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import meep as mp
try:
import meep.adjoint as mpa
except:
import adjoint as mpa
import unittest
from enum import Enum
import numpy as np
from autograd import numpy as npa
from autograd import tensor_jacobian_product
from utils import ApproxComparisonTestCase
import parameterized
rng = np.random.RandomState(2)
resolution = 20
dimensions = mp.CYLINDRICAL
Si = mp.Medium(index=3.4)
SiO2 = mp.Medium(index=1.44)
sr = 6
sz = 6
cell_size = mp.Vector3(sr, 0, sz)
dpml = 1.0
boundary_layers = [mp.PML(thickness=dpml)]
design_region_resolution = int(2 * resolution)
design_r = 5
design_z = 2
Nr, Nz = (
int(design_r * design_region_resolution) + 1,
int(design_z * design_region_resolution) + 1,
)
fcen = 1 / 1.55
width = 0.2
fwidth = width * fcen
## random design region
p = 0.5 * rng.rand(Nr * Nz)
## random epsilon perturbation for design region
deps = 1e-5
dp = deps * rng.rand(Nr * Nz)
def get_source(m):
source_center = mp.Vector3(
design_r / 2,
0,
-(sz / 2 - dpml + design_z / 2) / 2,
)
# exclude r=0 whenever |m| > 1
source_size = mp.Vector3(
design_r if abs(m) <= 1 else 0.5 * design_r,
0,
0,
)
src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)
source = [
mp.Source(
src,
component=mp.Er,
center=source_center,
size=source_size,
)
]
return source
def forward_simulation(design_params, m, far_x):
matgrid = mp.MaterialGrid(
mp.Vector3(Nr, 0, Nz),
SiO2,
Si,
weights=design_params.reshape(Nr, 1, Nz),
do_averaging=True,
)
geometry = [
mp.Block(
center=mp.Vector3(design_r / 2, 0, 0),
size=mp.Vector3(design_r, 0, design_z),
material=matgrid,
)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=boundary_layers,
sources=get_source(m),
geometry=geometry,
dimensions=dimensions,
m=m,
)
frequencies = [fcen]
mode = sim.add_near2far(
frequencies,
mp.Near2FarRegion(
center=mp.Vector3(design_r / 2, 0, (sz / 2 - dpml + design_z / 2) / 2),
size=mp.Vector3(design_r, 0, 0),
weight=+1,
),
)
sim.run(until_after_sources=1200)
Er = sim.get_farfield(mode, far_x[0])
sim.reset_meep()
return abs(Er[0]) ** 2
def adjoint_solver(design_params, m, far_x):
design_variables = mp.MaterialGrid(
mp.Vector3(Nr, 0, Nz), SiO2, Si, do_averaging=True
)
design_region = mpa.DesignRegion(
design_variables,
volume=mp.Volume(
center=mp.Vector3(design_r / 2, 0, 0),
size=mp.Vector3(design_r, 0, design_z),
),
)
geometry = [
mp.Block(
center=design_region.center,
size=design_region.size,
material=design_variables,
)
]
sim = mp.Simulation(
cell_size=cell_size,
boundary_layers=boundary_layers,
geometry=geometry,
sources=get_source(m),
resolution=resolution,
dimensions=dimensions,
m=m,
)
NearRegions = [
mp.Near2FarRegion(
center=mp.Vector3(design_r / 2, 0, (sz / 2 - dpml + design_z / 2) / 2),
size=mp.Vector3(design_r, 0, 0),
weight=+1,
)
]
FarFields = mpa.Near2FarFields(sim, NearRegions, far_x)
ob_list = [FarFields]
def J(alpha):
return npa.abs(alpha[0, 0, 0]) ** 2
opt = mpa.OptimizationProblem(
simulation=sim,
objective_functions=J,
objective_arguments=ob_list,
design_regions=[design_region],
fcen=fcen,
df=0,
nf=1,
maximum_run_time=1200,
)
f, dJ_du = opt([design_params])
sim.reset_meep()
return f, dJ_du
class TestAdjointSolver(ApproxComparisonTestCase):
@parameterized.parameterized.expand(
[
(0, [mp.Vector3(5, 0, 20)]),
(0, [mp.Vector3(4, 0, 28)]),
(-1, [mp.Vector3(5, 0, 20)]),
(1.2, [mp.Vector3(5, 0, 20)]),
]
)
def test_adjoint_solver_cyl_n2f_fields(self, m, far_x):
print("*** TESTING CYLINDRICAL Near2Far ADJOINT FEATURES ***")
print(f"Current test: m={m}, far_x={far_x}")
adjsol_obj, adjsol_grad = adjoint_solver(p, m, far_x)
## compute unperturbed S12
S12_unperturbed = forward_simulation(p, m, far_x)
## compare objective results
print(
f"|Er|^2 -- adjoint solver: {adjsol_obj}, traditional simulation: {S12_unperturbed}"
)
self.assertClose(adjsol_obj, S12_unperturbed, epsilon=1e-3)
## compute perturbed S12
S12_perturbed = forward_simulation(p + dp, m, far_x)
## compare gradients
if adjsol_grad.ndim < 2:
adjsol_grad = np.expand_dims(adjsol_grad, axis=1)
adj_scale = (dp[None, :] @ adjsol_grad).flatten()
fd_grad = S12_perturbed - S12_unperturbed
print(f"Directional derivative -- adjoint solver: {adj_scale}, FD: {fd_grad}")
tol = 0.6 if m == 0 else 0.3
self.assertClose(adj_scale, fd_grad, epsilon=tol)
if __name__ == "__main__":
unittest.main()
|
