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import math
import meep as mp
from meep import mpb
# Photonic crystal slab consisting of a triangular lattice of air
# holes in a finite_thickness dielectric slab, optionally with a
# substrate on one side of the slab. See the paper: S. G. Johnson,
# S. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski,
# "Guided modes in photonic crystal slabs," PRB 60, 5751 (August
# 1999).
# Note that this structure has mirror symmetry throught the z=0 plane,
# and we are looking at k_vectors in the xy plane only. Thus, we can
# break up the modes into even and odd (analogous to TE and TM), using
# the run_zeven and run_zodd functions.
h = 0.5 # the thickness of the slab
eps = 12.0 # the dielectric constant of the slab
loweps = 1.0 # the dielectric constant of the substrate
r = 0.3 # the radius of the holes
supercell_h = 4 # height of the supercell
# triangular lattice with vertical supercell:
geometry_lattice = mp.Lattice(
size=mp.Vector3(1, 1, supercell_h),
basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
basis2=mp.Vector3(math.sqrt(3) / 2, -0.5),
)
geometry = [
mp.Block(
material=mp.Medium(epsilon=loweps),
center=mp.Vector3(z=0.25 * supercell_h),
size=mp.Vector3(mp.inf, mp.inf, 0.5 * supercell_h),
),
mp.Block(material=mp.Medium(epsilon=eps), size=mp.Vector3(mp.inf, mp.inf, h)),
mp.Cylinder(r, material=mp.air, height=supercell_h),
]
# 1st Brillouin zone of a triangular lattice:
Gamma = mp.Vector3()
M = mp.Vector3(y=0.5)
K = mp.Vector3(1 / -3, 1 / 3)
only_K = False # run with only_K=true to only do this k_point
k_interp = 4 # the number of k points to interpolate
k_points = [K] if only_K else mp.interpolate(k_interp, [Gamma, M, K, Gamma])
resolution = mp.Vector3(32, 32, 16)
num_bands = 9
ms = mpb.ModeSolver(
geometry_lattice=geometry_lattice,
geometry=geometry,
resolution=resolution,
num_bands=num_bands,
k_points=k_points,
)
def main():
# Run even and odd bands, outputting fields only at the K point:
if loweps == 1.0:
# we only have even/odd classification for symmetric structure
ms.run_zeven(mpb.output_at_kpoint(K, mpb.output_hfield_z))
ms.run_zodd(mpb.output_at_kpoint(K, mpb.output_dfield_z))
else:
ms.run(mpb.output_at_kpoint(K, mpb.output_hfield_z), mpb.display_zparities)
ms.display_eigensolver_stats()
if __name__ == "__main__":
main()
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