implemented new filtering system based on a Filter Class. Previously, filtering was made expensive by extreme padding, now this has been fixed by choosing a more appropriate padding size. The gradient chain based on unitcells has been implemented but the results have yet to be tested using FDTD, which will be the next step. Added some utilities to visualize the effect of filter radius on given input masks and added all data concerning unit cell simulations. Still to be done is to fix materials in the MEEP simulations, so as to account for true material behavior instead of relying on constant refractive indices.

2026-10-14 23:26:38 +00:00 · 2026-10-14 16:40:05 +02:00
parent 7a71b43b72
commit 625cd64f53
34 changed files with 1891 additions and 196 deletions
@@ -0,0 +1,29 @@
+nohup: ignoring input
+Rank 0 is processing diameter 0.100 (index 0)
+Rank 1 is processing diameter 0.361 (index 12)
+Rank 0 is processing diameter 0.122 (index 1)
+Rank 1 is processing diameter 0.383 (index 13)
+Rank 0 is processing diameter 0.143 (index 2)
+Rank 1 is processing diameter 0.404 (index 14)
+Rank 0 is processing diameter 0.165 (index 3)
+Rank 1 is processing diameter 0.426 (index 15)
+Rank 0 is processing diameter 0.187 (index 4)
+Rank 1 is processing diameter 0.448 (index 16)
+Rank 0 is processing diameter 0.209 (index 5)
+Rank 1 is processing diameter 0.470 (index 17)
+Rank 0 is processing diameter 0.230 (index 6)
+Rank 0 is processing diameter 0.252 (index 7)
+Rank 1 is processing diameter 0.491 (index 18)
+Rank 0 is processing diameter 0.274 (index 8)
+Rank 1 is processing diameter 0.513 (index 19)
+Rank 0 is processing diameter 0.296 (index 9)
+Rank 1 is processing diameter 0.535 (index 20)
+Rank 0 is processing diameter 0.317 (index 10)
+Rank 1 is processing diameter 0.557 (index 21)
+Rank 0 is processing diameter 0.339 (index 11)
+Rank 1 is processing diameter 0.578 (index 22)
+Rank 1 is processing diameter 0.600 (index 23)
+
+Elapsed run time = 17749.7805 s
+
+Elapsed run time = 17750.1165 s
@@ -0,0 +1,25 @@
+% Model:              cyljnderUnjtCell_solved.mph
+% Versjon:            COMSOL 6.1.0.282
+% Date:               Aug 7 2026, 11:04
+% Table:              Table 3 - Global Evaluatjon 3
+% tPost (nm)                                      R (nm)                                            lambda0 (µm)                                      S21 (1)
+900                                               50                                                1.55                                              -0.845669386929+0.5044362611307165j
+900                                               63.157894736842096                                1.55                                              -0.8251549977113691+0.5387569255954204j
+900                                               76.31578947368419                                 1.55                                              -0.7941914472021001+0.5854009666643545j
+900                                               89.47368421052632                                 1.55                                              -0.7471355423796626+0.6469515347910716j
+900                                               102.6315789473684                                 1.55                                              -0.6739731961216431+0.7260451361240156j
+900                                               115.78947368421052                                1.55                                              -0.5559252634519462+0.8236596878659627j
+900                                               128.94736842105263                                1.55                                              -0.35623973597781955+0.9314716653309569j
+900                                               142.1052631578947                                 1.55                                              -0.005446778866258663+0.9995911107511558j
+900                                               155.26315789473682                                1.55                                              0.5624693373844357+0.8192539801083378j
+900                                               168.42105263157896                                1.55                                              0.9716453344468975-0.026879486169522106j
+900                                               181.57894736842104                                1.55                                              0.33229983484123915-0.9109913324745208j
+900                                               194.73684210526312                                1.55                                              -0.5138804677648452-0.8375112454139356j
+900                                               207.89473684210526                                1.55                                              -0.8979812315659875-0.41599951560137755j
+900                                               221.05263157894737                                1.55                                              -0.8666228661809928-0.35839703156981834j
+900                                               234.21052631578942                                1.55                                              -0.9706534677777011+0.1672691323977627j
+900                                               247.36842105263153                                1.55                                              -0.875683679549086+0.4301009457755804j
+900                                               260.52631578947364                                1.55                                              -0.7186563387658285+0.6394472785795947j
+900                                               273.6842105263158                                 1.55                                              -0.6152456609406248+0.5634675095025711j
+900                                               286.8421052631579                                 1.55                                              -0.3669553952916399+0.7919528013254294j
+900                                               300                                               1.55                                              -0.07785011501821787+0.7863645334693915j
@@ -0,0 +1,51 @@
+'''
+Utility script to test the gradients functionality of the unit cell class of mpid
+Given the simulated transmittance phase values and associated tune parameter, 
+the unit cell class should return the gradient of the simulated phase with respect to the tuning parameter.
+the class also provides a method to compute the gradient at a specific tuning parameter value, through interpolation.
+'''
+
+import numpy as np
+from matplotlib import pyplot as plt
+from mpid import UnitCell
+
+wavelength_um_1_53 = 1.53
+wavelength_um_1_55 = 1.55
+wavelength_um_1_57 = 1.57
+unit_cell_diameters = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_diameters.npy")
+unit_cell_phases_wvl_1530 = np.load("unit_cell/unit_cell_center_1530_h900nm_res50_wvl_mode_phase.npy")
+unit_cell_phases_wvl_1550 = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_mode_phase.npy")
+unit_cell_phases_wvl_1570 = np.load("unit_cell/unit_cell_center_1570_h900nm_res50_wvl_mode_phase.npy")
+
+unit_cell_1530 = UnitCell(wavelength=wavelength_um_1_53, tune_param=unit_cell_diameters, sim_phase=unit_cell_phases_wvl_1530)
+unit_cell_1550 = UnitCell(wavelength=wavelength_um_1_55, tune_param=unit_cell_diameters, sim_phase=unit_cell_phases_wvl_1550)
+unit_cell_1570 = UnitCell(wavelength=wavelength_um_1_57, tune_param=unit_cell_diameters, sim_phase=unit_cell_phases_wvl_1570)
+
+fig, ax = plt.subplots(figsize=(6, 6))
+plt.rcParams['mathtext.default'] = 'regular'
+ax.plot(unit_cell_1530.get_tune_param(), unit_cell_1530.get_gradient(), color='r', label=r"$\lambda=1530\:[nm]$", linewidth=3)
+ax.plot(unit_cell_1550.get_tune_param(), unit_cell_1550.get_gradient(), color='g', label=r"$\lambda=1550\:[nm]$", linewidth=3)
+ax.plot(unit_cell_1570.get_tune_param(), unit_cell_1570.get_gradient(), color='b', label=r"$\lambda=1570\:[nm]$", linewidth=3)
+ax.set_xlabel("diameter [um]", fontsize=20)
+ax.set_ylabel(r"$\partial \phi/\partial d$", fontsize=20, rotation='vertical')
+ax.yaxis.set_label_coords(-0.11, 0.5)
+ax.set_aspect('auto')
+ax.set_xticks(np.arange(min(unit_cell_diameters), max(unit_cell_diameters)+0.1, 0.1))
+ax.tick_params(axis='x', labelsize=20)
+ax.tick_params(axis='y', labelsize=20)
+plt.tight_layout()
+plt.savefig("unit_cell_gradient.pdf")
+
+fig, ax = plt.subplots(figsize=(6, 6))
+ax.plot(unit_cell_1530.get_tune_param(), unit_cell_1530.get_sim_phase(), color='r', label=r"$\lambda=1530\:[nm]$", linewidth=3)
+ax.plot(unit_cell_1550.get_tune_param(), unit_cell_1550.get_sim_phase(), color='g', label=r"$\lambda=1550\:[nm]$", linewidth=3)
+ax.plot(unit_cell_1570.get_tune_param(), unit_cell_1570.get_sim_phase(), color='b', label=r"$\lambda=1570\:[nm]$", linewidth=3)
+ax.set_xlabel("diameter [um]", fontsize=20)
+ax.set_ylabel(r"$\phi\:$[rad]", fontsize=20)
+ax.tick_params(axis='x', labelsize=20)
+ax.tick_params(axis='y', labelsize=20)
+ax.legend(fontsize=20, loc='best')
+ax.set_aspect('auto')
+ax.set_xticks(np.arange(min(unit_cell_diameters), max(unit_cell_diameters)+0.1, 0.1))
+plt.tight_layout()
+plt.savefig("unit_cell_phase.pdf")
@@ -0,0 +1,169 @@
+import meep as mp
+mp.verbosity(0)
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from mpi4py import MPI
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+resolution = 50 # pixels/unit length
+
+wvl_min = 1.53
+wvl_max = 1.57
+wvl_cen = 1.57
+fmin = 1/wvl_max
+fmax = 1/wvl_min
+fcen = 1/wvl_cen
+df = fmax-fmin
+nfreq = 1
+
+dpml = 1.0 #PML thickness
+dsub = 1.5 + wvl_cen #substrate thickness
+dpad = dsub #padding between cell and PML
+
+k_point = mp.Vector3(0,0,0) #used for PBC
+
+n_si = 3.45 #silicon refractive index
+si = mp.Medium(index=n_si)
+n_sio2 = 1.444
+sio2 = mp.Medium(index=n_sio2)
+n_air = 1.0 #air refractive index
+air = mp.Medium(index=n_air)
+
+P = 0.7 #unit cell pitch
+h = 0.9 #pillar height
+
+def unitCell_paramsweep(D):
+    sim_x_size = dpml + dsub + dpad + dpml
+    sim_z_size = P
+    sim_y_size = P
+
+    cell_size = mp.Vector3(sim_x_size, sim_y_size, sim_z_size)
+
+    source_position = mp.Vector3(-wvl_cen,0,0) #source position in the middle of the substrate
+    source = mp.Source(
+        mp.GaussianSource(fcen, fwidth=df),
+        component = mp.Ez,
+        center = source_position,
+        size = mp.Vector3(0, sim_y_size, sim_z_size),
+    )
+
+    pml_layers = [mp.PML(dpml,direction=mp.X)]
+
+    monitor_position = mp.Vector3(h + wvl_cen,0,0)
+    obs_point = monitor_position
+    stop_cond = mp.stop_when_fields_decayed(50, mp.Ez, obs_point, 1e-9)
+    #stop_cond = 10
+    sim = mp.Simulation(
+        resolution = resolution,
+        cell_size = cell_size,
+        boundary_layers = pml_layers,
+        k_point = k_point,
+        default_material = sio2,
+        sources = [source],
+    )
+
+    flux_mon = sim.add_flux(
+        [fcen],
+        mp.FluxRegion(center=monitor_position, size=mp.Vector3(0, sim_y_size, sim_z_size))
+    )
+
+    sim.run(until_after_sources=stop_cond)
+    input_flux = mp.get_fluxes(flux_mon)
+
+    sim.reset_meep()
+
+    pillar_geo = mp.Cylinder(
+        material = si,
+        radius = D/2,
+        height = h,
+        center = mp.Vector3(h/2,0,0),
+        axis=mp.Vector3(1,0,0),
+    )
+
+    substrate_geo = mp.Block(
+        material = sio2,
+        size = mp.Vector3(dsub+dpml, mp.inf, mp.inf),
+        center = mp.Vector3(-(dsub+dpml)/2,0,0),
+    )
+
+    geometries = [substrate_geo, pillar_geo]
+
+    sim = mp.Simulation(
+        resolution = resolution,
+        cell_size = cell_size,
+        boundary_layers = pml_layers,
+        geometry = geometries,
+        k_point = k_point,
+        sources = [source],
+    )
+
+    mode_mon = sim.add_flux(
+        [fcen],
+        mp.FluxRegion(center=monitor_position, size=mp.Vector3(0, sim_y_size, sim_z_size))
+    )
+
+    sim.run(until_after_sources=stop_cond)
+
+    freqs = mp.get_eigenmode_freqs(mode_mon)
+    res = sim.get_eigenmode_coefficients(
+        mode_mon, [1], eig_parity=mp.ODD_Z + mp.EVEN_Y
+    )
+    coeffs = res.alpha
+
+    mode_wvl = [1/freqs[nf] for nf in range(nfreq)]
+    mode_tran = [abs(coeffs[0,nf,0])**2 / input_flux[nf] for nf in range(nfreq)]
+    mode_phase = [np.angle(coeffs[0,nf,0]) for nf in range(nfreq)]
+
+    return mode_wvl, mode_tran, mode_phase
+
+if rank == 0:
+    diameters = np.linspace(0.1, 0.6, 24)
+else:
+    diameters = None
+diameters = comm.bcast(diameters, root=0)
+
+local_diameters = np.array_split(diameters, size)[rank]
+local_indices = np.array_split(np.arange(len(diameters)), size)[rank]
+
+local_mode_tran_arr = np.zeros(len(diameters))
+local_mode_phase_arr = np.zeros(len(diameters))
+
+for local_i, (global_i, D) in enumerate(zip(local_indices, local_diameters)):
+    print(f"Rank {rank} is processing diameter {D:.3f} (index {global_i})")
+    mode_wvl, mode_tran, mode_phase = unitCell_paramsweep(D)
+    local_mode_tran_arr[global_i] = mode_tran[0]
+    local_mode_phase_arr[global_i] = mode_phase[0]
+
+comm.Barrier()
+mode_tran_arr = comm.gather(local_mode_tran_arr, root=0)
+mode_phase_arr = comm.gather(local_mode_phase_arr, root=0)
+final_mode_tran_arr = np.zeros(len(diameters))
+final_mode_phase_arr = np.zeros(len(diameters))
+if rank == 0:
+    for i in range(size):
+        final_mode_tran_arr += mode_tran_arr[i]
+        final_mode_phase_arr += mode_phase_arr[i]
+    
+    
+    np.save("unit_cell_center_wvl_diameters.npy", diameters)
+    np.save("unit_cell_center_wvl_mode_wvl.npy", mode_wvl)
+    np.save("unit_cell_center_wvl_mode_tran.npy", final_mode_tran_arr)
+    np.save("unit_cell_center_wvl_mode_phase.npy", final_mode_phase_arr)
+
+    plt.figure()
+    plt.subplot(1,2,1)
+    plt.plot(diameters,final_mode_tran_arr)
+    plt.xlabel("Pillar Diameter (um)")
+    plt.ylabel("Transmission")
+    plt.subplot(1,2,2)
+    plt.plot(diameters,final_mode_phase_arr)
+    plt.xlabel("Pillar Diameter (um)")
+    plt.ylabel("Phase (rad)")
+    plt.subplots_adjust(wspace=0.5)
+    plt.savefig("unit_cell_fcen.pdf")
+
@@ -0,0 +1,203 @@
+import meep as mp
+mp.verbosity(0)
+
+import numpy as np
+import matplotlib.pyplot as plt
+from mpi4py import MPI
+
+comm = MPI.COMM_WORLD
+rank = comm.Get_rank()
+size = comm.Get_size()
+
+resolution = 50 # pixels/unit length
+
+wvl_min = 1.5
+wvl_max = 1.6
+wvl_cen = 0.5*(wvl_min+wvl_max)
+fmin = 1/wvl_max
+fmax = 1/wvl_min
+fcen = 1/wvl_cen
+df = fmax-fmin
+nfreq = 20
+
+dpml = 1.0 #PML thickness
+dsub = 1.5 + wvl_cen #substrate thickness
+dpad = dsub #padding between cell and PML
+
+k_point = mp.Vector3(0,0,0) #used for PBC
+
+n_si = 3.45 #silicon refractive index
+si = mp.Medium(index=n_si)
+n_sio2 = 1.45
+sio2 = mp.Medium(index=n_sio2)
+n_air = 1.0 #air refractive index
+air = mp.Medium(index=n_air)
+
+P = 0.7 #unit cell pitch
+h = 0.9 #pillar height
+
+def unitCell_paramsweep(D):
+    print("Rank {}: Running simulation for diameter {}".format(rank, D))
+    sim_x_size = dpml + dsub + dpad + dpml
+    sim_z_size = P
+    sim_y_size = P
+
+    cell_size = mp.Vector3(sim_x_size, sim_y_size, sim_z_size)
+
+    source_position = mp.Vector3(-wvl_cen,0,0) #source position in the middle of the substrate
+    source = mp.Source(
+        mp.GaussianSource(fcen, fwidth=df),
+        component = mp.Ez,
+        center = source_position,
+        size = mp.Vector3(0, sim_y_size, sim_z_size),
+    )
+
+    pml_layers = [mp.PML(dpml,direction=mp.X)]
+
+    monitor_position = mp.Vector3(h + wvl_cen,0,0)
+    obs_point = monitor_position
+    stop_cond = mp.stop_when_fields_decayed(50, mp.Ez, obs_point, 1e-9)
+    #stop_cond = 10
+    sim = mp.Simulation(
+        resolution = resolution,
+        cell_size = cell_size,
+        boundary_layers = pml_layers,
+        k_point = k_point,
+        default_material = sio2,
+        sources = [source],
+    )
+
+    flux_mon = sim.add_flux(
+        fcen, 
+        df,
+        nfreq, 
+        mp.FluxRegion(center=monitor_position, size=mp.Vector3(0, sim_y_size, sim_z_size))
+    )
+
+    sim.run(until_after_sources=stop_cond)
+    input_flux = mp.get_fluxes(flux_mon)
+
+    sim.reset_meep()
+
+    pillar_geo = mp.Cylinder(
+        material = si,
+        radius = D/2,
+        height = h,
+        center = mp.Vector3(h/2,0,0),
+        axis=mp.Vector3(1,0,0),
+    )
+
+    substrate_geo = mp.Block(
+        material = sio2,
+        size = mp.Vector3(dsub+dpml, mp.inf, mp.inf),
+        center = mp.Vector3(-(dsub+dpml)/2,0,0),
+    )
+
+    geometries = [substrate_geo, pillar_geo]
+
+    sim = mp.Simulation(
+        resolution = resolution,
+        cell_size = cell_size,
+        boundary_layers = pml_layers,
+        geometry = geometries,
+        k_point = k_point,
+        sources = [source],
+    )
+
+    mode_mon = sim.add_flux(
+        fcen, df, nfreq, mp.FluxRegion(center=monitor_position, size=mp.Vector3(0, sim_y_size, sim_z_size))
+    )
+
+    sim.run(until_after_sources=stop_cond)
+
+    freqs = mp.get_eigenmode_freqs(mode_mon)
+    res = sim.get_eigenmode_coefficients(
+        mode_mon, [1], eig_parity=mp.ODD_Z + mp.EVEN_Y
+    )
+    coeffs = res.alpha
+
+    mode_wvl = [1/freqs[nf] for nf in range(nfreq)]
+    mode_tran = [abs(coeffs[0,nf,0])**2 / input_flux[nf] for nf in range(nfreq)]
+    mode_phase = [np.angle(coeffs[0,nf,0]) for nf in range(nfreq)]
+
+    return mode_wvl, mode_tran, mode_phase
+
+if rank == 0:
+    diameters = np.linspace(0.1, 0.6, 24)
+else:
+    diameters = None
+diameters = comm.bcast(diameters, root=0)
+local_diameters = np.array_split(diameters, size)[rank]
+local_indices = np.array_split(np.arange(len(diameters)), size)[rank]
+
+local_mode_tran_arr = np.zeros((len(diameters), nfreq))
+local_mode_phase_arr = np.zeros((len(diameters), nfreq))
+
+for local_i, (global_i, D) in enumerate(zip(local_indices,local_diameters)):
+    mode_wvl, mode_tran, mode_phase = unitCell_paramsweep(D)
+    local_mode_tran_arr[global_i,:] = mode_tran
+    local_mode_phase_arr[global_i,:] = mode_phase
+
+
+mode_tran_arr = comm.gather(local_mode_tran_arr, root=0)
+mode_phase_arr = comm.gather(local_mode_phase_arr, root=0)
+
+if rank == 0:
+    final_mode_tran_arr = np.zeros((len(diameters), nfreq))
+    final_mode_phase_arr = np.zeros((len(diameters), nfreq))
+    num_diameters_per_rank = len(diameters) // size
+    for i in range(0, size):
+        for j in range(num_diameters_per_rank):
+           global_index = i * num_diameters_per_rank + j
+           final_mode_tran_arr[global_index, :] = mode_tran_arr[i][global_index, :]
+           final_mode_phase_arr[global_index, :] = mode_phase_arr[i][global_index, :]
+
+
+    np.save("unit_cell_param_sweep_diameters.npy", diameters)
+    np.save("unit_cell_param_sweep_mode_wvl.npy", mode_wvl)
+    np.save("unit_cell_param_sweep_mode_tran.npy", final_mode_tran_arr)
