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from __future__ import division
import math
import meep as mp
from meep import mpb
# 2d system: triangular lattice of air holes in dielectric
# This structure has a complete band gap (i.e. a gap in both TE and TM
# simultaneously) for a hole radius of 0.45a and a dielectric constant of
# 12. (See, e.g., the book "Photonic Crystals" by Joannopoulos et al.)
# first, define the lattice vectors and k-points for a 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))
kz = 0 # use non-zero kz to consider vertical propagation
k_points = [
mp.Vector3(z=kz), # Gamma
mp.Vector3(0, 0.5, kz), # M
mp.Vector3(1 / -3, 1 / 3, kz), # K
mp.Vector3(z=kz) # Gamma
]
k_interp = 4
k_points = mp.interpolate(k_interp, k_points)
# Now, define the geometry, etcetera:
eps = 12 # the dielectric constant of the background
r = 0.45 # the hole radius
default_material = mp.Medium(epsilon=eps)
geometry = [mp.Cylinder(r, material=mp.air)]
resolution = 32
num_bands = 8
ms = mpb.ModeSolver(
geometry_lattice=geometry_lattice,
geometry=geometry,
k_points=k_points,
default_material=default_material,
resolution=resolution,
num_bands=num_bands
)
def main():
if kz == 0:
ms.run_te()
ms.run_tm()
else:
ms.run() # if kz != 0 there are no purely te and tm bands
if __name__ == '__main__':
main()
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