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import os
import unittest
import numpy as np
import meep as mp
class TestPrism(unittest.TestCase):
def nonconvex_marching_squares(self, idx, npts):
resolution = 25
cell = mp.Vector3(10, 10)
data_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), "data"))
vertices_file = os.path.join(data_dir, f"nonconvex_prism_vertices{idx}.npz")
vertices_obj = np.load(vertices_file)
## prism verticies precomputed from analytic "blob" shape using
## marching squares algorithm of skimage.measure.find_contours
## ref: https://github.com/NanoComp/meep/pull/1142
vertices_data = vertices_obj[f"N{npts}"]
vertices = [mp.Vector3(v[0], v[1], 0) for v in vertices_data]
geometry = [mp.Prism(vertices, height=mp.inf, material=mp.Medium(epsilon=12))]
sim = mp.Simulation(cell_size=cell, geometry=geometry, resolution=resolution)
sim.init_sim()
prism_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
print(f"epsilon-sum:, {abs(prism_eps)} (prism-msq)")
return prism_eps
def convex_marching_squares(self, npts):
resolution = 50
cell = mp.Vector3(3, 3)
data_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), "data"))
vertices_file = os.path.join(data_dir, "convex_prism_vertices.npz")
vertices_obj = np.load(vertices_file)
## prism vertices precomputed for a circle of radius 1.0 using
## marching squares algorithm of skimage.measure.find_contours
## ref: https://github.com/NanoComp/meep/issues/1060
vertices_data = vertices_obj[f"N{npts}"]
vertices = [mp.Vector3(v[0], v[1], 0) for v in vertices_data]
geometry = [mp.Prism(vertices, height=mp.inf, material=mp.Medium(epsilon=12))]
sim = mp.Simulation(cell_size=cell, geometry=geometry, resolution=resolution)
sim.init_sim()
prism_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
sim.reset_meep()
geometry = [
mp.Cylinder(
radius=1.0,
center=mp.Vector3(),
height=mp.inf,
material=mp.Medium(epsilon=12),
)
]
sim = mp.Simulation(cell_size=cell, geometry=geometry, resolution=resolution)
sim.init_sim()
cyl_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
print(
f"epsilon-sum:, {abs(prism_eps)} (prism-msq), {abs(cyl_eps)} (cylinder), {abs((prism_eps-cyl_eps)/cyl_eps)} (relative error)"
)
return abs((prism_eps - cyl_eps) / cyl_eps)
def convex_circle(self, npts, r, sym):
resolution = 50
cell = mp.Vector3(3, 3)
### prism vertices computed as equally-spaced points
### along the circumference of a circle with radius r
angles = 2 * np.pi / npts * np.arange(npts)
vertices = [mp.Vector3(r * np.cos(ang), r * np.sin(ang)) for ang in angles]
geometry = [mp.Prism(vertices, height=mp.inf, material=mp.Medium(epsilon=12))]
sim = mp.Simulation(
cell_size=cell,
geometry=geometry,
symmetries=[mp.Mirror(direction=mp.X), mp.Mirror(direction=mp.Y)]
if sym
else [],
resolution=resolution,
)
sim.init_sim()
prism_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
sim.reset_meep()
geometry = [
mp.Cylinder(
radius=r,
center=mp.Vector3(),
height=mp.inf,
material=mp.Medium(epsilon=12),
)
]
sim = mp.Simulation(
cell_size=cell,
geometry=geometry,
symmetries=[mp.Mirror(direction=mp.X), mp.Mirror(direction=mp.Y)]
if sym
else [],
resolution=resolution,
)
sim.init_sim()
cyl_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
print(
f"epsilon-sum:, {abs(prism_eps)} (prism-cyl), {abs(cyl_eps)} (cylinder), {abs((prism_eps-cyl_eps)/cyl_eps)} (relative error)"
)
return abs((prism_eps - cyl_eps) / cyl_eps)
def spiral_gds(self):
data_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), "data"))
gdsii_file = os.path.join(data_dir, "spiral.gds")
resolution = 25
cell_size = mp.Vector3(12, 16)
geometry = mp.get_GDSII_prisms(mp.Medium(index=3.5), gdsii_file, 0, 0, mp.inf)
sim = mp.Simulation(
cell_size=cell_size, geometry=geometry, resolution=resolution
)
sim.init_sim()
prism_eps = sim.integrate_field_function([mp.Dielectric], lambda r, eps: eps)
print(f"epsilon-sum:, {abs(prism_eps)} (prism-gds)")
return prism_eps
# lots of tests, turned off by default since they run too long;
# rename to test_something to run these tests.
def bigtest_prism(self):
print("Testing Non-Convex Prism #1 using marching squares algorithm...")
