def make_objective_fdfd(eps: goos.Shape, stage: str, sim_3d: bool):
dx = 20
if sim_3d:
sim_z_extent = 2500
src_z_extent = 1000
pml_thickness = [10 * dx] * 6
timing_comp = 1
solver = "maxwell_cg"
else:
sim_z_extent = 0
src_z_extent = 20
pml_thickness = [10 * dx] * 4 + [0] * 2
timing_comp = 2
solver = "local_direct"
sim = maxwell.fdfd_simulation(
name="sim_{}".format(stage),
wavelength=1550,
eps=eps,
solver=solver,
sources=[
maxwell.WaveguideModeSource(center=[-1400, 0, 0],
extents=[0, 2500, src_z_extent],
normal=[1, 0, 0],
mode_num=0,
power=1),
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=dx),
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, sim_z_extent],
),
pml_thickness=pml_thickness),
background=goos.material.Material(index=1.0),
outputs=[
maxwell.Epsilon(name="eps"),
maxwell.ElectricField(name="field"),
maxwell.WaveguideModeOverlap(name="overlap",
center=[0, 1400, 0],
extents=[2500, 0, src_z_extent],
normal=[0, 1, 0],
mode_num=0,
power=1),
],
)
obj = goos.rename(-goos.abs(sim["overlap"]), name="obj_{}".format(stage))
return obj, sim
def make_objective(eps: goos.Shape, stage: str, sim_3d: bool):
if sim_3d:
sim_z_extent = 2500
solver_info = maxwell.MaxwellSolver(solver="maxwell_cg",
err_thresh=1e-2)
pml_thickness = [400] * 6
else:
sim_z_extent = 40
solver_info = maxwell.DirectSolver()
pml_thickness = [400, 400, 400, 400, 0, 0]
sim = maxwell.fdfd_simulation(
name="sim_{}".format(stage),
wavelength=1550,
eps=eps,
solver_info=solver_info,
sources=[
maxwell.WaveguideModeSource(center=[-1400, 0, 0],
extents=[0, 2500, 1000],
normal=[1, 0, 0],
mode_num=0,
power=1)
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=40),
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, sim_z_extent],
),
pml_thickness=pml_thickness),
background=goos.material.Material(index=1.0),
outputs=[
maxwell.Epsilon(name="eps"),
maxwell.ElectricField(name="field"),
maxwell.WaveguideModeOverlap(name="overlap",
center=[0, 1400, 0],
extents=[2500, 0, 1000],
normal=[0, 1, 0],
mode_num=0,
power=1),
],
)
obj = goos.rename(-goos.abs(sim["overlap"]), name="obj_{}".format(stage))
return obj, sim
def make_objective_fdtd(eps: goos.Shape, stage: str, sim_3d: bool):
if sim_3d:
sim_z_extent = 2500
src_z_extent = 1000
pml_thickness = [400, 400, 400, 400, 400, 400]
# Dominant E-component is Ey.
timing_comp = 1
# Simulate across 4 cores.
sim_cores = 4
else:
sim_z_extent = 0
src_z_extent = 0
# No PMLs in the vertical direction for 2D.
pml_thickness = [400, 400, 400, 400, 0, 0]
