def test_render_pixelated_cont_shape():
with goos.OptimizationPlan() as plan:
def initializer(size):
return [[1, 0], [0.5, 0.75], [0, 0.8], [1, 0.8]]
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=goos.Constant([200, 0, 0]),
extents=[1000, 1000, 220],
material=goos.material.Material(index=2),
material2=goos.material.Material(index=4),
pixel_size=[250, 500, 220])
rect = goos.Cuboid(extents=goos.Constant([1000, 1000, 220]),
pos=goos.Constant([200, 0, 0]),
material=goos.material.Material(index=2))
render = maxwell.RenderShape(
design,
region=goos.Box3d(center=[0, 0, 0], extents=[1500, 1500, 200]),
mesh=maxwell.UniformMesh(dx=40),
background=goos.material.Material(index=1.0),
wavelength=1550)
np.testing.assert_almost_equal(
np.real(render.get().array[2][10:, 8, 3]), [
1., 8.5, 16., 16., 16., 16., 16., 14.5, 10., 10., 10., 10.,
10., 10., 4., 4., 4., 4., 4., 4., 13., 16., 16., 16., 16., 16.,
8.5
])
def test_render_cylinder():
with goos.OptimizationPlan() as plan:
cyl = goos.Cylinder(pos=goos.Constant([0, 0, 0]),
radius=goos.Constant(60),
height=goos.Constant(60),
material=goos.material.Material(index=3.45))
render = maxwell.RenderShape(
cyl,
region=goos.Box3d(center=[0, 0, 0], extents=[200, 200, 40]),
mesh=maxwell.UniformMesh(dx=40),
background=goos.material.Material(index=1.0),
wavelength=1550)
np.testing.assert_array_almost_equal(
render.get().array,
[[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [2.20393657], [8.15133225], [8.14708434], [2.20801505]],
[[1.], [4.81696873], [9.176875], [9.176875], [4.81254501]],
[[1.], [2.20393657], [8.15133225], [8.14708434], [2.20801505]],
[[1.], [1.], [1.], [1.], [1.]]],
[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [2.20452237], [4.81426614], [2.20733312], [1.]],
[[1.], [8.1503488], [9.176875], [8.14865466], [1.]],
[[1.], [8.1503488], [9.176875], [8.14865466], [1.]],
[[1.], [2.20452237], [4.81426614], [2.20733312], [1.]]],
[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [1.06734618], [5.08385966], [5.07819579], [1.07209387]],
[[1.], [5.0825484], [11.9025], [11.9025], [5.08028954]],
[[1.], [5.0825484], [11.9025], [11.9025], [5.08028954]],
[[1.], [1.06734618], [5.08385966], [5.07819579], [1.07209387]]]])
def test_render_prism():
with goos.OptimizationPlan() as plan:
rect = goos.Cuboid(extents=goos.Constant([80, 80, 100]),
pos=goos.Constant([0, 0, 0]),
material=goos.material.Material(index=3.45))
render = maxwell.RenderShape(
rect,
region=goos.Box3d(center=[0, 0, 0], extents=[160, 200, 40]),
mesh=maxwell.UniformMesh(dx=40),
background=goos.material.Material(index=1.0),
wavelength=1550)
np.testing.assert_array_almost_equal(
render.get().array,
[[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [1.], [11.9025], [11.9025], [1.]],
[[1.], [1.], [11.9025], [11.9025], [1.]],
[[1.], [1.], [1.], [1.], [1.]]],
[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [3.725625], [6.45125], [3.725625], [1.]],
[[1.], [6.45125], [11.9025], [6.45125], [1.]],
[[1.], [3.725625], [6.45125], [3.725625], [1.]]],
[[[1.], [1.], [1.], [1.], [1.]],
[[1.], [1.], [6.45125], [6.45125], [1.]],
[[1.], [1.], [11.9025], [11.9025], [1.]],
[[1.], [1.], [6.45125], [6.45125], [1.]]]])
