def nlo_coeffs(efield, indicator, ccnl):
"""
Returns the nonlinear coupling coeffs after integration
efield is assumed to be nonbloch
"""
(x, y, z) = getscale(mpb)
# (x, dx, y, dy, z, dz) = getscale(mpb, retstep=True)
Nx = np.size(x)
# Ny = np.size(y)
# Nz = np.size(z)
# Symbols : ((+,+), |+|), ((+,+), |-|)
# compute the field quantities
e2 = np.abs(efield.x)**2 + np.abs(efield.y)**2 + np.abs(efield.z)**2
e4 = e2**2
ex4 = np.abs(efield.x)**4
ey4 = np.abs(efield.y)**4
ez4 = np.abs(efield.z)**4
e2complex = efield.x**2 + efield.y**2 + efield.z**2
ex2 = np.abs(efield.x)**2
ey2 = np.abs(efield.y)**2
ez2 = np.abs(efield.z)**2
ex2complex = efield.x**2
ey2complex = efield.y**2
ez2complex = efield.z**2
for cc_type in ccnl.keys():
cc = np.zeros(Nx, dtype=complex)
print('Solving for NL coefficient {0}'.format(cc_type))
if cc_type == (('+', '+'), '|+|'):
integrand = indicator*(e4 + 2*(ex4 + ey4 + ez4))
elif cc_type == (('+', '+'), '|-|'):
integrand = indicator*e4
elif cc_type == (('+', '-'), ('+', '-')):
integrand = indicator*(ex4 + ey4 + ez4)
elif cc_type == (('+', '+'), ('+', '-')):
integrand = indicator*((e2complex + 2*ex2complex)*ex2 + (e2complex + 2*ey2complex)*ey2 + (e2complex + 2*ez2complex)*ez2)
elif cc_type == (('+', '-'), '|-|'):
integrand = indicator*((e2 + 2*ex2)*np.conjugate(ex2complex) + (e2 + 2*ey2)*np.conjugate(ey2complex) + (e2 + 2*ez2)*np.conjugate(ez2complex))
elif cc_type == (('+', '-'), '|+|'):
integrand = indicator*(e2*np.conjugate(ex2complex + ey2complex + ez2complex))
elif cc_type == (('+', '+'), ('-', '+')):
integrand = indicator*(np.conjugate(ex2complex)*ex2 + np.conjugate(ey2complex)*ey2 + np.conjugate(ez2complex)*ez2)
elif cc_type == (('+', '-'), ('-', '+')):
integrand = indicator*(np.conjugate((e2complex + 2*ex2complex)*ex2complex + (e2complex + 2*ey2complex)*ey2complex + (e2complex + 2*ez2complex)*ez2complex))
for i in range(Nx):
cc[i] = spintegrate.simps(spintegrate.simps(integrand[i,:,:], z, axis=1), y, axis=0)
# cc[i] = spintegrate.simps(spintegrate.simps(integrand[i,:,:], dx=dz, axis=1), dx=dy, axis=0)
ccnl[cc_type] = cc # modified in place. [:] is NECESSARY
print('Done!')
def plotfields(mpb, field_type, kindex=None, band=None, comp=None, mpbpostprocess=False,
epsilon_contour_options={}, figsize=None, field_file=None, epsilon_file=None, plot_options={}):
"""
Plots fields
Inputs
------
mpbpostprocess : False (default), assumes no post processing of the fields
has been performed using mpb-data
field_type : 'e', 'epsilon', 'epsilon-ft'
plot_options : specifies extra plot options such as axes limits
"""
if figsize is not None:
plt.figure(figsize=figsize)
else:
plt.figure()
if epsilon_file is None:
epsilon = readfield(mpb, field_type='epsilon_isotropic_trace', mpbpostprocess=mpbpostprocess)
elif isinstance(epsilon_file, str):
epsilon = readfield(mpb, field_type='epsilon_isotropic_trace', mpbpostprocess=mpbpostprocess, field_file=epsilon_file)
if field_type == 'e':
if field_file is None:
E = readfield(mpb, kindex, band, field_type, mpbpostprocess=mpbpostprocess)
elif isinstance(field_file, str):
E = readfield(mpb, kindex, band, field_type, mpbpostprocess=mpbpostprocess, field_file=field_file)
E.create_complex()
if comp is None:
E2 = np.abs(E.x)**2 + np.abs(E.y)**2 + np.abs(E.z)**2
if E2.ndim == 1:
# (x) = getscale(mpb)
# (xgrid, ygrid) = np.meshgrid(x, x)
# creates a E2.ndim x E2.ndim square grid
E2grid = np.tile(E2, (E2.shape[0], 1))
epsilon_grid = np.tile(epsilon.dset, (epsilon.dset.shape[0], 1))