d1_a = self.nonconvex_marching_squares(1, 208)
d1_b = self.nonconvex_marching_squares(1, 448)
d1_ref = 458.27922623563074 ## self.nonconvex_marching_squares(1,904)
self.assertLess(abs((d1_b - d1_ref) / d1_ref), abs((d1_a - d1_ref) / d1_ref))
print("Testing Non-Convex Prism #2 using marching squares algorithm...")
d2_a = self.nonconvex_marching_squares(2, 128)
d2_b = self.nonconvex_marching_squares(2, 256)
d2_ref = 506.79940504342534 ## self.nonconvex_marching_squares(2,516)
self.assertLess(abs((d2_b - d2_ref) / d2_ref), abs((d2_a - d2_ref) / d2_ref))
print("Testing Non-Convex Prism #3 using marching squares algorithm...")
d3_a = self.nonconvex_marching_squares(3, 164)
d3_b = self.nonconvex_marching_squares(3, 336)
d3_ref = 640.0738356076143 ## self.nonconvex_marching_squares(3,672)
self.assertLess(abs((d3_b - d3_ref) / d3_ref), abs((d3_a - d3_ref) / d3_ref))
print("Testing Convex Prism using marching squares algorithm...")
d = [
self.convex_marching_squares(92),
self.convex_marching_squares(192),
self.convex_marching_squares(392),
]
self.assertLess(d[1], d[0])
self.assertLess(d[2], d[1])
print("Testing Convex Prism #1 using circle formula (without symmetry)...")
r = 1.0458710786934182
d_nosym = [
self.convex_circle(51, r, False),
self.convex_circle(101, r, False),
self.convex_circle(201, r, False),
]
self.assertLess(d_nosym[1], d_nosym[0])
self.assertLess(d_nosym[2], d_nosym[1])
print("Testing Convex Prism #1 using circle formula (with symmetry)...")
d_sym = [
self.convex_circle(51, r, True),
self.convex_circle(101, r, True),
self.convex_circle(201, r, True),
]
self.assertLess(d_sym[1], d_sym[0])
self.assertLess(d_sym[2], d_sym[1])
self.assertAlmostEqual(d_nosym[0], d_sym[0], places=3)
self.assertAlmostEqual(d_nosym[1], d_sym[1], places=3)
self.assertAlmostEqual(d_nosym[2], d_sym[2], places=3)
print("Testing Convex Prism #2 using circle formula (without symmetry)...")
r = 1.2896871096581341
d_nosym = [
self.convex_circle(31, r, False),
self.convex_circle(61, r, False),
self.convex_circle(121, r, False),
]
self.assertLess(d_nosym[1], d_nosym[0])
self.assertLess(d_nosym[2], d_nosym[1])
print("Testing Convex Prism #2 using circle formula (with symmetry)...")
d_sym = [
self.convex_circle(31, r, True),
self.convex_circle(61, r, True),
self.convex_circle(121, r, True),
]
self.assertLess(d_sym[1], d_sym[0])
self.assertLess(d_sym[2], d_sym[1])
self.assertAlmostEqual(d_nosym[0], d_sym[0], places=3)
self.assertAlmostEqual(d_nosym[1], d_sym[1], places=3)
self.assertAlmostEqual(d_nosym[2], d_sym[2], places=3)
print("Testing Non-Convex Prism from GDSII file...")
d = self.spiral_gds()
d_ref = 455.01744881372224
self.assertAlmostEqual(d, d_ref, places=5)
def test_prism(self):
print("Testing Non-Convex Prism #3 using marching squares algorithm...")
d3_a = self.nonconvex_marching_squares(3, 164)
d3_b = self.nonconvex_marching_squares(3, 336)
d3_ref = 640.0738356076143 ## self.nonconvex_marching_squares(3,672)
self.assertLess(abs((d3_b - d3_ref) / d3_ref), abs((d3_a - d3_ref) / d3_ref))
self.assertLess(abs((d3_b - d3_ref) / d3_ref), 0.02)
if __name__ == "__main__":
unittest.main()
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