def main(save_folder: str,
min_feature: float = 100,
sim_3d: bool = False,
visualize: bool = False) -> None:
goos.util.setup_logging(save_folder)
with goos.OptimizationPlan(save_path=save_folder) as plan:
wg_in = goos.Cuboid(pos=goos.Constant([-2000, 0, 0]),
extents=goos.Constant([3000, 400, 220]),
material=goos.material.Material(index=3.45))
wg_out = goos.Cuboid(pos=goos.Constant([0, 2000, 0]),
extents=goos.Constant([400, 3000, 220]),
material=goos.material.Material(index=3.45))
def initializer(size):
return np.random.random(size) * 0.2 + 0.5
# Continuous optimization.
var, design = goos.cubic_param_shape(
initializer=initializer,
pos=goos.Constant([0, 0, 0]),
extents=[2000, 2000, 220],
pixel_spacing=40,
control_point_spacing=1.5 * min_feature,
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.45),
var_name="var_cont")
sigmoid_factor = goos.Variable(4, parameter=True, name="discr_factor")
design = goos.cast(goos.Sigmoid(sigmoid_factor * (2 * design - 1)),
goos.Shape)
eps = goos.GroupShape([wg_in, wg_out, design])
# This node is purely for debugging purposes.
eps_rendered = maxwell.RenderShape(
design,
region=goos.Box3d(center=[0, 0, 0], extents=[3000, 3000, 0]),
mesh=maxwell.UniformMesh(dx=40),
wavelength=1550,
)
if visualize:
goos.util.visualize_eps(eps_rendered.get().array[2])
obj, sim = make_objective_fdtd(eps, "cont", sim_3d=sim_3d)
for factor in [4, 8]:
sigmoid_factor.set(factor)
goos.opt.scipy_minimize(
obj,
"L-BFGS-B",
monitor_list=[sim["eps"], sim["field"], sim["overlap"], obj],
max_iters=6,
name="opt_cont{}".format(factor))
plan.save()
plan.run()
if visualize:
goos.util.visualize_eps(eps_rendered.get().array[2])
def test_gaussian_source_2d():
grid = gridlock.Grid(simspace.create_edge_coords(
goos.Box3d(center=[0, 0, 0], extents=[14000, 40, 3000]), 40),
ext_dir=gridlock.Direction.z,
initial=1,
num_grids=3)
grid.render()
eps = np.array(grid.grids)
dxes = [grid.dxyz, grid.autoshifted_dxyz()]
sim = maxwell.FdfdSimProp(eps=eps,
source=np.zeros_like(eps),
wlen=1550,
dxes=dxes,
pml_layers=[10, 10, 0, 0, 10, 10],
grid=grid,
solver=maxwell.DIRECT_SOLVER)
src = maxwell.GaussianSourceImpl(
maxwell.GaussianSource(w0=5200,
center=[0, 0, 0],
extents=[14000, 0, 0],
normal=[0, 0, -1],
power=1,
theta=0,
psi=0,
polarization_angle=np.pi / 2,
normalize_by_sim=True))
src.before_sim(sim)
fields = maxwell.DIRECT_SOLVER.solve(
omega=2 * np.pi / sim.wlen,
dxes=sim.dxes,
epsilon=fdfd_tools.vec(sim.eps),
mu=None,
J=fdfd_tools.vec(sim.source),
pml_layers=sim.pml_layers,
bloch_vec=sim.bloch_vec,
)
fields = fdfd_tools.unvec(fields, grid.shape)
field_y = fields[1].squeeze()
np.testing.assert_allclose(field_y[:, 53],
np.zeros_like(field_y[:, 53]),
atol=1e-4)
