Author: Carson Valdez, Graduate Student at Stanford University
Here we model the quasi fundamental TE mode of orthogonal integrated waveguides with the horizontal and vertical polarization states with a normally incident centered free space beam. Using Tidy3D finite-difference time-domain (FDTD), simulations of electromagnetic waves incident on such a PSGC model the coupling to the four ports of the coupler as a function of polarization angle.
[1]:
########################################## Import Libraries #########################################
#####################################################################################################
import numpy as np
import matplotlib.pyplot as plt
import tidy3d as td
from tidy3d import web
from tidy3d.plugins.mode import ModeSolver
#####################################################################################################
#####################################################################################################
13:25:03 EST WARNING: Configuration found in legacy location '~/.tidy3d'. Consider running 'tidy3d config migrate'.
Design Parameters¶
Define Global Parameters for the Simulation
[2]:
####################################### Wavelength Parameters #######################################
#####################################################################################################
lda0 = 1.55 # Central wavelength
freq0 = td.C_0 / lda0 # Central frequency
ldas = np.linspace(1.5, 1.6, 101) # Wavelength range
freqs = td.C_0 / ldas # Frequency range
fwidth = 0.5 * (np.max(freqs) - np.min(freqs)) # Width of the source frequency range
######################################### Material Libraries ########################################
#####################################################################################################
si = td.material_library["cSi"]["Palik_Lossless"] # Load Silicon Library
sio2 = td.material_library["SiO2"]["Palik_Lossless"] # Load Silicon Dioxide Library
######################################### Device Parameters #########################################
#####################################################################################################
w_wg = 13.0 # Waveguide Width
t_wg = 0.22 # Silicon Layer Thickness
l_wg = 5.0 # I/O straight waveguide length
ff = 0.5 # Grating Fill Factor
pitch = 0.556 # Grating Pitch
Ng = 23 # Number of Grating Periods
t_box = 3.0 # Buried Oxide Thickness
t_sub = 1.0 # Substrate Thickness (Arbitrary)
t_clad = 4.0 # Cladding Thickness
t_etch = 0.07 # Etch Depth
w_etch = ff*pitch # Etch Width
w0 = 5.2 # Beam_Waist
theta = 0 # Beam Angle 1
phi = 0 # Beam Angle 2
pol_angle = 0 # Polarization Angle (0 = Ex, np.pi = Ey)
inf_eff = 1000 # Effective infinity
#####################################################################################################
#####################################################################################################
Lx = 2*l_wg+w_wg # simulation domain size in x direction
Ly = 2*l_wg+w_wg # simulation domain size in y direction
Lz = t_sub + t_clad + t_box + t_wg # simulation domain size in z direction
sim_size = (Lx, Ly, Lz)
Geometry¶
Define the Geometric Structure
[3]:
######################################### Generate Geometry #########################################
#####################################################################################################
Substrate = td.Structure(
geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -inf_eff),
rmax=(inf_eff, inf_eff, -t_wg/2 - t_box)),
medium=si,
)
Buried_Ox = td.Structure(
geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -t_wg/2 - t_box),
rmax=(inf_eff, inf_eff, -t_wg/2)),
medium=sio2,
)
Cladding = td.Structure(
geometry=td.Box.from_bounds(rmin=(-inf_eff, -inf_eff, -t_wg/2),
rmax=(inf_eff, inf_eff, t_wg/2 + t_clad + inf_eff)),
medium=sio2,
)
Waveguide_Horz = td.Structure(
geometry=td.Box.from_bounds(rmin=(-inf_eff, -w_wg/2, -t_wg/2),
rmax=(inf_eff, w_wg/2, t_wg/2)),
medium=si,
)
Waveguide_Vert = td.Structure(
geometry=td.Box.from_bounds(rmin=(-w_wg/2, -inf_eff, -t_wg/2),
rmax=(w_wg/2, inf_eff, t_wg/2)),
medium=si,
)
PSGC = [Substrate, Buried_Ox, Cladding, Waveguide_Horz, Waveguide_Vert]
#####################################################################################################
#####################################################################################################
for i in range(Ng):
for j in range(Ng):
etch = td.Structure(
geometry=td.Box.from_bounds(rmin=( (i-int((Ng-1)/2))*pitch - w_etch/2, (j-int((Ng-1)/2))*pitch - w_etch/2, t_wg/2-t_etch),
rmax=( (i-int((Ng-1)/2))*pitch + w_etch/2, (j-int((Ng-1)/2))*pitch + w_etch/2, t_wg/2)),
medium=sio2,
)
PSGC.append(etch)
#####################################################################################################
#####################################################################################################
Source, Monitors, and Meshing¶
Define a normally incident, centered gaussian beam source along with mode monitors at each of the ports of the PSGC. Field monitors are used to record cross sections of the simulated fields. Lastly a mesh override is defined over the full silicon layer.