# Dominant E-component is Ez.
timing_comp = 2
# Simulate using only a single CPU.
sim_cores = 1
sim = meep.fdtd_simulation(
name="sim_{}".format(stage),
eps=eps,
sources=[
meep.WaveguideModeSource(center=[-1400, 0, 0],
extents=[0, 2500, src_z_extent],
normal=[1, 0, 0],
mode_num=0,
power=1,
wavelength=1550,
bandwidth=100),
],
sim_space=meep.SimulationSpace(dx=20,
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, sim_z_extent],
),
pml_thickness=pml_thickness),
# `SimulationTiming` handles termination condition for FDTD.
# In this case, we rely on Meep's `stop_when_fields_decayed` which
# waits until the field component indexed by `timing_comp`
# at pos (0, 0, 0) has decayed (after the source has finished).
sim_timing=meep.SimulationTiming(stopping_conditions=[
meep.StopWhenFieldsDecayed(
time_increment=100,
component=timing_comp,
pos=[0, 0, 0],
threshold=1e-4,
)
]),
background=goos.material.Material(index=1.0),
outputs=[
meep.Epsilon(name="eps", wavelength=1550),
meep.ElectricField(name="field", wavelength=1550),
meep.WaveguideModeOverlap(name="overlap",
wavelength=1550,
center=[0, 1400, 0],
extents=[2500, 0, src_z_extent],
normal=[0, 1, 0],
mode_num=0,
power=1),
],
sim_cores=sim_cores,
)
obj = goos.rename(-goos.abs(sim["overlap"]), name="obj_{}".format(stage))
return obj, sim
def make_objective(eps: goos.Shape, stage: str, params: Options):
"""Creates the objective.
The function sets up the simulation and the objective function for the
grating optimization. The simulation is a FDFD simulation with a
Gaussian beam source that couples into a the waveguide.
The optimization minimizes `(1 - coupling_eff)**2` where `coupling_eff` is
the fiber-to-chip coupling efficiency.
Args:
eps: The permittivity distribution, including the waveguide and
grating.
stage: Name of the optimization stage. Used to name the nodes.
params: Options for the optimization problem.
Returns:
A tuple `(obj, sim)` where `obj` is the objective and `sim` is the
simulation.
"""
solver = "local_direct"
sim_left_x = -params.wg_len
sim_right_x = params.coupler_len + params.buffer_len
pml_thick = params.dx * 10
sim_z_center = (params.wg_thickness / 2 + params.beam_dist -
params.box_size) / 2
sim_z_extent = (params.wg_thickness + params.beam_dist + params.box_size +
2000 + pml_thick * 2)
sim = maxwell.fdfd_simulation(
name="sim_{}".format(stage),
wavelength=params.wlen,
eps=eps,
solver=solver,
sources=[
maxwell.GaussianSource(
w0=params.beam_width / 2,
center=[
params.coupler_len / 2, 0,
params.wg_thickness / 2 + params.beam_dist
],
extents=[params.beam_extents, 0, 0],
normal=[0, 0, -1],
power=1,
theta=np.deg2rad(params.source_angle_deg),
psi=np.pi / 2,
polarization_angle=0,
normalize_by_sim=True)
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=params.dx),
sim_region=goos.Box3d(
center=[(sim_left_x + sim_right_x) / 2, 0, sim_z_center],
extents=[sim_right_x - sim_left_x, 0, sim_z_extent],
),
pml_thickness=[pml_thick, pml_thick, 0, 0, pml_thick, pml_thick]),
background=goos.material.Material(index=params.eps_bg),
outputs=[
maxwell.Epsilon(name="eps"),
maxwell.ElectricField(name="field"),
maxwell.WaveguideModeOverlap(name="overlap",
center=[-params.wg_len / 2, 0, 0],
extents=[0, 1000, 2000],
normal=[-1, 0, 0],
mode_num=0,
power=1),
],
)
obj = (1 - goos.abs(sim["overlap"]))**2
obj = goos.rename(obj, name="obj_{}".format(stage))
return obj, sim
def test_simulate_wg_opt():
with goos.OptimizationPlan() as plan:
wg_in = goos.Cuboid(pos=goos.Constant([-2000, 0, 0]),
extents=goos.Constant([3000, 800, 40]),
material=goos.material.Material(index=3.45))
wg_out = goos.Cuboid(pos=goos.Constant([2000, 0, 0]),
extents=goos.Constant([3000, 800, 40]),
material=goos.material.Material(index=3.45))
def initializer(size):
# Set the seed immediately before calling `random` to ensure
# reproducibility.
np.random.seed(247)
return np.random.random(size) * 0.1 + np.ones(size) * 0.7
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=goos.Constant([0, 0, 0]),
extents=[1000, 800, 40],
pixel_size=[40, 40, 40],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.45),
)
eps = goos.GroupShape([wg_in, wg_out, design])
sim = meep.FdtdSimulation(
eps=eps,
sources=[
meep.WaveguideModeSource(
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=2,
power=1,
wavelength=1550,
bandwidth=100,
)
],
sim_space=meep.SimulationSpace(
dx=40,
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, 0],
),
pml_thickness=[400, 400, 400, 400, 0, 0]),
sim_timing=meep.SimulationTiming(stopping_conditions=[
meep.StopWhenFieldsDecayed(
time_increment=50,
component=2,
pos=[0, 0, 0],
threshold=1e-6,
)
], ),
background=goos.material.Material(index=1.0),
outputs=[
meep.Epsilon(wavelength=1550),
meep.ElectricField(wavelength=1550),
meep.WaveguideModeOverlap(wavelength=1550,
center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
])
obj = -goos.abs(sim[2])
import meep as mp
mp.quiet()
goos.opt.scipy_minimize(obj,
"L-BFGS-B",
monitor_list=[obj],
max_iters=5)
plan.run()