# Calculate what the amplitude of the Gaussian field should look like.
# Amplitude determined empirically through simulation.
coords = (np.arange(len(field_y[:, 20])) - len(field_y[:, 20]) / 2) * 40
target_gaussian = np.exp(-coords**2 / 5200**2) * 0.00278
np.testing.assert_allclose(np.abs(field_y[:, 20]),
target_gaussian,
atol=1e-4)
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 test_pixelated_multietch_grating_fit_edge_locs():
# Grating defined in xz-plane.
with goos.OptimizationPlan() as plan:
height_index = goos.Variable([2, 0, 1, 2], parameter=True)
edge_locs_target = goos.Variable([0, 1, 1.5, 2], parameter=True)
grating_target = goos.grating.PixelatedGrating(
edge_locs_target,
height_index=height_index,
height_fracs=[0, 0.5, 1],
pos=[0, 0, 0],
extents=[2, 10, 0.220],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.5),
grating_dir=0,
grating_dir_spacing=0.5,
etch_dir_divs=2,
use_edge_locs=True)
edge_locs = goos.Variable([0, 0.8, 1.6, 2])
grating = goos.grating.PixelatedGrating(
edge_locs,
height_index=height_index,
height_fracs=[0, 0.5, 1],
pos=[0, 0, 0],
extents=[2, 10, 0.220],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.5),
grating_dir=0,
grating_dir_spacing=0.5,
etch_dir_divs=2,
use_edge_locs=True)
from spins.goos_sim import maxwell
region = goos.Box3d(center=[0, 0, 0], extents=[3, 11, 0.5])
mesh = maxwell.UniformMesh(dx=0.1)
eps_diff = goos.Norm(
maxwell.RenderShape(
grating, region=region, mesh=mesh, wavelength=1.55) -
maxwell.RenderShape(
grating_target, region=region, mesh=mesh, wavelength=1.55))
goos.opt.scipy_minimize(eps_diff, "L-BFGS-B", max_iters=20)
plan.run()
np.testing.assert_almost_equal(grating.get().array,
grating_target.get().array)
def test_pixelated_multietch_grating_xz_gradient(use_edge_locs, params, pol):
# Brute force calculate the gradient.
# Grating defined in xz-plane.
with goos.OptimizationPlan() as plan:
edge_locs = goos.Variable(params)
height_index = goos.Variable([0, 1, 0, 1])
grating = goos.grating.PixelatedGrating(
edge_locs,
height_index=height_index,
height_fracs=[0.4, 1],
pos=[0, 0, 0],
extents=[2, 10, 0.220],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.5),
grating_dir=0,
grating_dir_spacing=0.5,
etch_dir_divs=4,
etch_polarity=pol,
use_edge_locs=use_edge_locs)
from spins.goos_sim import maxwell
shape = maxwell.RenderShape(grating,
region=goos.Box3d(center=[0, 0, 0],
extents=[4, 10, 0.220]),
mesh=maxwell.UniformMesh(dx=0.25),
wavelength=1550)
np.random.seed(247)
obj = goos.dot(shape, np.random.random(shape.get().array.shape))
val_orig = edge_locs.get().array
step = 1e-5
grad_num = np.zeros_like(val_orig)
for i in range(len(val_orig)):
delta = np.zeros_like(val_orig)
delta[i] = 1
edge_locs.set(val_orig + step * delta)
f_plus = obj.get(run=True).array
edge_locs.set(val_orig - step * delta)
f_minus = obj.get(run=True).array
grad_num[i] = (f_plus - f_minus) / (2 * step)
grad_backprop = obj.get_grad([edge_locs])[0].array_grad
np.testing.assert_allclose(grad_backprop, grad_num)
def test_render_pixelated_cont_shape_grad():
with goos.OptimizationPlan() as plan:
def initializer(size):
return [[1, 0], [0.5, 0.75], [0, 0.8], [1, 0.8]]
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=[200, 0, 0],
extents=[1000, 1000, 220],
material=goos.material.Material(index=2),
material2=goos.material.Material(index=4),
pixel_size=[250, 500, 220])
render = maxwell.RenderShape(
design,
region=goos.Box3d(center=[0, 0, 0], extents=[1500, 1500, 200]),
mesh=maxwell.UniformMesh(dx=40),
background=goos.material.Material(index=1.0),
wavelength=1550)
# Compute a random objective function to test gradient.
np.random.seed(247)
obj = goos.dot(np.random.random(render.get().array.shape), render)
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)
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(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 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_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
extents=goos.Constant([3000, 400, 220]),
material=goos.material.Material(index=1))
# Define output waveguide.
wg_out = goos.Cuboid(pos=goos.Constant([0, 2000, 0]),
extents=goos.Constant([400, 3000, 220]),
material=goos.material.Material(index=1))
# Group these background structures together.
eps_background_structures = goos.GroupShape([wg_in, wg_out])
'''
Visualize the constant background structures we just defined.
