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from __future__ import division
import math
import meep as mp
from meep import mpb
# A honeycomb lattice of dielectric rods in air. (This structure has
# a complete (overlapping TE/TM) band gap.) A honeycomb lattice is really
# just a triangular lattice with two rods per unit cell, so we just
# take the lattice, k_points, etcetera from mpb_tri_rods.py.
r = 0.14 # the rod radius
eps = 12 # the rod dielectric constant
# triangular lattice:
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))
# Two rods per unit cell, at the correct positions to form a honeycomb
# lattice, and arranged to have inversion symmetry:
geometry = [mp.Cylinder(r, center=mp.Vector3(1 / 6, 1 / 6), height=mp.inf,
material=mp.Medium(epsilon=eps)),
mp.Cylinder(r, center=mp.Vector3(1 / -6, 1 / -6), height=mp.inf,
material=mp.Medium(epsilon=eps))]
# The k_points list, for the Brillouin zone of a triangular lattice:
k_points = [
mp.Vector3(), # Gamma
mp.Vector3(y=0.5), # M
mp.Vector3(1 / -3, 1 / 3), # K
mp.Vector3() # Gamma
]
k_interp = 4 # number of k_points to interpolate
k_points = mp.interpolate(k_interp, k_points)
resolution = 32
num_bands = 8
ms = mpb.ModeSolver(
geometry_lattice=geometry_lattice,
geometry=geometry,
k_points=k_points,
resolution=resolution,
num_bands=num_bands
)
def main():
ms.run_tm()
ms.run_te()
# Since there is a complete gap, we could instead see it just by using:
# run()
# The gap is between bands 12 and 13 in this case. (Note that there is
# a false gap between bands 2 and 3, which disappears as you increase the
# k_point resolution.)
if __name__ == '__main__':
main()
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