# plt.contourf(xgrid, ygrid, E2grid)
# plt.pcolormesh(E2grid)
plt.imshow(E2grid)
plt.colorbar()
# plt.contour(xgrid, ygrid, epsilon_grid, colors='k', linewidths=lw)
plt.contour(epsilon_grid, colors='w', **epsilon_contour_options)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
plt.xlim(0, E2grid.shape[0]-1)
plt.ylim(0, E2grid.shape[1]-1)
elif E2.ndim == 2:
# (x, y) = getscale(mpb)
# (xgrid, ygrid) = np.meshgrid(x, y)
# plt.contourf(xgrid, ygrid, E2)
# plt.pcolormesh(E2)
plt.imshow(E2)
plt.colorbar()
# plt.contour(xgrid, ygrid, epsilon.dset, colors='k', linewidths=lw)
plt.contour(epsilon.dset, colors='w', **epsilon_contour_options)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
# Determine which grid is on the axis. If Ny > Nx, the yindices
# are placed on the x-axis
if E2.shape[0] >= E2.shape[1]:
plt.xlim(0, E2.shape[0]-1)
plt.ylim(0, E2.shape[1]-1)
else:
plt.xlim(0, E2.shape[1]-1)
plt.ylim(0, E2.shape[0]-1)
elif E2.ndim == 3:
# ASSUME SLAB GEOMETRY
# xy cross section
plt.imshow(E2[:, :, E2.shape[2]/2], aspect='equal')
plt.colorbar()
plt.contour(epsilon.dset[:, :, epsilon.dset.shape[2]/2], colors='w', **epsilon_contour_options)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
# Determine which grid is on the axis. If Ny > Nx, the yindices
# are placed on the x-axis
if E2.shape[0] >= E2.shape[1]:
plt.xlim(0, E2.shape[0]-1)
plt.ylim(0, E2.shape[1]-1)
else:
plt.xlim(0, E2.shape[1]-1)
plt.ylim(0, E2.shape[0]-1)
elif field_type == 'epsilon':
if len(epsilon.dset.shape) == 1:
epsilon_grid = np.tile(epsilon.dset, (epsilon.dset.shape[0], 1))
# epsilon_grid_ft = fftshift(fft2(epsilon_grid))
(x) = getscale(mpb)
(xgrid, ygrid) = np.meshgrid(x, x)
# plt.pcolormesh(xgrid, ygrid, epsilon_grid, cmap='Greys')
plt.imshow(epsilon_grid, cmap='Greys')
plt.colorbar()
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
plt.xlim(0, epsilon_grid.shape[0]-1)
plt.ylim(0, epsilon_grid.shape[1]-1)
# plt.figure()
# plt.imshow(np.abs(epsilon_grid_ft)**2)
# plt.colorbar()
elif len(epsilon.dset.shape) == 2:
# Greys or gray
# plt.pcolor(epsilon.dset, cmap='Greys')
# filter out DC_component
# epsilon_ft[np.unravel_index(np.argmax(epsilon_ft), np.shape(epsilon_ft))] = 0
plt.imshow(epsilon.dset, cmap='Greys')
plt.colorbar()
plt.xlim(0, epsilon.dset.shape[0]-1)
plt.ylim(0, epsilon.dset.shape[1]-1)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
elif len(epsilon.dset.shape) == 3:
# ASSUME PC SLAB GEOMETRY ONLY
# plot in middle of slab
# xy cross section
# plt.imshow(epsilon.dset[:, :, epsilon.dset.shape[2]/2], cmap='Greys', aspect='equal')
# yz cross section
# plt.imshow(epsilon.dset[epsilon.dset.shape[0]/2, :, :], cmap='Greys', aspect='equal')
plt.imshow(epsilon.dset[0, :, :], cmap='Greys', aspect='equal')
plt.colorbar()
# plt.xlim(0, epsilon.dset.shape[0]-1)
# plt.ylim(0, epsilon.dset.shape[1]-1)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
elif field_type == 'epsilon-ft':
if len(epsilon.dset.shape) == 1:
pass
elif len(epsilon.dset.shape) == 2:
# zero pad
epsilon_ft = fftshift(fft2(np.pad(epsilon.dset[:,:], (512, 512), 'constant')))
plt.imshow((np.abs(epsilon_ft)/np.max(np.abs(epsilon_ft)))**2, cmap='Greys', vmin=0, vmax=0.1)
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
elif len(epsilon.dset.shape) == 3:
pass
ax = plt.gca()
ax.set_xticks(())
ax.set_yticks(())
if 'xlims' in plot_options:
xa = plot_options['xlims'][0]
xb = plot_options['xlims'][1]
plt.xlim(xa, xb)
if 'ylims' in plot_options:
ya = plot_options['ylims'][0]
yb = plot_options['ylims'][1]
plt.ylim(ya, yb)
epsilon.close()