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from __future__ import division
import math
import meep as mp
from meep import mpb
from scipy.optimize import minimize_scalar
from scipy.optimize import ridder
def print_heading(h):
stars = "*" * 10
print("{0} {1} {0}".format(stars, h))
# Our First Band Structure
print_heading("Square lattice of rods in air")
num_bands = 8
k_points = [mp.Vector3(), # Gamma
mp.Vector3(0.5), # X
mp.Vector3(0.5, 0.5), # M
mp.Vector3()] # Gamma
k_points = mp.interpolate(4, k_points)
geometry = [mp.Cylinder(0.2, material=mp.Medium(epsilon=12))]
geometry_lattice = mp.Lattice(size=mp.Vector3(1, 1))
resolution = 32
ms = mpb.ModeSolver(num_bands=num_bands,
k_points=k_points,
geometry=geometry,
geometry_lattice=geometry_lattice,
resolution=resolution)
print_heading("Square lattice of rods: TE bands")
ms.run_te()
print_heading("Square lattice of rods: TM bands")
ms.run_tm()
print_heading("Square lattice of rods: TM, w/efield")
ms.run_tm(mpb.output_efield_z)
print_heading("Square lattice of rods: TE, w/hfield & dpwr")
ms.run_te(mpb.output_at_kpoint(mp.Vector3(0.5), mpb.output_hfield_z, mpb.output_dpwr))
# Bands of a Triangular Lattice
print_heading("Triangular lattice of rods in air")
ms.geometry_lattice = mp.Lattice(size=mp.Vector3(1, 1),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(math.sqrt(3) / 2, -0.5))
ms.k_points = [mp.Vector3(), # Gamma
mp.Vector3(y=0.5), # M
mp.Vector3(-1 / 3, 1 / 3), # K
mp.Vector3()] # Gamma
ms.k_points = mp.interpolate(4, k_points)
ms.run_tm()
# Maximizing the First TM Gap
print_heading('Maximizing the first TM gap')
def first_tm_gap(r):
ms.geometry = [mp.Cylinder(r, material=mp.Medium(epsilon=12))]
ms.run_tm()
return -1 * ms.retrieve_gap(1)
ms.num_bands = 2
ms.mesh_size = 7
result = minimize_scalar(first_tm_gap, method='bounded', bounds=[0.1, 0.5], tol=0.1)
print("radius at maximum: {}".format(result.x))
print("gap size at maximum: {}".format(result.fun * -1))
ms.mesh_size = 3 # Reset to default value of 3
# A Complete 2D Gap with an Anisotropic Dielectric
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])))
print_heading('5x5 point defect, targeted solver')
ms.num_bands = 1 # only need to compute a single band, now!
ms.target_freq = (0.2812 + 0.4174) / 2
ms.tolerance = 1e-8
ms.run_tm()
# Tuning the Point-defect Mode
print_heading('Tuning the 5x5 point defect')
old_geometry = ms.geometry # save the 5x5 grid with a missing rod
def rootfun(eps):
# add the cylinder of epsilon = eps to the old geometry:
ms.geometry = old_geometry + [mp.Cylinder(0.2, material=mp.Medium(epsilon=eps))]
ms.run_tm() # solve for the mode (using the targeted solver)
print("epsilon = {} gives freq. = {}".format(eps, ms.get_freqs()[0]))
return ms.get_freqs()[0] - 0.314159 # return 1st band freq. - 0.314159
rooteps = ridder(rootfun, 1, 12)
print("root (value of epsilon) is at: {}".format(rooteps))
rootval = rootfun(rooteps)
print("root function at {} = {}".format(rooteps, rootval))
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