High-Q silicon resonator¶

# standard python imports
import numpy as np
import matplotlib.pyplot as plt

# tidy3D import
import tidy3d as td
from tidy3d import web

nm = 1e-3

# define the frequencies we want to measure
Nfreq = 1000
wavelengths = nm * np.linspace(1050, 1400, Nfreq)
freqs = td.constants.C_0 / wavelengths

# define the frequency center and width of our pulse
freq0 = freqs[len(freqs) // 2]
freqw = freqs[0] - freqs[-1]

# Define material properties
n_SiO2 = 1.46
n_Si = 3.52
SiO2 = td.Medium(permittivity=n_SiO2**2)
Si = td.Medium(permittivity=n_Si**2)

# space between resonators and source
spc = 1.5

# geometric parameters
Px = Py = P = 650 * nm  # periodicity in x and y
t = 260 * nm  # thickness of silcon
g = 80 * nm  # gap size
L = 480 * nm  # length in x
w_sum = 400 * nm  # sum of lengths in y

# resolution (should be commensurate with periodicity)
dl = P / 32

# computes widths in y (w1 and w2) given the difference in lengths in y and the sum of lengths
def calc_ws(delta):
    """delta is a tunable parameter used to break symmetry.
    w_sum = w1 + w2
    delta = w1 - w2
    w_sum + delta = 2 * w1
    """
    w1 = (w_sum + delta) / 2
    w2 = w_sum - w1
    return w1, w2

# total size in z and [x,y,z]
Lz = spc + t + t + spc
sim_size = [Px, Py, Lz]

# sio2 substrate
substrate = td.Structure(
    geometry=td.Box(
        center=[0, 0, -Lz / 2],
        size=[td.inf, td.inf, 2 * (spc + t)],
    ),
    medium=SiO2,
    name="substrate",
)

# creates a list of structures given a value of 'delta'
def geometry(delta):
    w1, w2 = calc_ws(delta)
    center_y = (w1 - w2) / 2.0

    cell1 = td.Structure(
        geometry=td.Box(
            center=[0, center_y + (g + w1) / 2.0, t / 2.0],
            size=[L, w1, t],
        ),
        medium=Si,
        name="cell1",
    )

    cell2 = td.Structure(
        geometry=td.Box(
            center=[0, center_y - (g + w2) / 2.0, t / 2.0],
            size=[L, w2, t],
        ),
        medium=Si,
        name="cell2",
    )

    return [substrate, cell1, cell2]

# time dependence of source
gaussian = td.GaussianPulse(freq0=freq0, fwidth=freqw)

# plane wave source
source = td.PlaneWave(
    source_time=gaussian,
    direction="-",
    size=(td.inf, td.inf, 0),
    center=(0, 0, Lz / 2 - spc + 2 * dl),
    pol_angle=0.0,
)

# Simulation run time.  Note you need to run a long time to calculate high Q resonances.
run_time = 7e-12

# monitor fields on other side of structure (substrate side) at range of frequencies
monitor = td.FluxMonitor(
    center=[0.0, 0.0, -Lz / 2 + spc - 2 * dl],
    size=[td.inf, td.inf, 0],
    freqs=freqs,
    name="flux",
)

grid_spec = td.GridSpec(
    grid_x=td.UniformGrid(dl=dl),
    grid_y=td.UniformGrid(dl=dl),
    grid_z=td.AutoGrid(min_steps_per_wvl=32),
)

# normalizing run (no Si) to get baseline transmission vs freq
# can be run for shorter time as there are no resonances
sim_empty = td.Simulation(
    size=sim_size,
    grid_spec=grid_spec,
    structures=[substrate],
    sources=[source],
    monitors=[monitor],
    run_time=run_time / 10,
    boundary_spec=td.BoundarySpec(
        x=td.Boundary.periodic(), y=td.Boundary.periodic(), z=td.Boundary.pml()
    ),
)

# run with delta = 0
sim_d0 = td.Simulation(
    size=sim_size,
    grid_spec=grid_spec,
    structures=geometry(0),
    sources=[source],
    monitors=[monitor],
    run_time=run_time,
    boundary_spec=td.BoundarySpec(
        x=td.Boundary.periodic(), y=td.Boundary.periodic(), z=td.Boundary.pml()
    ),
)

# run with delta = 20nm
sim_d20 = td.Simulation(
    size=sim_size,
    grid_spec=grid_spec,
    structures=geometry(20 * nm),
    sources=[source],
    monitors=[monitor],
    run_time=run_time,
    boundary_spec=td.BoundarySpec(
        x=td.Boundary.periodic(), y=td.Boundary.periodic(), z=td.Boundary.pml()
    ),
)