def test_geometric_objects_lattice_duplicates(self):
geometry_lattice = mp.Lattice(size=mp.Vector3(1, 7),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(math.sqrt(3) / 2, -0.5))
eps = 12
r = 0.2
geometry = [mp.Cylinder(r, material=mp.Medium(epsilon=eps))]
geometry = mp.geometric_objects_lattice_duplicates(geometry_lattice, geometry)
med = mp.Medium(epsilon=12)
expected = [
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=3.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=2.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=1.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=0.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-1.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-2.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-3.0)),
]
for exp, res in zip(expected, geometry):
self.assertEqual(exp.center, res.center)
self.assertEqual(exp.radius, res.radius)
def triangular_with_defect():
k_points = [mp.Vector3(),
mp.Vector3(0., 0.5),
mp.Vector3(-1 / 3, 1 / 3),
mp.Vector3()]
k_points = mp.interpolate(10, k_points)
geometry_lattice = mp.Lattice(size=mp.Vector3(5, 5),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(math.sqrt(3) / 2, -0.5))
geometry = [mp.Cylinder(0.25, material=gaas)]
geometry = mp.geometric_objects_lattice_duplicates(geometry_lattice, geometry)
defect = mp.Cylinder(0.2, material=gaas)
geometry.append(defect)
default_material = bcb
resolution = 32
mesh_size = 7
num_bands = 5
ms = mpb.ModeSolver(num_bands=num_bands,
k_points=k_points,
geometry=geometry,
geometry_lattice=geometry_lattice,
resolution=resolution,
default_material=default_material,
mesh_size=mesh_size)
return ms
def test_geometric_objects_lattice_duplicates(self):
geometry_lattice = mp.Lattice(size=mp.Vector3(1, 7),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(
math.sqrt(3) / 2, -0.5))
eps = 12
r = 0.2
geometry = [mp.Cylinder(r, material=mp.Medium(epsilon=eps))]
geometry = mp.geometric_objects_lattice_duplicates(
geometry_lattice, geometry)
med = mp.Medium(epsilon=12)
expected = [
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=3.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=2.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=1.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=0.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-1.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-2.0)),
mp.Cylinder(0.2, material=med, center=mp.Vector3(y=-3.0)),
]
for exp, res in zip(expected, geometry):
self.assertEqual(exp.center, res.center)
self.assertEqual(exp.radius, res.radius)
def test_point_defect_state(self):
ms = self.init_solver()
ms.geometry_lattice = mp.Lattice(size=mp.Vector3(5, 5))
ms.geometry = [mp.Cylinder(0.2, material=mp.Medium(epsilon=12))]
ms.geometry = mp.geometric_objects_lattice_duplicates(
ms.geometry_lattice, ms.geometry)
ms.geometry.append(mp.Cylinder(0.2, material=mp.air))
ms.resolution = 16
ms.k_points = [mp.Vector3(0.5, 0.5)]
ms.num_bands = 50
ms.run_tm()
mpb.fix_efield_phase(ms, 25)
mpb.output_efield_z(ms, 25)
mpb.fix_dfield_phase(ms, 25)
ms.get_dfield(25)
ms.compute_field_energy()
c = mp.Cylinder(1.0, material=mp.air)
e = ms.compute_energy_in_objects([c])
self.assertAlmostEqual(0.6227482574427817, e, places=3)
ms.num_bands = 1
ms.target_freq = (0.2812 + 0.4174) / 2
ms.tolerance = 1e-8
ms.run_tm()
expected_brd = [
((0.37730041222979477, mp.Vector3(0.5, 0.5, 0.0)),
(0.37730041222979477, mp.Vector3(0.5, 0.5, 0.0))),
]
self.check_band_range_data(expected_brd, ms.band_range_data)
old_geometry = ms.geometry # save the 5x5 grid with a missing rod
def rootfun(eps):
ms.geometry = old_geometry + [
mp.Cylinder(0.2, material=mp.Medium(epsilon=eps))
]
ms.run_tm()
return ms.get_freqs()[0] - 0.314159
rooteps = ridder(rootfun, 1, 12)
rootval = rootfun(rooteps)
self.assertAlmostEqual(5.288830111797463, rooteps, places=3)
self.assertAlmostEqual(9.300716530269426e-9, rootval, places=3)