'''
with plan:
eps_rendered = maxwell.RenderShape(
eps_background_structures,
region=goos.Box3d(center=[0, 0, 0], extents=[3000, 3000, 0]),
mesh=maxwell.UniformMesh(dx=40),
wavelength=635,
)
goos.util.visualize_eps(eps_rendered.get().array[2])
'''
Define and initialize the design region.
'''
with plan:
# Use random initialization, where each pixel is randomly assigned
# a value in the range [0.3,0.7].
def initializer(size):
# Set the seed immediately before calling `random` to ensure
# reproducibility.
np.random.seed(247)
def test_simulate_wg_straight_2d_multicore():
with goos.OptimizationPlan() as plan:
eps = goos.Cuboid(pos=goos.Constant([0, 0, 0]),
extents=goos.Constant([6000, 500, 40]),
material=goos.material.Material(index=3.45))
sim = meep.FdtdSimulation(
eps=eps,
sources=[
meep.WaveguideModeSource(
center=[-500, 0, 0],
extents=[0, 2500, 0],
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, 0],
),
pml_thickness=[800, 800, 800, 800, 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),
meep.WaveguideModeOverlap(wavelength=1550,
center=[-1000, 0, 0],
extents=[0, 2500, 0],
normal=[-1, 0, 0],
mode_num=0,
power=1),
meep.WaveguideModeOverlap(wavelength=1550,
center=[0, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1),
meep.WaveguideModeOverlap(wavelength=1500,
center=[0, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1,
normalize=True),
meep.WaveguideModeOverlap(wavelength=1500,
center=[0, 0, 0],
extents=[0, 2500, 0],
normal=[1, 0, 0],
mode_num=0,
power=1,
normalize=False),
],
sim_cores=2,
)
out = sim.get()
# Plot the fields.
#import matplotlib.pyplot as plt
#eps = out[0].array
#plt.imshow(eps)
#plt.figure()
#field = out[1].array
#plt.imshow(np.real(field[2]))
#plt.show()
# Power transmitted should be unity but numerical dispersion could
# affect the actual transmitted power. Last time we checked, the power
# ~0.96.
# 1550 nm overlap.
assert np.abs(out[4].array)**2 >= 0.96
assert np.abs(out[4].array)**2 <= 1.04
# 1525 nm overlap (with normalization)
assert np.abs(out[5].array)**2 >= 0.96
assert np.abs(out[5].array)**2 <= 1.04
# The unnormalized power should be roughly ~30%.
assert np.abs(out[6].array)**2 < 0.40
assert np.abs(out[6].array)**2 > 0.20
# 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 / np.abs(out[2].array)**2 < 0.01
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_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_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 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 main(save_folder: str,
min_feature: float = 100,
use_cubic: bool = True,
visualize: bool = False) -> None:
goos.util.setup_logging(save_folder)
with goos.OptimizationPlan(save_path=save_folder) as plan:
wg_1 = goos.Cuboid(pos=goos.Constant([1600, -4500, 0]),
extents=goos.Constant([600, 1000, 230]),
material=goos.material.Material(index=3.45))
wg_2 = goos.Cuboid(pos=goos.Constant([-1600, -4500, 0]),
extents=goos.Constant([600, 1000, 230]),
material=goos.material.Material(index=3.45))
wg_3 = goos.Cuboid(pos=goos.Constant([1600, 4500, 0]),
extents=goos.Constant([600, 1000, 230]),
material=goos.material.Material(index=3.45))
wg_4 = goos.Cuboid(pos=goos.Constant([-1600, 4500, 0]),
extents=goos.Constant([600, 1000, 230]),
material=goos.material.Material(index=3.45))
wg_5 = goos.Cuboid(pos=goos.Constant([4500, -1600, 0]),
extents=goos.Constant([1000, 600, 230]),
material=goos.material.Material(index=3.45))
wg_6 = goos.Cuboid(pos=goos.Constant([4500, 1600, 0]),
extents=goos.Constant([1000, 600, 230]),
material=goos.material.Material(index=3.45))
wg_7 = goos.Cuboid(pos=goos.Constant([-4500, 0, 0]),
extents=goos.Constant([1000, 600, 230]),
material=goos.material.Material(index=3.45))
substrate = goos.Cuboid(pos=goos.Constant([0, 0, -500]),
extents=goos.Constant([11000, 11000, 770]),
material=goos.material.Material(index=1.4))
def initializer(size):
