def test_NPML(self):
# NPML a number
with self.assertRaises(AssertionError):
Simulation(self.omega, self.eps_r, self.dl, 10, self.pol)
# NPML too many elements
with self.assertRaises(AssertionError):
Simulation(self.omega, self.eps_r, self.dl, [10, 10, 10], self.pol)
def test_1D(self):
Nx = self.eps_r.shape[0]
eps_1d = np.ones((Nx, ))
S = Simulation(self.omega, eps_1d, self.dl, [10, 0], self.pol)
S.src = np.zeros(S.eps_r.shape, dtype=np.complex64)
S.src[Nx // 2, 0] = 1j
(Hx, Hy, Ez) = S.solve_fields()
def test_pol(self):
# polarization not a string
with self.assertRaises(AssertionError):
Simulation(self.omega, self.eps_r, self.dl, self.NPML, 5)
# polarization not the right string
with self.assertRaises(AssertionError):
Simulation(self.omega, self.eps_r, self.dl, self.NPML,
'WrongPolarization')
def solve(self,
epsilons: np.array,
omega=OMEGA_1550,
src_x=None,
clip_buffers=False):
total_length = self.device_length + 2 * self.buffer_length + 2 * self.npml
start = self.npml + self.buffer_length
end = start + self.device_length
permittivities = np.ones(total_length, dtype=np.float64)
# set permittivity and reflection zone
permittivities[:start] = self.buffer_permittivity
permittivities[start:end] = epsilons
permittivities[end:] = self.buffer_permittivity
if src_x is None:
src_x = int(self.device_length / 2)
sim = Simulation(omega,
permittivities,
self.dl, [self.npml, 0],
self.mode,
L0=self.L0,
use_dirichlet_bcs=self.use_dirichlet_bcs)
sim.src[src_x + self.npml + self.buffer_length] = 1j
if clip_buffers:
clip0 = self.npml + self.buffer_length
clip1 = -(self.npml + self.buffer_length)
else:
clip0 = None
clip1 = None
if self.mode == "Ez":
Hx, Hy, Ez = sim.solve_fields()
permittivities = permittivities[clip0:clip1]
Hx = Hx[clip0:clip1]
Hy = Hy[clip0:clip1]
Ez = Ez[clip0:clip1]
return permittivities, src_x, Hx, Hy, Ez
elif self.mode == "Hz":
Ex, Ey, Hz = sim.solve_fields()
permittivities = permittivities[clip0:clip1]
Ex = Ex[clip0:clip1]
Ey = Ey[clip0:clip1]
Hz = Hz[clip0:clip1]
return permittivities, src_x, Ex, Ey, Hz
else:
raise ValueError("Polarization must be Ez or Hz!")
def get_operators(self, omega=OMEGA_1550):
total_length = self.device_length + 2 * self.buffer_length + 2 * self.npml
perms = np.ones((total_length, total_length), dtype=np.float64)
start = self.npml + self.buffer_length
end = start + self.device_length
# set permittivity and reflection zone
perms[:, :start] = self.buffer_permittivity
perms[:start, :] = self.buffer_permittivity
perms[:, end:] = self.buffer_permittivity
perms[end:, :] = self.buffer_permittivity
sim = Simulation(omega,
perms,
self.dl, [self.npml, self.npml],
self.mode,
L0=self.L0,
use_dirichlet_bcs=self.use_dirichlet_bcs)
Dyb, Dxb, Dxf, Dyf = unpack_derivs(sim.derivs)
N = np.asarray(perms.shape)
M = np.prod(N)
vector_eps_z = EPSILON0 * self.L0 * perms.reshape((-1, ))
T_eps_z = sp.spdiags(vector_eps_z, 0, M, M, format='csr')
curl_curl = (Dxf @ Dxb + Dyf @ Dyb)
other = omega**2 * MU0 * self.L0 * T_eps_z
return curl_curl.todense(), other.todense()
def test_freq(self):
# negative frequency
with self.assertRaises(AssertionError):
Simulation(-self.omega, self.eps_r, self.dl, self.NPML, self.pol)