# within the band gap, much like the analogous waveguide in a square
# lattice of rods (see "Photonic Crystals" by Joannopoulos et al.).
supercell_y = 7 # the (odd) number of lateral supercell periods
geometry_lattice = mp.Lattice(size=mp.Vector3(1, supercell_y),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(math.sqrt(3) / 2, -0.5))
eps = 12 # the dielectric constant of the rods
r = 0.2 # the rod radius in the bulk crystal
geometry = [mp.Cylinder(r, material=mp.Medium(epsilon=eps))]
# duplicate the bulk crystal rods over the supercell:
geometry = mp.geometric_objects_lattice_duplicates(geometry_lattice, geometry)
# add a rod of air, to erase a row of rods and form a waveguide:
geometry += [mp.Cylinder(r, material=mp.air)]
Gamma = mp.Vector3()
K_prime = mp.lattice_to_reciprocal(mp.Vector3(0.5),
geometry_lattice) # edge of Brillouin zone.
k_points = mp.interpolate(4, [Gamma, K_prime])
# the bigger the supercell, the more bands you need to compute to get
# to the defect modes (the lowest band is "folded" supercell_y times):
extra_bands = 5 # number of extra bands to compute above the gap
num_bands = supercell_y + extra_bands
resolution = 32
print_heading('Anisotropic complete 2d gap')
ms.geometry = [mp.Cylinder(0.3, material=mp.Medium(epsilon_diag=mp.Vector3(1, 1, 12)))]
ms.default_material = mp.Medium(epsilon_diag=mp.Vector3(12, 12, 1))
ms.num_bands = 8
ms.run() # just use run, instead of run_te or run_tm, to find the complete gap
# Finding a Point-defect State
print_heading('5x5 point defect')
ms.geometry_lattice = mp.Lattice(size=mp.Vector3(5, 5))
ms.geometry = [mp.Cylinder(0.2, material=mp.Medium(epsilon=12))]
ms.geometry = mp.geometric_objects_lattice_duplicates(ms.geometry_lattice, ms.geometry)
ms.geometry.append(mp.Cylinder(0.2, material=mp.air))
ms.resolution = 16
ms.k_points = [mp.Vector3(0.5, 0.5)]
ms.num_bands = 50
ms.run_tm()
mpb.output_efield_z(ms, 25)
ms.get_dfield(25) # compute the D field for band 25
ms.compute_field_energy() # compute the energy density from D
c = mp.Cylinder(1.0, material=mp.air)
print("energy in cylinder: {}".format(ms.compute_energy_in_objects([c])))
freqss = [] gapss = [] for index in integer_list: # Loop over kz_list theta_list = [] theta2_list = [] geometry = [] geometry_lattice = mp.Lattice(size=mp.Vector3(1, 1)) ms = mpb.ModeSolver(num_bands=num_bands, k_points=k_vectors[index], geometry=geometry, geometry_lattice=geometry_lattice, resolution=resolution) # Create ModeSolver object ms.default_material = mp.Medium(epsilon = pc_epsilon) # Define background material to be that of the photonic crystal if question == 'y': ms.target_freq = omega_prime ms.geometry_lattice = mp.Lattice(size=mp.Vector3(L, L)) # Creates an L x L lattice ms.geometry = [mp.Block(material=mp.air, size=mp.Vector3(r,r,mp.inf))] # One hole at each lattice point ms.geometry = mp.geometric_objects_lattice_duplicates(ms.geometry_lattice, ms.geometry) # Duplicate geometry all over the lattice if block == 'y': ms.geometry.append(mp.Block(material=mp.Medium(epsilon=core_epsilon), size=mp.Vector3(l_core, l_core, mp.inf))) # Inserts core into the center of the photonic crystal ms.run() freqs = ms.all_freqs freqss.append(freqs) gaps = ms.gap_list # List of band gaps and their boundaries gapss.append(gaps) real_gaps = [] # List of gap-midgap ratios, expressed as percentages gap_bounds = [] gap_bounds_freqs = [] midgaps = [] midgap_freqs = []