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 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 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)
def test_simulate_2d():
with goos.OptimizationPlan() as plan:
sim_region = goos.Box3d(center=[0, 0, 0], extents=[4000, 4000, 40])
sim_mesh = maxwell.UniformMesh(dx=40)
waveguide = goos.Cuboid(pos=goos.Constant([0, 0, 0]),
extents=goos.Constant([6000, 500, 40]),
material=goos.material.Material(index=3.45))
eps = maxwell.RenderShape(waveguide,
region=sim_region,
mesh=sim_mesh,
background=goos.material.Material(index=1.0),
wavelength=1550)
sim = maxwell.SimulateNode(
wavelength=1550,
simulation_space=maxwell.SimulationSpace(
sim_region=sim_region,
mesh=sim_mesh,
pml_thickness=[400, 400, 400, 400, 0, 0],
),
eps=eps,
sources=[
maxwell.WaveguideModeSource(
center=[-500, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1,
)
],
solver_info=maxwell.DirectSolver(),
outputs=[
maxwell.Epsilon(name="eps"),
maxwell.ElectricField(name="fields"),
maxwell.WaveguideModeOverlap(name="overlap_forward",
wavelength=1550,
center=[1000, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap_backward",
wavelength=1550,
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[-1, 0, 0],
mode_num=0,
power=1),
maxwell.WaveguideModeOverlap(name="overlap_forward2",
wavelength=1550,
center=[0, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
])
out = sim.get()
# Power transmitted should be unity but numerical dispersion could
# affect the actual transmitted power.
assert np.abs(out[4].array)**2 >= 0.99
assert np.abs(out[4].array)**2 <= 1.01
# Check that waveguide power is roughly constant along waveguide.
np.testing.assert_allclose(np.abs(out[2].array)**2,
np.abs(out[4].array)**2,
rtol=1e-2)
# Check that we get minimal leakage of power flowing backwards.
assert np.abs(out[3].array)**2 < 0.01