[4]:
########################################## Generate Source ##########################################
#####################################################################################################
pulse = td.GaussianPulse(freq0=freq0, fwidth=fwidth)
# Source definition
gauss_source = td.GaussianBeam(
center=(0, 0, t_wg + 2),
size=(Lx, Ly, 0),
source_time=pulse,
direction='-',
pol_angle=pol_angle,
angle_theta=theta,
angle_phi=phi,
waist_radius=w0,
waist_distance=0,
name="gauss_source",
)
########################################### Mode Monitors ###########################################
#####################################################################################################
mode_spec = td.ModeSpec(num_modes=5, target_neff=3.5, group_index_step = True, )
left = td.ModeMonitor(
center=(-Lx/2 + 1, 0, t_wg/2),
size=(0, w_wg + 5, 6 * t_wg),
freqs=freqs,
mode_spec=mode_spec,
name="left",
)
right = td.ModeMonitor(
center=(Lx/2 - 1, 0, t_wg/2),
size=(0, w_wg + 5, 6 * t_wg),
freqs=freqs,
mode_spec=mode_spec,
name="right",
)
top = td.ModeMonitor(
center=(0, Ly/2 - 1, t_wg/2),
size=(w_wg + 5, 0, 6 * t_wg),
freqs=freqs,
mode_spec=mode_spec,
name="top",
)
bot = td.ModeMonitor(
center=(0, -Ly/2 + 1, t_wg/2),
size=(w_wg + 5, 0, 6 * t_wg),
freqs=freqs,
mode_spec=mode_spec,
name="bot",
)
########################################### Field Monitors ##########################################
#####################################################################################################
XY_cross = td.FieldMonitor(
center=(0, 0, t_wg/2), size=(td.inf, td.inf, 0), freqs=[freq0], name="XY_cross"
)
XZ_cross = td.FieldMonitor(
center=(0, 0, t_wg/2), size=(td.inf, 0, td.inf), freqs=[freq0], name="XZ_cross"
)
YZ_cross = td.FieldMonitor(
center=(0, 0, t_wg/2), size=(0, td.inf, td.inf), freqs=[freq0], name="YZ_cross"
)
############################################ Fine Meshing ###########################################
#####################################################################################################
override_gc = td.MeshOverrideStructure(
name = 'override_gc',
geometry = td.Box(center = [0, 0, 0], size = [td.inf, td.inf, 6*t_wg]),
dl = [0.02, 0.02, 0.02],
)
Set Up Simulation¶
[5]:
run_time = 2e-12 # simulation run time
# construct simulation
sim = td.Simulation(
center=(0, 0, t_wg/2),
size=sim_size,
grid_spec = td.GridSpec(grid_x = td.AutoGrid(min_steps_per_wvl = 20, dl_min = 0), grid_y = td.AutoGrid(min_steps_per_wvl = 20, dl_min = 0), grid_z = td.AutoGrid(min_steps_per_wvl = 20, dl_min = 0), wavelength = lda0, override_structures = [override_gc], ),
structures=PSGC,
sources=[gauss_source],
monitors=[left, right, top, bot, XY_cross, XZ_cross, YZ_cross],
run_time=run_time,
version = '2.10.0',
subpixel = td.SubpixelSpec(pec = td.PECConformal(), ),
medium=sio2,
)
sim.plot_eps(z = t_wg/2 - t_etch/2, freq=freq0, vlim = (-10, 10), hlim = (-10, 10))
sim.plot_eps(y=0, freq=freq0, vlim = (-4, 4), hlim = (-10, 10))
plt.show()
13:25:04 EST WARNING: More than 200 structures use the same medium. For performance, use a 'GeometryGroup' or boolean operations to combine geometries that share a medium.
[6]:
sim.plot_3d()
Modal Analysis¶
Simulate the mode profiles at each of the output ports to determine the fundamental mode index.
[7]:
mode_spec = td.ModeSpec(num_modes=5, target_neff=3.5, group_index_step = True, )
mode_solver = ModeSolver(
simulation=sim,
plane=td.Box(center=left.center, size=left.size),
mode_spec=mode_spec,
freqs=[freq0],
)
mode_data = mode_solver.solve()
13:25:05 EST WARNING: Use the remote mode solver with subpixel averaging for better accuracy through 'tidy3d.web.run(...)' or the deprecated 'tidy3d.plugins.mode.web.run(...)'.