+    np.save("unit_cell_param_sweep_mode_phase.npy", final_mode_phase_arr)
+
+    plt.figure()
+    plt.subplot(1,2,1)
+    plt.pcolormesh(
+        mode_wvl,
+        diameters,
+        final_mode_tran_arr,
+        cmap='hot_r',
+        shading='gouraud',
+        vmin=0,
+        vmax=final_mode_tran_arr.max(),
+    )
+
+    plt.axis([wvl_min, wvl_max, diameters[0], diameters[-1]])
+    plt.xlabel("Wavelength (um)")
+    plt.xticks([t for t in np.linspace(wvl_min, wvl_max, 3)])
+    plt.ylabel("Pillar Diameter (um)")
+    plt.title("Transmission")
+    cbar=plt.colorbar()
+    cbar.set_ticks([t for t in np.arange(0, 1.2, 0.2)])
+
+    plt.subplot(1,2,2)
+    plt.pcolormesh(
+        mode_wvl,
+        diameters,
+        final_mode_phase_arr,
+        cmap='RdBu',
+        shading='gouraud',
+        vmin=final_mode_phase_arr.min(),
+        vmax=final_mode_phase_arr.max(),
+    )
+
+    plt.axis([wvl_min, wvl_max, diameters[0], diameters[-1]])
+    plt.xlabel("Wavelength (um)")
+    plt.xticks([t for t in np.linspace(wvl_min, wvl_max, 3)])
+    plt.ylabel("Pillar Diameter (um)")
+    plt.title("phase")
+    cbar=plt.colorbar()
+    cbar.set_ticks([t for t in np.arange(-3, 4, 1)])
+
+
+    plt.subplots_adjust(wspace=0.5)
+    plt.savefig("unit_cell_param_sweep.pdf")
+
@@ -0,0 +1,42 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+#import the parameter sweep arrays for the central wavelength
+diameters = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_diameters.npy")
+print(diameters)
+mode_wvl = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_mode_wvl.npy")
+mode_tran_arr = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_mode_tran.npy")
+print(mode_tran_arr)
+mode_phase_arr = np.load("unit_cell/unit_cell_center_1550_h900nm_res50_wvl_mode_phase.npy")
+print(mode_wvl)
+unwrap_mode_phase_arr = np.abs(np.unwrap(mode_phase_arr - mode_phase_arr[0], period=2*np.pi))
+#import the reference value array
+ref_results = np.loadtxt("unit_cell/results_S21_p700nm_h900nm.txt", skiprows=5,dtype=complex)
+R_ref = np.real(ref_results[:,1])
+S21_ref = ref_results[:,3]
+S21_ref_mag = np.abs(S21_ref)
+S21_ref_phase = np.abs(np.unwrap(np.angle(S21_ref) - np.angle(S21_ref[0]), period=2*np.pi))
+
+
+
+plt.figure()
+plt.subplot(1,2,1)
+plt.plot(1e3*diameters/2,mode_tran_arr, '^r-.', label='FDTD')
+plt.plot(R_ref,S21_ref_mag, '*k--',label='FEM')
+plt.xlabel("Pillar Radius (nm)")
+plt.xticks([t for t in np.linspace(1e3*diameters[0]/2, 1e3*diameters[-1]/2, 5)])
+plt.gca().set_xticklabels([f"{t:.0f}" for t in np.linspace(1e3*diameters[0]/2, 1e3*diameters[-1]/2, 5)])
+plt.ylabel("Transmission")
+plt.legend()
+
+plt.subplot(1,2,2)
+plt.plot(1e3*diameters/2,unwrap_mode_phase_arr, '^r-.', label='FDTD')
+plt.plot(R_ref,S21_ref_phase, '*k--', label='FEM')
+plt.xlabel("Pillar Radius (nm)")
+plt.xticks([t for t in np.linspace(1e3*diameters[0]/2, 1e3*diameters[-1]/2, 5)])
+plt.gca().set_xticklabels([f"{t:.0f}" for t in np.linspace(1e3*diameters[0]/2, 1e3*diameters[-1]/2, 5)])
+plt.ylabel("Phase (rad)")
+plt.legend()
+
+plt.subplots_adjust(wspace=0.5)
+plt.savefig("unit_cell/unit_cell_param_sweep_lineplot.pdf")