# geometric parameters for a 1 -> 2 port device L = 6 # length of box (L0) H = 4 # height of box (L0) w = .3 # width of waveguides (L0) d = H/1.5 # distance between waveguides (L0) l = 4 # length of waveguide from PML to box (L0) spc = 2 # space between box and PML (L0) # define permittivity of three port system eps_r, design_region = three_port(L, H, w, d, l, spc, dl, NPML, eps_m) (Nx, Ny) = eps_r.shape nx, ny = int(Nx/2), int(Ny/2) # halfway grid points # make a new simulation object simulation = Simulation(omega, eps_r, dl, NPML, pol) # set the input waveguide modal source simulation.add_mode(neff=np.sqrt(eps_m), direction_normal='x', center=[NPML[0]+int(l/2/dl), ny], width=int(H/2/dl), scale=source_amp) simulation.setup_modes() # make a new simulation to get the modal profile of the top output port top = Simulation(omega, eps_r, dl, NPML, 'Ez') top.add_mode(neff=np.sqrt(eps_m), direction_normal='x', center=[-NPML[0]-int(l/2/dl), ny+int(d/2/dl)], width=int(H/2/dl)) top.setup_modes() J_top = np.abs(top.src) # make a new simulation to get the modal profile of the bottom output port bot = Simulation(omega, eps_r, dl, NPML, 'Ez') bot.add_mode(neff=np.sqrt(eps_m), direction_normal='x', center=[-NPML[0]-int(l/2/dl), ny-int(d/2/dl)], width=int(H/2/dl)) bot.setup_modes()
def test_born_newton(self):
"""Tests whether born and newton methods get the same result"""
n0 = 3.4
omega = 2 * np.pi * 200e12
dl = 0.01
chi3 = 2.8E-18
width = 1
L = 5
L_chi3 = 4
width_voxels = int(width / dl)
L_chi3_voxels = int(L_chi3 / dl)
Nx = int(L / dl)
Ny = int(3.5 * width / dl)
eps_r = np.ones((Nx, Ny))
eps_r[:,
int(Ny / 2 -
width_voxels / 2):int(Ny / 2 +
width_voxels / 2)] = np.square(n0)
nl_region = np.zeros(eps_r.shape)
nl_region[int(Nx / 2 - L_chi3_voxels / 2):int(Nx / 2 +
L_chi3_voxels / 2),
int(Ny / 2 - width_voxels / 2):int(Ny / 2 +
width_voxels / 2)] = 1
simulation = Simulation(omega, eps_r, dl, [15, 15], 'Ez')
simulation.add_mode(n0, 'x', [17, int(Ny / 2)], width_voxels * 3)
simulation.setup_modes()
simulation.add_nl(chi3,
nl_region,
eps_scale=True,
eps_max=np.max(eps_r))
srcval_vec = np.logspace(1, 3, 3)
pwr_vec = np.array([])
T_vec = np.array([])
for srcval in srcval_vec:
simulation.setup_modes()
simulation.src *= srcval
# Newton
simulation.solve_fields_nl(solver_nl='newton')
E_newton = simulation.fields["Ez"]
# Born
simulation.solve_fields_nl(solver_nl='born')
E_born = simulation.fields["Ez"]
# More solvers (if any) should be added here with corresponding calls to assert_allclose() below
assert_allclose(E_newton, E_born, rtol=1e-3)
# geometric parameters L1 = 6 # length waveguides in design region (L0) L2 = 6 # width of box (L0) H1 = 6 # height waveguides in design region (L0) H2 = 6 # height of box (L0) w = .3 # width of waveguides (L0) l = 3 # length of waveguide from PML to box (L0) spc = 2 # space between box and PML (L0) # define permittivity of three port system eps_r, design_region = ortho_port(L1, L2, H1, H2, w, l, dl, NPML, eps_m) (Nx, Ny) = eps_r.shape nx, ny = int(Nx/2), int(Ny/2) # halfway grid points simulation = Simulation(omega,eps_r,dl,NPML,pol) # set the modal source and probes simulation = Simulation(omega, eps_r, dl, NPML, 'Ez') simulation.add_mode(np.sqrt(eps_m), 'x', [NPML[0]+int(l/2/dl), ny], int(H1/2/dl), scale=source_amp) simulation.setup_modes() # left modal profile right = Simulation(omega, eps_r, dl, NPML, 'Ez') right.add_mode(np.sqrt(eps_m), 'x', [-NPML[0]-int(l/2/dl), ny], int(H1/2/dl)) right.setup_modes() J_right = np.abs(right.src) # top modal profile top = Simulation(omega, eps_r, dl, NPML, 'Ez') top.add_mode(np.sqrt(eps_m), 'y', [nx, -NPML[1]-int(l/2/dl)], int(L1/2/dl))
if plot_all:
