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Fig4_time_evolution.py
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import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec
from matplotlib import animation
import pandas as pd
import math
from multiprocessing import Pool
import TMM
matplotlib.rcParams.update({'font.size': 7})
matplotlib.rcParams.update({'axes.linewidth': 0.5})
matplotlib.rcParams.update({'ytick.direction': 'in'})
matplotlib.rcParams.update({'xtick.direction': 'in'})
matplotlib.rcParams.update({'ytick.major.width': 0.5})
matplotlib.rcParams.update({'xtick.major.width': 0.5})
matplotlib.rcParams.update({'ytick.minor.width': 0.5})
matplotlib.rcParams.update({'xtick.minor.width': 0.5})
matplotlib.rcParams.update({'figure.figsize': [3.375 *2, 2.5 * 1.8]})
matplotlib.rcParams.update({'savefig.pad_inches': 0.02}) #default 0.1
matplotlib.rcParams.update({'savefig.format': 'png'}) #default 0.1
matplotlib.rcParams.update({'figure.subplot.bottom': 0.05,
'figure.subplot.hspace': 0,
'figure.subplot.left': 0.05,
'figure.subplot.right': 0.95,
'figure.subplot.top': 0.95,
'figure.subplot.wspace': 0}) #default 0.125, 0.2, 0.125, 0.9, 0.88, 0.2
#%% Initial wave
dt = 0.01
Xp = 200
ct = np.arange(-Xp/2, Xp/2-dt/10, dt)
Nx = len(ct)
dk = 2*np.pi/Xp
k = (np.arange(Nx)-Nx/2)*dk
k0 = 2*np.pi/1
sigma_x = 1
D_init = np.exp(-0.5* (ct/sigma_x)**2) # Gaussian pulse for the initial displacement field
D_init_F = np.fft.fftshift( np.fft.fft(np.fft.ifftshift(D_init))*dt )
fig, ax = plt.subplots(2,1, figsize=(3.3,2))
ax[0].plot(ct, np.real(D_init), lw=0.75)
ax[0].set(xlim=(-Xp/2,Xp/2), xlabel=r'$ct/a$', ylabel=r'$D(x, t=0)$')
ax[1].plot(k/k0, D_init_F, lw=0.75)
ax[1].set(xlim=(-2,2), xlabel=r'$k/k_0$', ylabel=r'$\tilde{D}(k_x, t=0)$')
fig.tight_layout()
#%% Structure factor
a = 1
Tp = 100
tau = np.arange(-(Tp)*a, (Tp)*a+dt/10, dt)
delta = 0.0001
omega = np.linspace(-1.2*k0, 1.2*k0, 2401)
domega = omega[1]-omega[0]
omega1 = 0.5*k0 # Minimum "material" frequency for filtering
omega2 = 1*k0 # Maximum "material" frequency for filtering
omega_center = (omega1 + omega2)/2
sigma = 2/np.abs(omega2-omega1)
rect = lambda x: (np.abs(x)<0.5) + (np.abs(x)==0.5)*0.5
S = rect( (np.abs(omega)-0.75*k0)/(0.5*k0)) * delta**2 * np.pi * k0/(omega+k0*1e-10)**2 # Designed structure factor for filtering
R = np.sum([s*np.exp(-1j*om*tau)*domega/(2*np.pi) for s, om in zip(S, omega)], axis=0)
fig, ax = plt.subplots(2,1, figsize=(3.3,2))
ax[0].plot(omega/k0, S/delta**2)
ax[0].set(xlim=(-2.5,2.5))
ax[1].plot(tau, R/delta**2)
ax[1].set(xlim=(-5,5))
fig.tight_layout()
#%% realization generation
t = np.arange(0*a, (Tp-dt/10)*a, dt)
tau0_idx = np.argmin(np.abs(tau))
def row(R, i):
return np.array(R[tau0_idx+(0-i):tau0_idx+(len(t)-i)] )
with Pool(30) as pool:
cov_alpha = np.array(pool.starmap(row, zip([R]*len(t), range(len(t)))))
np.random.seed(2)
