# How do I calculate the mode polarization fraction?#

Date

Category

2023-12-18 21:59:37

Mode Solver

You can follow the example below to obtain the 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 polarization fraction.
print("TE polarization fraction:")
print(np.asarray(mode_data.pol_fraction['te']).squeeze())

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


The TE and TM polarization fractions are defined as the field intensity along the first or the second of the two tangential axes. More precisely, if E1 and E2 are the electric field components along the two tangential axes, the TE fraction is defined as integrate(E1.abs**2) / integrate(E1.abs**2 + E2.abs**2), and the TM fraction is equal to one minus the TE fraction. The tangential axes are defined by popping the normal axis from the list of x, y, z, so e.g. x and z for propagation in the y direction.
For more details on how to set up, run and visualize the solver results, please refer to this notebook.