print('-> solving FDFD for continuous epsilon')
F = fdfd(omega0, dl, eps_total, NPML)
Hx, Hy, Ez = F.solve(source)
plt.imshow(np.abs(imarr(Ez)), cmap='magma')
plt.title('|Ez| for continuous permitivity')
plt.xlabel('x')
plt.ylabel('y')
plt.colorbar()
plt.show()
""" DEFINE MODAL SOURCE / PROBE """
print('-> setting up modal source')
# make an angler simulation with the starting permittivity, to compute the modal source
sim = Simulation(omega0, eps_base, dl, [npml, npml], pol='Ez', L0=1)
center_y = npml + int((spc + subs + h1 / 2) / dl)
sim.add_mode(neff_hole,
'x',
center=[npml + int(spc / dl), center_y],
width=int(5 * h1 / dl),
scale=1,
order=1)
sim.setup_modes()
# get the wg mode profile as an array
wg_mode = np.flipud(np.abs(sim.src.copy())).reshape((Nx, Ny, 1))
# compute the power in the waveguide mode for normalization
wg_mode_p = np.sum(np.square(np.abs(wg_mode)))
def setUp(self):
# create a simulation to test just like in notebook
lambda0 = 2e-6 # free space wavelength (m)
c0 = 3e8 # speed of light in vacuum (m/s)
omega = 2 * np.pi * c0 / lambda0 # angular frequency (2pi/s)
dl = 1.1e-1 # grid size (L0)
NPML = [15, 15] # number of pml grid points on x and y borders
pol = 'Ez' # polarization (either 'Hz' or 'Ez')
source_amp = 100 # amplitude of modal source (A/L0^2?)
# material constants
n_index = 2.44 # refractive index
eps_m = n_index**2 # relative permittivity
max_ind_shift = 5.8e-2 # maximum allowed nonlinear index shift
# geometric parameters
L = 4 # length of box (L0)
H = 4 # height of box (L0)
w = .2 # width of waveguides (L0)
d = H / 2.44 # distance between waveguides (L0)
l = 3 # length of waveguide from PML to box (L0)
spc = 2 # space between box and PML (L0)
# define permittivity of three port system
(eps_r, design_region) = three_port(L,
H,
w,
d,
dl,
l,
spc,
NPML,
eps_start=eps_m)
(Nx, Ny) = eps_r.shape
nx, ny = int(Nx / 2), int(Ny / 2) # halfway grid points
# set the modal source and probes
self.simulation = Simulation(omega, eps_r, dl, NPML, 'Ez')
self.simulation.add_mode(np.sqrt(eps_m),
'x', [NPML[0] + int(l / 2 / dl), ny],
int(H / 2 / dl),
scale=source_amp)
self.simulation.setup_modes()
self.simulation.init_design_region(design_region, eps_m)
# top modal profile
top = Simulation(omega, eps_r, dl, NPML, 'Ez')
top.add_mode(np.sqrt(eps_m), 'x',
[-NPML[0] - int(l / 2 / dl), ny + int(d / 2 / dl)],
int(H / 2 / dl))
top.setup_modes()
J_top = np.abs(top.src)
# bottom modal profile
bot = Simulation(omega, eps_r, dl, NPML, 'Ez')
bot.add_mode(np.sqrt(eps_m), 'x',
[-NPML[0] - int(l / 2 / dl), ny - int(d / 2 / dl)],
int(d / dl))
bot.setup_modes()
J_bot = np.abs(bot.src)
# define linear and nonlinear parts of objective function + the total objective function form
J = lambda e, e_nl: npa.sum(npa.square(npa.abs(e)) * J_top) + npa.sum(
npa.square(npa.abs(e_nl)) * J_bot)
import autograd.numpy as npa
def J(e, e_nl):
linear_top = 1 * npa.sum(npa.square(npa.abs(e)) * J_top)
linear_bot = -1 * npa.sum(npa.square(npa.abs(e)) * J_bot)
nonlinear_top = -1 * npa.sum(npa.square(npa.abs(e_nl)) * J_top)
nonlinear_bot = 1 * npa.sum(npa.square(npa.abs(e_nl)) * J_bot)
objfn = linear_top + nonlinear_top + nonlinear_bot + linear_top
return objfn
self.design_region = design_region
self.optimization = Optimization(J=J,
simulation=self.simulation,
design_region=self.design_region,
eps_m=eps_m)