dalpha = np.random.multivariate_normal(np.zeros_like(np.hstack([t])), cov_alpha)
smooth = 1/(1 + np.exp(-(t-Tp*0.1)/(0.25*a))) + 1/(1 + np.exp((t-Tp*0.9)/(0.25*a))) - 1
alpha = 1+ smooth* dalpha
fig, ax = plt.subplots(3,1, figsize=(3.3,3))
ax[0].plot(omega/k0, S/delta**2, lw=0.75)
ax[0].set(xlabel=r'$\omega/ck_0$', xlim=(-1,4), ylabel=r'$S(\omega)/\delta^2$')
ax[1].plot(tau, np.real(R)/delta**2, lw=0.75)
ax[1].plot(tau, np.imag(R)/delta**2, lw=0.75)
ax[1].set(xlabel=r'$\tau/t_0$', xlim=(-4,4), ylabel=r'$S(\tau)/\delta^2$')
ax[2].plot(t, (np.real(alpha)-1)/delta, lw=0.75)
ax[2].plot(t, np.imag(alpha)/delta, lw=0.75)
ax[2].set(xlabel=r'$t/t_0$', xlim=(0, 100), ylabel=r'$\Delta\alpha(t)/\delta$')
fig.tight_layout()
#%% Time evolution
t_ext = dt*np.arange(len(t)*2)
alpha_ext = np.hstack([alpha, np.ones_like(alpha)])
sys = TMM.time_dep(dt*np.ones_like(t_ext), 1/alpha_ext, np.ones_like(t_ext), 1, 1)
sys_inc = TMM.time_dep(dt*np.ones_like(t_ext), np.ones_like(t_ext), np.ones_like(t_ext), 1, 1)
def evol_function(k, D):
if k>=0:
return D*sys.evolution(k, 'f')[0]
else:
return D*sys.evolution(k, 'b')[0]
def evol_function_inc(k, D):
if k>=0:
return D*sys_inc.evolution(k, 'f')[0]
else:
return D*sys_inc.evolution(k, 'b')[0]
with Pool(30) as pool:
D_evol = pool.starmap(evol_function, zip(k, D_init_F))
D_evol_inc = pool.starmap(evol_function_inc, zip(k, D_init_F))
D_evol = np.column_stack(D_evol) # Time-evoluted total field in k-space
D_evol_inc = np.column_stack(D_evol_inc) # Time-evoluted incident field in k-space
D_evol_sca = D_evol - D_evol_inc # Time-evoluted scattering field in k-space
D = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(D_evol, axes=1), axis=1)/dt,axes=1)
D_inc = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(D_evol_inc, axes=1), axis=1)/dt,axes=1)
D_sca = D - D_inc # Time-evoluted scattering field in real space
P_sca = np.abs(D_sca)**2
psi_sca_z0 = D_sca[:-1,10000]
psi_sca_z0_F = np.sum([psi0*np.exp(1j*omega*t0)*dt for psi0, t0 in zip(psi_sca_z0, t_ext)], axis=0) # Time-evoluted scattering field in omega-axis
#%% Fig 4
cmap1 = matplotlib.cm.get_cmap('inferno')
newcolors = cmap1(np.linspace(0,0.85,256))
cmap = matplotlib.colors.ListedColormap(newcolors)
fig = plt.figure(figsize=(7.08, 2.7))
gs = GridSpec(nrows=105, ncols=200)
ax = np.array([[fig.add_subplot(gs[5:15,57:95]), fig.add_subplot(gs[5:15,110:148]), fig.add_subplot(gs[5:25,2:33]), fig.add_subplot(gs[5:42,168:198])],
[fig.add_subplot(gs[15:25,57:95]), fig.add_subplot(gs[15:25,110:148]), fig.add_subplot(gs[40:60,2:33]), fig.add_subplot(gs[58:95,168:198])],
[fig.add_subplot(gs[25:35,57:95]), fig.add_subplot(gs[25:35,110:148]), fig.add_subplot(gs[75:95,2:33]), np.nan],
[fig.add_subplot(gs[35:45,57:95]), fig.add_subplot(gs[35:45,110:148]), np.nan, np.nan],
[fig.add_subplot(gs[45:55,57:95]), fig.add_subplot(gs[45:55,110:148]), np.nan, np.nan],