# Set the seed immediately before calling `random` to ensure
# reproducibility.
#np.random.seed(247)
return np.ones(size) * 0.5
#return np.random.random(size) * 0.2 + 0.5
# Continuous optimization.
var, design = goos.pixelated_cont_shape(
initializer=initializer,
pos=goos.Constant([0, 0, 0]),
extents=[8000, 8000, 230],
material=goos.material.Material(index=1),
material2=goos.material.Material(index=3.45),
pixel_size=[50, 50, 230],
var_name="var_cont")
sigmoid_factor = goos.Variable(4, parameter=True, name="discr_factor")
design = goos.cast(goos.Sigmoid(sigmoid_factor * (2 * design - 1)),
goos.Shape)
eps = goos.GroupShape(
[wg_1, wg_2, wg_3, wg_4, wg_5, wg_6, wg_7, design, substrate])
# This node is purely for debugging purposes.
eps_rendered = maxwell.RenderShape(
eps,
region=goos.Box3d(center=[0, 0, 0], extents=[10000, 10000, 0]),
mesh=maxwell.UniformMesh(dx=50),
wavelength=635,
)
if visualize:
goos.util.visualize_eps(eps_rendered.get().array[2])
obj, sim1, sim2, sim3, sim4, sim5, sim6, sim7 = make_objective(
eps, "cont")
for factor in [4, 8, 12]:
sigmoid_factor.set(factor)
goos.opt.scipy_minimize(
obj,
"L-BFGS-B",
monitor_list=[
sim1["eps"], sim1["field"], sim1["overlap1"],
sim1["overlap2"], sim1["overlap3"], sim1["overlap4"],
sim1["overlap5"], sim1["overlap6"], sim1["overlap7"],
sim2["eps"], sim2["field"], sim2["overlap1"],
sim2["overlap2"], sim2["overlap3"], sim2["overlap4"],
sim2["overlap5"], sim2["overlap6"], sim2["overlap7"],
sim3["eps"], sim3["field"], sim3["overlap1"],
sim3["overlap2"], sim3["overlap3"], sim3["overlap4"],
sim3["overlap5"], sim3["overlap6"], sim3["overlap7"],
sim4["eps"], sim4["field"], sim4["overlap1"],
sim4["overlap2"], sim4["overlap3"], sim4["overlap4"],
sim4["overlap5"], sim4["overlap6"], sim4["overlap7"],
sim5["eps"], sim5["field"], sim5["overlap1"],
sim5["overlap2"], sim5["overlap3"], sim5["overlap4"],
sim5["overlap5"], sim5["overlap6"], sim5["overlap7"],
sim6["eps"], sim6["field"], sim6["overlap1"],
sim6["overlap2"], sim6["overlap3"], sim6["overlap4"],
sim6["overlap5"], sim6["overlap6"], sim6["overlap7"],
sim7["eps"], sim7["field"], sim7["overlap1"],
sim7["overlap2"], sim7["overlap3"], sim7["overlap4"],
sim7["overlap5"], sim7["overlap6"], sim7["overlap7"], obj
],
max_iters=25,
name="opt_cont{}".format(factor))
plan.save()
plan.run()
if visualize:
goos.util.visualize_eps(eps_rendered.get().array[2])