Plot Modes¶
[8]:
mode_idx = 0
f, (ax1, ax2, ax3) = plt.subplots(3, 1, tight_layout=True, figsize=(15, 7))
abs(mode_data.Ex.isel(mode_index=mode_idx)).plot(x="y", y="z", ax=ax1, cmap="magma")
abs(mode_data.Ey.isel(mode_index=mode_idx)).plot(x="y", y="z", ax=ax2, cmap="magma")
abs(mode_data.Ez.isel(mode_index=mode_idx)).plot(x="y", y="z", ax=ax3, cmap="magma")
ax1.set_title("|Ex(y, z)|")
ax1.set_aspect("equal")
ax2.set_title("|Ey(y, z)|")
ax2.set_aspect("equal")
ax3.set_title("|Ez(y, z)|")
ax3.set_aspect("equal")
plt.show()
Define Job and Estimate Cost¶
[9]:
job = web.Job(simulation=sim, task_name="PSGC", verbose=True)
estimated_cost = web.estimate_cost(job.task_id)
13:25:18 EST Created task 'PSGC' with resource_id 'fdve-2744f6c2-0dbe-4758-9dea-3db64168985d' and task_type 'FDTD'.
View task using web UI at 'https://tidy3d.simulation.cloud/workbench?taskId=fdve-2744f6c2-0db e-4758-9dea-3db64168985d'.
Task folder: 'default'.
Output()
13:25:25 EST Estimated FlexCredit cost: 12.539. Minimum cost depends on task execution details. Use 'web.real_cost(task_id)' to get the billed FlexCredit cost after a simulation run.
13:25:29 EST Estimated FlexCredit cost: 12.539. Minimum cost depends on task execution details. Use 'web.real_cost(task_id)' to get the billed FlexCredit cost after a simulation run.
Run Job and Record Data (Approximately 5 credits)¶
[10]:
sim_data = job.run(path="data_TM/simulation_data.hdf5")
13:25:32 EST status = success
Output()
13:26:09 EST Loading simulation from data_TM/simulation_data.hdf5
13:26:10 EST WARNING: More than 200 structures use the same medium. For performance, use a 'GeometryGroup' or boolean operations to combine geometries that share a medium.
WARNING: Warning messages were found in the solver log. For more information, check 'SimulationData.log' or use 'web.download_log(task_id)'.
Plot Field Cross Sections¶
[11]:
f1 = plt.figure(figsize=(15,6))
ax = f1.add_subplot(1,1,1)
sim_data.plot_field(
field_monitor_name="XY_cross", field_name="E", val="abs^2", f=freq0, ax=ax)
plt.show()
f1 = plt.figure(figsize=(15,6))
ax = f1.add_subplot(1,1,1)
sim_data.plot_field(
# field_monitor_name="XZ_cross", field_name="Ey", val="real", f=freq0, ax=ax)
field_monitor_name="YZ_cross", field_name="Ex", val="abs^2", f=freq0, ax=ax)
plt.show()
PSGC Efficiency¶
[12]:
amp_left = sim_data["left"].amps.sel(mode_index=0, direction="-")
T_left = np.abs(amp_left) ** 2
amp_right = sim_data["right"].amps.sel(mode_index=0, direction="+")
T_right = np.abs(amp_right) ** 2
amp_top = sim_data["top"].amps.sel(mode_index=0, direction="+")
T_top = np.abs(amp_top) ** 2
amp_bot = sim_data["bot"].amps.sel(mode_index=0, direction="-")
T_bot = np.abs(amp_bot) ** 2
f1 = plt.figure(figsize=(16,5))
ax = f1.add_subplot(1,2,1)
ax.plot(ldas, T_left, linestyle = 'dashed', color= 'blue')
ax.plot(ldas, T_right, linestyle = 'dotted', color= 'magenta')
ax.plot(ldas, T_top, linestyle = 'dashed', color= 'red')
ax.plot(ldas, T_bot, linestyle = 'dotted', color= 'green')
ax.plot(ldas, T_bot + T_top + T_right + T_left, 'black')
ax.grid()
ax.set_xlabel('Wavelength [$\mu{m}$]', fontsize = 14)
ax.set_ylabel('Coupling Efficiency [$\%$]', fontsize = 14)
ax.set_title('PSGC Coupling Spectrum (Horizontal Polarization)', fontsize = 15)
ax.legend(['Left Port', 'Right Port', 'Top Port', 'Bottom Port', 'Total'], fontsize = 10)
plt.show()
[ ]:
TERMS & CONDITIONS
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Try this real URL to see an example: