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import math
import meep as mp
from meep import mpb
# A line_defect waveguide in a 2d triangular lattice of dielectric
# rods (c.f. tri_rods.ctl), formed by a row of missing rods along the
# "x" direction. (Here, "x" and "y" refer to the first and second
# basis directions.) This structure supports a single guided band
# 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
ms = mpb.ModeSolver(
geometry_lattice=geometry_lattice,
geometry=geometry,
k_points=k_points,
num_bands=num_bands,
resolution=resolution,
)
def main():
# Compute the TM modes, outputting the Ez field in the *middle* of the
# band. (In general, the guided mode in such an air defect may have
# exited the gap by the time it reaches the edge of the Brillouin
# zone at K_prime.)
ms.run_tm(
mpb.output_at_kpoint(k_points[len(k_points) // 2]),
ms.fix_efield_phase,
mpb.output_efield_z,
)
if __name__ == "__main__":
main()
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