# Check that we can optimize. We choose something over 60% as
# incorrect gradients will typically not reach this point.
assert obj.get().array < -0.85
# As a final check, compare simulation results against Maxwell.
# Note that dx = 40 for Meep is actually too innaccurate. We therefore
# resimulate the final structure for both Meep and Maxwell.
from spins.goos_sim import maxwell
sim_fdfd = maxwell.fdfd_simulation(
wavelength=1550,
eps=eps,
sources=[
maxwell.WaveguideModeSource(
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=2,
power=1,
)
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=20),
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, 0],
),
pml_thickness=[400, 400, 400, 400, 0, 0]),
background=goos.material.Material(index=1.0),
outputs=[
maxwell.Epsilon(),
maxwell.ElectricField(),
maxwell.WaveguideModeOverlap(center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
],
solver="local_direct")
sim_fdtd_hi = meep.FdtdSimulation(
eps=eps,
sources=[
meep.WaveguideModeSource(
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=2,
power=1,
wavelength=1550,
bandwidth=100,
)
],
sim_space=meep.SimulationSpace(
dx=20,
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, 0],
),
pml_thickness=[400, 400, 400, 400, 0, 0]),
sim_timing=meep.SimulationTiming(stopping_conditions=[
meep.StopWhenFieldsDecayed(
time_increment=50,
component=2,
pos=[0, 0, 0],
threshold=1e-6,
)
], ),
background=goos.material.Material(index=1.0),
outputs=[
meep.Epsilon(wavelength=1550),
meep.ElectricField(wavelength=1550),
meep.WaveguideModeOverlap(wavelength=1550,
center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
])
fdtd_hi_power = goos.abs(sim_fdtd_hi[2])**2
fdfd_power = goos.abs(sim_fdfd[2])**2
# Check that power is correct within 0.5%.
assert np.abs(fdfd_power.get().array - fdtd_hi_power.get().array) < 0.005
def make_objective(eps: goos.Shape, stage: str):
sim_z_extent = 1800
simcenter_positon_z = 300
sources_wx = 8000
sources_wy = 8000
solver_info = maxwell.MaxwellSolver(solver="maxwell_cg", err_thresh=1e-2)
pml_thickness = [400, 400, 400, 400, 400, 400]
sources_position_z = 800
wavelength = 635
background = goos.material.Material(index=1.0)
simulation_space = maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=50),
sim_region=goos.Box3d(
center=[0, 0, simcenter_positon_z],
extents=[10000, 10000, sim_z_extent],
),
pml_thickness=pml_thickness)
sources1 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=2,
p=0,
polarization_angle=0,
power=1),
]
sources2 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=3,
p=0,
polarization_angle=0,
power=1),
]
sources3 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=-3,
p=0,
polarization_angle=0,
power=1),
]
sources4 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=-2,
p=0,
polarization_angle=0,
power=1),
]
sources5 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=1,
p=0,
polarization_angle=0,
power=1),
]
sources6 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=-1,
p=0,
polarization_angle=0,
power=1),
]
sources7 = [
maxwell.LaguerreGaussianSource(w0=1400,
center=[0, 0, sources_position_z],
beam_center=[0, 0, sources_position_z],
extents=[sources_wx, sources_wy, 0],
normal=[0, 0, -1],
theta=0,
psi=0,
m=0,
p=0,
polarization_angle=0,
power=1),
]
outputs = [
maxwell.Epsilon(name="eps"),
maxwell.ElectricField(name="field"),
maxwell.WaveguideModeOverlap(name="overlap1",
center=[1600, -4500, 0],
extents=[800, 0, 400],
normal=[0, -1, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap2",
center=[-1600, -4500, 0],
extents=[800, 0, 400],
normal=[0, -1, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap3",
center=[1600, 4500, 0],
extents=[800, 0, 400],
normal=[0, 1, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap4",
center=[-1600, 4500, 0],
extents=[800, 0, 400],
normal=[0, 1, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap5",
center=[4500, -1600, 0],
