# How do I calculate the waveguide mode polarization fraction?#

Date

Category

2023-12-18 22:09:16

Mode Solver

You can follow the example below to obtain the waveguide mode polarization fraction of the optical modes calculated using the Tidy3D mode solver. We have considered a 500 x 220 nm silicon-on-insulator (SOI) waveguide operating at 1.55 $$\mu$$m.

import numpy as np
from tidy3d.plugins.mode import ModeSolver
from tidy3d.plugins.mode.web import run as run_mode_solver

# Define the waveguide.
waveguide = tidy3d.Structure(
geometry=tidy3d.Box(size=(tidy3d.inf, 0.5, 0.22)),
medium=tidy3d.Medium(permittivity=3.47**2),
)

# Build a simulation object including the waveguide.
sim = tidy3d.Simulation(
size=(10, 2.5, 1.5),
grid_spec=tidy3d.GridSpec.auto(min_steps_per_wvl=20, wavelength=1.55),
structures=[waveguide],
run_time=1e-12,
boundary_spec=tidy3d.BoundarySpec.all_sides(boundary=tidy3d.PML()),
)

# Plane where we want to solve the modes.
plane = tidy3d.Box(center=(0, 0, 0), size=(0, 2.5, 1.5))

# Mode specification.
mode_spec = tidy3d.ModeSpec(
num_modes=4,
target_neff=3.47,
group_index_step=True,
)

# Build the mode solver.
freq0 = tidy3d.C_0 / 1.55
mode_solver = ModeSolver(
simulation=sim,
plane=plane,
mode_spec=mode_spec,
freqs=[freq0],
)

# Run the server-side mode solver.
mode_data = run_mode_solver(mode_solver)

# Get the mode waveguide polarization fraction.
print("TE waveguide polarization fraction:")
print(np.asarray(mode_data.pol_fraction_waveguide['te']).squeeze())

print("TM waveguide polarization fraction:")
print(np.asarray(mode_data.pol_fraction_waveguide['tm']).squeeze())


The TE and TM polarization fraction using the waveguide definition. If E1 and E2 are the electric field components along the two tangential axes and En is the component along the propagation direction, the TE fraction is defined as 1 - integrate(En.abs**2) / integrate(E1.abs**2 + E2.abs**2 + En.abs**2), and the TM fraction is defined as 1 - integrate(Hn.abs**2) / integrate(H1.abs**2 + H2.abs**2 + Hn.abs**2), with H denoting the magnetic field components.
For more details on how to set up, run and visualize the solver results, please refer to this notebook.