_2d = w_symm.reshape((nx+1, ny+1))
+
+    w_full = np.zeros((Nx, Ny))
+
+    w_full[:nx+1, :ny+1] = w_symm_2d
+    w_full[:nx+1, ny+1:] = np.flip(w_full[:nx+1, :ny], axis=1)
+    w_full[nx+1:, :ny+1] = np.flip(w_full[:nx, :ny+1], axis=0)
+    w_full[nx+1:, ny+1:] = np.flip(np.flip(w_full[:nx, :ny], axis=1), axis=0)
+    w_full[nx, ny] = w_symm_2d[-1, -1]
+
+    return w_full.flatten()
+
+###########################
+#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
+
+w_norm_symm_1 = symmetrize(w_norm[:S])
+w_norm_symm_2 = symmetrize(w_norm[S:])
+
+w_norm_symm = np.concatenate((w_norm_symm_1, w_norm_symm_2), axis=0)
+
+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
+#the upper bounds are set to 1 only within the fibre cladding diameter and zero outside
+mask_upper_bounds = norm_phase_max * np.where( X.flatten()**2 + Y.flatten()**2 < (max_available_diameter/2)**2, 1, 0)
+mask_upper_bounds_symm = mask_upper_bounds.reshape((Nx,Ny))[:nx+1, :ny+1].flatten()
+
+mask_upper_bounds_symm = np.concatenate((mask_upper_bounds_symm, mask_upper_bounds_symm),axis=0)
+mask_lower_bounds_symm = np.zeros_like(mask_upper_bounds_symm)
+###########################
+
+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 reduce_symmetrized_gradient(g_full):
+    g_2d = g_full.reshape((Nx, Ny))
+
+    g_reduced = g_2d[:nx+1, :ny+1]
+    third = g_2d[nx+1:,:ny+1]
+    second = g_2d[:nx+1, ny+1:]
+    fourth = g_2d[nx+1:, ny+1:]
+
+    g_2d[:nx, ny+1:] += np.flip(fourth, axis = 0)
+    g_2d[:nx, :ny+1] += np.flip(third, axis = 0)
+    g_2d[:nx+1, :ny] += np.flip(second, axis = 1)
+    
+    return g_2d[:nx+1, :ny+1].flatten()
+
+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 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.
+    '''
+    ms1_first_quadrant = x[:dof//2].reshape(nx+1, ny+1)
+    ms2_first_quadrant = x[dof//2:].reshape(nx+1, ny+1)
+
+    ms1 = expand_symmetrize(ms1_first_quadrant)
+    ms2 = expand_symmetrize(ms2_first_quadrant)
+
+    all_ms = np.concatenate((ms1, ms2))
+
+    w_norm[:] = all_ms
+
+    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:
+        full_grad1, full_grad2 = adjoint_propagate()
+        reduced_grad1 = reduce_symmetrized_gradient(full_grad1)
+        reduced_grad2 = reduce_symmetrized_gradient(full_grad2)
+        reduced_grads = np.concatenate((reduced_grad1, reduced_grad2), axis=0)
+        grad[:] = reduced_grads * 2 * np.pi          
+    return C
+
+def metaprop():
+    #initialize nlopt solver
+    solver = nlopt.opt(nlopt.LD_CCSAQ, dof)
+    
+    solver.set_lower_bounds(mask_lower_bounds_symm.flatten())
+    solver.set_upper_bounds(mask_upper_bounds_symm.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_symm[:] = solver.optimize(w_norm_symm)
+        w_norm[:S] = expand_symmetrize(w_norm_symm[:dof//2])
+        w_norm[S:] = expand_symmetrize(w_norm_symm[dof//2:])
+
+    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()
\ No newline at end of file
diff --git a/metaprop_fibermode_doublet_sym.py b/metaprop_fibermode_doublet_sym.py
index 0753c76..1287107 100644
--- a/metaprop_fibermode_doublet_sym.py
+++ b/metaprop_fibermode_doublet_sym.py
@@ -39,7 +39,7 @@ k0 = 2 * np.pi / lda0
 k1 = 2 * np.pi / lda1
 k2 = 2 * np.pi / lda2
 
-opt_max_eval = 150
+opt_max_eval = 200
 
 unit_cell_pitch = 700e-9 #equivalent to spatial sampling
 
@@ -84,9 +84,12 @@ phase_max = 2 * np.pi
 
 ##############################
 #Source
-beam_waist = 5.2e-6
+beam_waist = 5.2e-6 #[um]
 #output fibre
-output_fiber_core_diameter = 19e-6
+output_fiber_core_diameter = 19e-6 #[um]
+#fibre cladding diameter
+fibre_cladding_diameter = 125e-6 #[um]
+max_available_diameter = 122e-6
 ##############################
 
 ##############################
@@ -491,12 +494,12 @@ phase_mask = phase_given_w(w_norm)
 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)
+#the upper bounds are set to 1 only within the fibre cladding diameter and zero outside
+mask_upper_bounds = norm_phase_max * np.where( X.flatten()**2 + Y.flatten()**2 < (max_available_diameter/2)**2, 1, 0)
 mask_upper_bounds_symm = mask_upper_bounds.reshape((Nx,Ny))[:nx+1, :ny+1].flatten()
 
 mask_upper_bounds_symm = np.concatenate((mask_upper_bounds_symm, mask_upper_bounds_symm),axis=0)
 mask_lower_bounds_symm = np.zeros_like(mask_upper_bounds_symm)
-
 ###########################
 
 intermediate_fields = [None, None]
@@ -610,7 +613,7 @@ def cost_fun(x, grad):
     Returns:
         The cost function value for the input parameter field x.
     '''
-    #since the objective function is to maximize the overlap, and the target mode is C4 symmetric, 
+    #since the objective function is to maximize the overlap, and the target mode is mirror symmetric, 
     #we can let the algorithm optimize only a fourth of the phase mask and then synthetize automatically the remaining three quadrants.
     #Since we have two metasurfaces, the total number of parameters the algorithm needs to optimize is S/2 (S/4 for each metasurface)
     ms1_first_quadrant = x[:dof//2].reshape(nx+1, ny+1)