extents=[0, 800, 400],
normal=[1, 0, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap6",
center=[4500, 1600, 0],
extents=[0, 800, 400],
normal=[1, 0, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap7",
center=[-4500, 0, 0],
extents=[0, 800, 400],
normal=[-1, 0, 0],
mode_num=0,
power=1),
]
sim1 = maxwell.fdfd_simulation(
name="sim1_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources1,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim2 = maxwell.fdfd_simulation(
name="sim2_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources2,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim3 = maxwell.fdfd_simulation(
name="sim3_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources3,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim4 = maxwell.fdfd_simulation(
name="sim4_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources4,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim5 = maxwell.fdfd_simulation(
name="sim5_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources5,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim6 = maxwell.fdfd_simulation(
name="sim6_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources6,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
sim7 = maxwell.fdfd_simulation(
name="sim7_{}".format(stage),
wavelength=wavelength,
eps=eps,
solver_info=solver_info,
sources=sources7,
simulation_space=simulation_space,
background=background,
outputs=outputs,
)
obj1 = goos.rename(
((goos.abs(sim1["overlap1"]) - 12)**2 + goos.abs(sim1["overlap2"])**2 +
goos.abs(sim1["overlap3"])**2 + goos.abs(sim1["overlap4"])**2 +
goos.abs(sim1["overlap5"])**2 + goos.abs(sim1["overlap6"])**2 +
goos.abs(sim1["overlap7"])**2),
name="obj1_{}".format(stage))
obj2 = goos.rename(
(goos.abs(sim2["overlap1"])**2 +
(goos.abs(sim2["overlap2"]) - 12)**2 + goos.abs(sim2["overlap3"])**2 +
goos.abs(sim2["overlap4"])**2 + goos.abs(sim2["overlap5"])**2 +
goos.abs(sim2["overlap6"])**2 + goos.abs(sim2["overlap7"])**2),
name="obj2_{}".format(stage))
obj3 = goos.rename(
(goos.abs(sim3["overlap1"])**2 + goos.abs(sim3["overlap2"])**2 +
(goos.abs(sim3["overlap3"]) - 12)**2 + goos.abs(sim3["overlap4"])**2 +
goos.abs(sim3["overlap5"])**2 + goos.abs(sim3["overlap6"])**2 +
goos.abs(sim3["overlap7"])**2),
name="obj3_{}".format(stage))
obj4 = goos.rename(
(goos.abs(sim4["overlap1"])**2 + goos.abs(sim4["overlap2"])**2 +
goos.abs(sim4["overlap3"])**2 +
(goos.abs(sim4["overlap4"]) - 12)**2 + goos.abs(sim4["overlap5"])**2 +
goos.abs(sim4["overlap6"])**2 + goos.abs(sim4["overlap7"])**2),
name="obj4_{}".format(stage))
obj5 = goos.rename(
(goos.abs(sim5["overlap1"])**2 + goos.abs(sim5["overlap2"])**2 +
goos.abs(sim5["overlap3"])**2 + goos.abs(sim5["overlap4"])**2 +
(goos.abs(sim5["overlap5"]) - 12)**2 + goos.abs(sim5["overlap6"])**2 +
goos.abs(sim5["overlap7"])**2),
name="obj5_{}".format(stage))
obj6 = goos.rename(
(goos.abs(sim6["overlap1"])**2 + goos.abs(sim6["overlap2"])**2 +
goos.abs(sim6["overlap3"])**2 + goos.abs(sim6["overlap4"])**2 +
goos.abs(sim6["overlap5"])**2 +
(goos.abs(sim6["overlap6"]) - 12)**2 + goos.abs(sim6["overlap7"])**2),
name="obj5_{}".format(stage))
obj7 = goos.rename(
(goos.abs(sim7["overlap1"])**2 + goos.abs(sim7["overlap2"])**2 +
goos.abs(sim7["overlap3"])**2 + goos.abs(sim7["overlap4"])**2 +
goos.abs(sim7["overlap5"])**2 + goos.abs(sim7["overlap6"])**2 +
(goos.abs(sim7["overlap7"]) - 12)**2),
name="obj5_{}".format(stage))
obj = obj1 + obj2 + obj3 + obj4 + 2 * obj5 + 2 * obj6 + 8 * obj7
return obj, sim1, sim2, sim3, sim4, sim5, sim6, sim7
def test_simulate_wg_opt():
with goos.OptimizationPlan() as plan:
wg_in = goos.Cuboid(pos=goos.Constant([-2000, 0, 0]),
extents=goos.Constant([3000, 800, 220]),
material=goos.material.Material(index=3.45))
wg_out = goos.Cuboid(pos=goos.Constant([2000, 0, 0]),
extents=goos.Constant([3000, 800, 220]),
material=goos.material.Material(index=3.45))
def initializer(size):
