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import meep as mp
from meep import mpb
# Compute modes of a rectangular Si strip waveguide on top of oxide.
# Note that you should only pay attention, here, to the guided modes,
# which are the modes whose frequency falls under the light line --
# that is, frequency < beta / 1.45, where 1.45 is the SiO2 index.
# Since there's no special lengthscale here, I'll just
# use microns. In general, if you use units of x, the frequencies
# output are equivalent to x/lambda# so here, the freqeuncies will be
# output as um/lambda, e.g. 1.5um would correspond to the frequency
# 1/1.5 = 0.6667.
w = 0.3 # Si width (um)
h = 0.25 # Si height (um)
Si = mp.Medium(index=3.45)
SiO2 = mp.Medium(index=1.45)
# Define the computational cell. We'll make x the propagation direction.
# the other cell sizes should be big enough so that the boundaries are
# far away from the mode field.
sc_y = 2 # supercell width (um)
sc_z = 2 # supercell height (um)
geometry_lattice = mp.Lattice(size=mp.Vector3(0, sc_y, sc_z))
# define the 2d blocks for the strip and substrate
geometry = [
mp.Block(
size=mp.Vector3(mp.inf, mp.inf, 0.5 * (sc_z - h)),
center=mp.Vector3(z=0.25 * (sc_z + h)),
material=SiO2,
),
mp.Block(size=mp.Vector3(mp.inf, w, h), material=Si),
]
# The k (i.e. beta, i.e. propagation constant) points to look at, in
# units of 2*pi/um. We'll look at num_k points from k_min to k_max.
num_k = 9
k_min = 0.1
k_max = 3.0
k_points = mp.interpolate(num_k, [mp.Vector3(k_min), mp.Vector3(k_max)])
resolution = 32 # pixels/um
# Increase this to see more modes. (The guided ones are the ones below the
# light line, i.e. those with frequencies < kmag / 1.45, where kmag
# is the corresponding column in the output if you grep for "freqs:".)
num_bands = 4
filename_prefix = "strip-" # use this prefix for output files
ms = mpb.ModeSolver(
geometry_lattice=geometry_lattice,
geometry=geometry,
k_points=k_points,
resolution=resolution,
num_bands=num_bands,
filename_prefix=filename_prefix,
)
def main():
# compute num_bands lowest frequencies as a function of k. Also display
# "parities", i.e. whether the mode is symmetric or anti_symmetric
# through the y=0 and z=0 planes.
ms.run(mpb.display_yparities, mpb.display_zparities)
###########################################################################
# Above, we outputted the dispersion relation: frequency (omega) as a
# function of wavevector kx (beta). Alternatively, you can compute
# beta for a given omega -- for example, you might want to find the
# modes and wavevectors at a fixed wavelength of 1.55 microns. You
# can do that using the find_k function:
omega = 1 / 1.55 # frequency corresponding to 1.55um
# Output the x component of the Poynting vector for num_bands bands at omega
ms.find_k(
mp.NO_PARITY,
omega,
1,
num_bands,
mp.Vector3(1),
1e-3,
omega * 3.45,
omega * 0.1,
omega * 4,
mpb.output_poynting_x,
mpb.display_yparities,
mpb.display_group_velocities,
)
if __name__ == "__main__":
main()
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