[fig.add_subplot(gs[55:65,57:95]), fig.add_subplot(gs[55:65,110:148]), np.nan, np.nan],
[fig.add_subplot(gs[65:75,57:95]), fig.add_subplot(gs[65:75,110:148]), np.nan, np.nan],
[fig.add_subplot(gs[75:85,57:95]), fig.add_subplot(gs[75:85,110:148]), np.nan, np.nan],
[fig.add_subplot(gs[85:95,57:95]), fig.add_subplot(gs[85:95,110:148]), np.nan, np.nan],])
# Fig 4d & 4e
SrcData_4de = [ct-ct[0]]
ax[0,0].set_title(r'Total field', fontsize=7)
ax[0,1].set_title(r'Scattering power', fontsize=7)
for i, ti in enumerate(1250*np.arange(9)):
c = cmap(0.999*ti/len(t))
ax[i,0].plot(ct-ct[0], np.abs(np.fft.fftshift(np.real(D[ti]))), lw=0.75, color=c)
ax[i,0].set_yscale('log')
ax[i,0].set(xlim=(0, Tp), ylim=(1e-6,np.max(np.abs(D))), yticks=[1e-5, 1e-2])
ax[i,1].plot(ct-ct[0], np.fft.ifftshift(P_sca[ti])/delta**2, lw=0.75, color=c)
SrcData_4de.append(np.abs(np.fft.fftshift(np.real(D[ti]))))
SrcData_4de.append(np.fft.ifftshift(P_sca[ti])/delta**2)
if i==8:
ax[i,1].set(xlim=(0, Tp), ylim=(0,np.max(P_sca)/delta**2), yticks=(0,0.2))
else:
ax[i,1].set(xlim=(0, Tp), ylim=(0,np.max(P_sca)/delta**2), yticks=(0,0.2))
if i<8:
ax[i,0].set(xticklabels=[])
ax[i,1].set(xticklabels=[])
else:
ax[i,0].set(xlabel=r'$z/ct_0$')
ax[i,1].set(xlabel=r'$z/ct_0$')
ax[4,0].set(ylabel=r'$|D_\mathrm{tot}(z)|$')
ax[4,1].set(ylabel=r'$|D_\mathrm{sca}(z)|^2$')
# Fig 4a, 4b & 4c
ax[0,2].set_title(r'Design', fontsize=7)
ax[0,2].plot(omega/k0, S*k0/delta**2, 'k', lw=0.75)
ax[0,2].set(xlim=(-1.2, 1.2), xlabel=r'$\omega /\omega_0$',
ylim=(0,12), ylabel=r'$S(\omega)$')
axt2 = ax[0,2].twinx()
axt2.fill_between(omega/k0, S>0, 0, color='midnightblue', alpha=0.2, edgecolor=None)
axt2.set(xlim=(-1.2, 1.2), ylim=(0,1), yticks=[])
ax[1,2].plot(tau, R/delta**2, 'k', lw=0.75)
ax[1,2].set(xlim=(-10, 10), xlabel=r'$\Delta t / t_0$',
ylim=(np.min(np.real(R/delta**2)),1.05), ylabel=r'$C(\Delta t) $',
yticks=[0,1], yticklabels=[0, ' $\delta^2$'])
ax[2,2].fill_between(t, np.real(1/alpha-1)/delta, -2.5, color='grey', alpha=0.5, edgecolor='k', lw=0.5)
ax[2,2].set(xlim=(5,30), ylim=(-2.5,2.5), yticks=(-2,0,2),
xlabel=r'$t/t_0$', ylabel=r'$\Delta\epsilon(t)/\delta$')
# Fig 4f
axins = ax[0,3].inset_axes([0.4,0.15,0.55,0.8])
axins.set_facecolor('white')
axt = ax[0,3].twinx()
axinst = axins.twinx()
scale_factor = np.exp(-(sigma_x*0.25*k0)**2/2)
SrcData_4f = [k/k0]
for ii, t_snapshot in enumerate(np.arange(9)*12.5):
c = cmap(0.999*t_snapshot/Tp)
ax[0,3].plot(k/k0, np.abs(D_evol_sca[int(t_snapshot/dt)])*k0/delta, lw=0.75, color=c)
axins.plot(k/k0, np.abs(D_evol_sca[int(t_snapshot/dt)])*k0/delta, lw=0.75, color=c)
SrcData_4f.append(np.abs(D_evol_sca[int(t_snapshot/dt)])*k0/delta)
ratio_conv = np.max(D_init_F*k0/delta)/(np.max(np.abs(D_evol_sca)*k0/delta)/scale_factor)
ax[0,3].plot(k/k0, np.abs(D_init_F)*k0/delta/ratio_conv, 'dodgerblue', ls='--', lw=0.75)
axinst.plot(k/k0, np.abs(D_init_F)*k0/delta, 'dodgerblue', ls='--', lw=0.75)
SrcData_4f.append(np.abs(D_init_F)*k0/delta)
axt.set_title('Scattering field', fontsize=7)
ax[0,3].set(xlim=(-0.6,0.6), xlabel=r'$kc/\omega_0$',
ylim=(0,np.max(np.abs(D_evol_sca)*k0/delta)/scale_factor), ylabel=r'$|D_\mathrm{sca}(k)|$')
axt.set(xlim=(-0.6,0.6),
ylim=(0,np.max(D_init_F*k0)))
axt.set_ylabel(r'$D_\mathrm{inc}(k)$ ($\times 10^4$)', color='dodgerblue')
axt.tick_params('y', colors='dodgerblue')
axt.spines["right"].set_edgecolor('dodgerblue')
axins.set(xlim=(-0.55,-0.2), xticks=[],
ylim=(0,np.max(np.abs(D_evol_sca)*k0/delta)), yticks=[])
axinst.set(xlim=(-0.55,-0.2), xticks=[],
ylim=(0,np.max(D_init_F*k0/delta)*scale_factor), yticks=[])
ax[0,3].indicate_inset_zoom(axins, edgecolor='k', lw=0.75)
# Fig 4g
ax[1,3].plot(omega/k0, np.abs(psi_sca_z0_F)*k0/delta, color='navy', lw=0.75)
axt = ax[1,3].twinx()
S2omega = rect( (np.abs(omega)-0.375*k0)/(0.25*k0) )
axt.fill_between(omega/k0, S2omega, 0, color='midnightblue', alpha=0.2, edgecolor=None)
ax[1,3].set(xlabel=r'$\omega / \omega_0 $', xlim=(0,0.6), ylim=(0,np.max(np.abs(psi_sca_z0_F)*k0/delta)),
ylabel=r'$|D_\mathrm{sca}(\omega)|$')
axt.set(xlim=(0,0.6), ylim=(0,1), yticks=[])
fig.tight_layout()
fig.savefig('fig4.pdf', dpi=1200, format='pdf')
fig_cb, cax = plt.subplots(figsize=(7.08, 2.7))
norm = matplotlib.colors.Normalize(vmin=0,vmax=100)
cb = plt.colorbar(matplotlib.cm.ScalarMappable(cmap=cmap, norm=norm), ax=cax,
orientation='horizontal', shrink=0.06)
cb.set_ticks([0,50,100])
cb.ax.tick_params(labelsize=6)
cb.ax.set_title(r'$t/t_0$', fontsize=6)
fig_cb.savefig('fig4_colorbar.pdf', dpi=1200, format='pdf')
#%% Source Data
SrcData_4a = np.column_stack([omega/k0, S*k0/delta**2])
Column_names = ["omega/omega_0", "S/delta^2"]
SrcData_4a = pd.DataFrame(SrcData_4a, columns=Column_names)
SrcData_4b = np.column_stack([tau, R/delta**2])
Column_names = ["Delta t/t_0", "C/delta^2"]
SrcData_4b = pd.DataFrame(np.real(SrcData_4b), columns=Column_names)
SrcData_4c = np.column_stack([t, np.real(1/alpha-1)/delta])
Column_names = ["t/t0", "DeltaEpsilon/delta"]
SrcData_4c = pd.DataFrame(SrcData_4c, columns=Column_names)
SrcData_4de = np.column_stack(SrcData_4de)
Column_names = ['z/ct0',
'|D_tot|, t=0', '|D_sca|^2, t=0',
'|D_tot|, t=12.5', '|D_sca|^2, t=12.5',
'|D_tot|, t=25', '|D_sca|^2, t=25',
'|D_tot|, t=37.5', '|D_sca|^2, t=37.5',
'|D_tot|, t=50', '|D_sca|^2, t=50',
'|D_tot|, t=62.5', '|D_sca|^2, t=62.5',
'|D_tot|, t=75', '|D_sca|^2, t=75',
'|D_tot|, t=87.5', '|D_sca|^2, t=87.5',
'|D_tot|, t=100', '|D_sca|^2, t=100']
SrcData_4de = pd.DataFrame(SrcData_4de, columns=Column_names)
SrcData_4f = np.column_stack(SrcData_4f)
Column_names = ['k/k0'] + ['|D_sca|, t='+str(12.5*i) for i in range(9)] + ['D_inc']
SrcData_4f = pd.DataFrame(SrcData_4f, columns=Column_names)
SrcData_4g = np.column_stack([omega/k0, np.abs(psi_sca_z0_F)*k0/delta])
Column_names = ['omega/k0', '|D_sca(z=0)|']
SrcData_4g = pd.DataFrame(SrcData_4g, columns=Column_names)
with pd.ExcelWriter("SourceData_Fig4.xlsx") as writer:
SrcData_4a.to_excel(writer, index=False, sheet_name="Fig. 4a")
SrcData_4b.to_excel(writer, index=False, sheet_name="Fig. 4b")
SrcData_4c.to_excel(writer, index=False, sheet_name="Fig. 4c")
SrcData_4de.to_excel(writer, index=False, sheet_name="Fig. 4de")
SrcData_4f.to_excel(writer, index=False, sheet_name="Fig. 4f")
SrcData_4g.to_excel(writer, index=False, sheet_name="Fig. 4g")
#%% Supp Movie: Animation
fig = plt.figure(figsize=(5, 2.5))
gs = GridSpec(nrows=100, ncols=100)
ax = np.array([fig.add_subplot(gs[10:20, 10:52]),
fig.add_subplot(gs[20:47, 10:52]),
fig.add_subplot(gs[53:63, 10:52]),
fig.add_subplot(gs[63:90, 10:52]),
fig.add_subplot(gs[10:90,68:95]),])
axt = ax[4].twinx()
ax[0].set(xlim=(0,Tp), xticks=[], yticks=[])
ax[1].set(xlim=(0,Tp), xticklabels=[],
ylim=(1e-6,np.max(np.abs(D))), ylabel=r'$|D_\mathrm{tot}(z,t)|$')
ax[1].set_yscale('log')
ax[2].set(xlim=(0,Tp), xticks=[], yticks=[])
ax[3].set(xlim=(0,Tp), xlabel=r'$z/ct_0$',
ylim=(0,np.max(P_sca)/delta**2), ylabel=r'$|D_\mathrm{sca}(z,t)|^2$')
ax[4].set(xlim=(-0.6, 0.6), xlabel=r'$k/c\omega_0$',
ylim=(0, 1.5*np.max(np.abs(D_evol_sca)/delta)), ylabel=r'$|D_\mathrm{sca}(k,t)|$',)
axt.set(xlim=(-0.6,0.6), ylim=(0,np.max(np.abs(D_init_F)*k0)))
axt.set_ylabel(r'$D_\mathrm{inc}(k) $', color='dodgerblue')
axt.tick_params('y', colors='dodgerblue')
axt.spines["right"].set_edgecolor('dodgerblue')
scale_factor = np.exp(-(sigma_x*0.25*k0)**2/2)
scale_factor2 = np.max(np.abs(D_evol_sca)/(delta))/scale_factor /np.max(np.abs(D_init_F))
ax[4].plot(k/k0, np.abs(D_init_F)*k0*scale_factor2, 'dodgerblue', ls='--', lw=0.75)
ax[4].set(xlim=(-0.6,0.6), xlabel=r'$kc/\omega_0$',
ylim=(0,np.max(np.abs(D_evol_sca)*k0/delta)/scale_factor), ylabel=r'$|D_\mathrm{sca}(k)|$')
line0, = ax[1].plot([], [], lw=0.5)
line1, = ax[3].plot([], [], lw=0.5)
line2, = ax[4].plot([], [], lw=1)
Z, X = np.meshgrid(ct[::10], np.linspace(0,1,2))
pcm0 = ax[0].pcolormesh(Z, X, Z*0, cmap=plt.cm.RdBu_r, vmin=-1, vmax=1)
pcm1 = ax[2].pcolormesh(Z, X, Z*0, cmap=plt.cm.RdBu_r, vmin=-0.62, vmax=0.62)
title = ax[4].text(-0.2, 3.2, "")
def init():
line0.set_data([], [])
line1.set_data([], [])
line2.set_data([], [])
return (line0, line1, line2,)
def animate(i):
c = cmap(0.999*i/len(t))
line0.set_data(ct, np.abs(D[i]))
line1.set_data(ct, P_sca[i]/delta**2)
line2.set_data(k/k0, np.abs(D_evol_sca[i])*k0/delta)
line0.set_color(c)
line1.set_color(c)
line2.set_color(c)
title.set_text(r'$t/t_0 ='+str(math.floor(t[i]))+'$')
pcm0.set_array( np.array([np.real(D[i, ::10])]*2) )
pcm1.set_array( np.array([np.real(D_sca[i, ::10]/delta)]*2) )
return (line0, line1, line2,)
anim = animation.FuncAnimation(fig, animate, init_func=init, frames=range(0,len(t),15), interval=1, blit=True)
anim.save('Supp_Movie.gif', fps=40, dpi=300)