# Set the seed immediately before calling `random` to ensure
# reproducibility.
np.random.seed(247)
return np.random.random(size) * 0.1 + np.ones(size) * 0.5
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=goos.Constant([0, 0, 0]),
extents=[1000, 800, 220],
pixel_size=[40, 40, 40],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.45),
)
eps = goos.GroupShape([wg_in, wg_out, design])
sim = maxwell.fdfd_simulation(
eps=eps,
wavelength=1550,
solver="local_direct",
sources=[
maxwell.WaveguideModeSource(
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=2,
power=1,
)
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=40),
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, 40],
),
pml_thickness=[400, 400, 400, 400, 0, 0]),
background=goos.material.Material(index=1.0),
outputs=[
maxwell.Epsilon(),
maxwell.ElectricField(),
maxwell.WaveguideModeOverlap(wavelength=1550,
center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
])
obj = -goos.abs(sim[2])
goos.opt.scipy_minimize(obj,
"L-BFGS-B",
monitor_list=[obj],
max_iters=15)
plan.run()
assert obj.get().array < -0.90
def test_simulate_wg_opt_grad():
with goos.OptimizationPlan() as plan:
wg_in = goos.Cuboid(pos=goos.Constant([-2000, 0, 0]),
extents=goos.Constant([3000, 800, 220]),
material=goos.material.Material(index=3.45))
wg_out = goos.Cuboid(pos=goos.Constant([2000, 0, 0]),
extents=goos.Constant([3000, 800, 220]),
material=goos.material.Material(index=3.45))
def initializer(size):
# Set the seed immediately before calling `random` to ensure
# reproducibility.
np.random.seed(247)
return np.random.random(size)
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=goos.Constant([0, 0, 0]),
extents=[1000, 800, 220],
pixel_size=[500, 400, 220],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.45),
)
eps = goos.GroupShape([wg_in, wg_out, design])
sim = maxwell.fdfd_simulation(
eps=eps,
wavelength=1550,
solver="local_direct",
sources=[
maxwell.WaveguideModeSource(
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=2,
power=1,
)
],
simulation_space=maxwell.SimulationSpace(
mesh=maxwell.UniformMesh(dx=40),
sim_region=goos.Box3d(
center=[0, 0, 0],
extents=[4000, 4000, 40],
),
pml_thickness=[400, 400, 400, 400, 0, 0]),
background=goos.material.Material(index=1.0),
outputs=[
maxwell.Epsilon(),
maxwell.ElectricField(),
maxwell.WaveguideModeOverlap(wavelength=1550,
center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
])
obj = -goos.abs(sim[2])
adjoint_grad = obj.get_grad([var])[0].array_grad
# Calculate brute force gradient.
var_val = var.get().array
eps = 0.001
num_grad = np.zeros_like(var_val)
for i in range(var_val.shape[0]):
for j in range(var_val.shape[1]):
temp_val = var_val.copy()
temp_val[i, j] += eps
var.set(temp_val)
fplus = obj.get(run=True).array
temp_val = var_val.copy()
temp_val[i, j] -= eps
var.set(temp_val)
fminus = obj.get(run=True).array
num_grad[i, j] = (fplus - fminus) / (2 * eps)
np.testing.assert_array_almost_equal(adjoint_grad, num_grad, decimal=3)