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Example Library / Mode Solver / Using the mode solver for optical mode analysis

Using the mode solver for optical mode analysis

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This tutorial shows how to use the mode solver plugin in Tidy3D.

# standard python imports
from __future__ import annotations

import matplotlib.pylab as plt
import numpy as np

# tidy3D import
import tidy3d as td
import tidy3d.web as web
from tidy3d.constants import C_0
from tidy3d.plugins.mode import ModeSolver

Setup

We first set up the mode solver with information about our system. We start by setting parameters

# size of simulation domain
Lx, Ly, Lz = 6, 6, 6
dl = 0.05

# waveguide information
wg_width = 1.5
wg_height = 1.0
wg_permittivity = 4.0

# central frequency
wvl_um = 2.0
freq0 = C_0 / wvl_um
fwidth = freq0 / 3

# run_time in ps
run_time = 1e-12

# automatic grid specification
grid_spec = td.GridSpec.auto(min_steps_per_wvl=20, wavelength=wvl_um)

Then we set up a simulation, in this case including a straight waveguide and periodic boundary conditions. Note that Tidy3D warns us that we have not added any sources in our Simulation object, however for purposes of mode solving it is not necessary.

waveguide = td.Structure(
    geometry=td.Box(size=(wg_width, td.inf, wg_height)),
    medium=td.Medium(permittivity=wg_permittivity),
)

sim = td.Simulation(
    size=(Lx, Ly, Lz),
    grid_spec=grid_spec,
    structures=[waveguide],
    run_time=run_time,
    boundary_spec=td.BoundarySpec.all_sides(boundary=td.Periodic()),
)

ax = sim.plot(z=0)
plt.show()

Initialize Mode Solver

With our system defined, we can now create our mode solver. We first need to specify on what plane we want to solve the modes using a td.Box() object.

plane = td.Box(center=(0, 0, 0), size=(4, 0, 3.5))

The mode solver can now compute the modes given a ModeSpec object that specifies everything about the modes we’re looking for, for example:

  • num_modes: how many modes to compute.

  • target_neff: float, default=None, initial guess for the effective index of the mode; if not specified, the modes with the largest real part of the effective index are computed.

The full list of specification parameters can be found here.

mode_spec = td.ModeSpec(
    num_modes=3,
    target_neff=2.0,
)

We can also specify a list of frequencies at which to solve for the modes.

num_freqs = 11
f0_ind = num_freqs // 2
freqs = np.linspace(freq0 - fwidth / 2, freq0 + fwidth / 2, num_freqs)

Finally, we can initialize the ModeSolver, and call the solve method.

mode_solver = ModeSolver(
    simulation=sim,
    plane=plane,
    mode_spec=mode_spec,
    freqs=freqs,
)
mode_data = mode_solver.solve()

We can also summarize useful mode information using to_dataframe(). Note that the group index was not computed; this can be included by setting group_index_step=True in the ModeSpec.

mode_data.to_dataframe()
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