Directional Coupler
Posted Updated 
Directional Coupler from GDSFactory
By Ram Prakash Shanmugam | Ram Prakash S
15 min read
Directional Coupler
Directional Coupler
Source Code
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# Import all the necessary packages
import gplugins.modes as gmode
import numpy as np
import matplotlib.pyplot as plt
import meep as mp
import gdsfactory as gf
import gplugins.gmeep as gm
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Using MPI version 4.1, 1 processes
[32m2025-10-02 00:21:52.537[0m | [1mINFO [0m | [36mgplugins.gmeep[0m:[36m<module>[0m:[36m39[0m - [1mMeep '1.31.0' installed at ['/home/ramprakash/anaconda3/envs/si_photo/lib/python3.13/site-packages/meep'][0m
Visualzing supermodes
Using gdsfactory and gplugins we can visualize the supermodes and effective index of even and odd modes
Source Code
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modes = gmode.find_modes_coupler(
core_widths=(0.5, 0.5),
gaps=(0.15,), # CHANGE GAP VALUE
core_material=3.45,
clad_material=1.45,
core_thickness=0.22,
resolution=40,
sz=6,
nmodes=2,
)
m1 = modes[1] # even mode
m2 = modes[2] # odd mode
# Look to see how big of a difference there is between the two refractive indices
print("Refractive index of even mode:", m1.neff)
print("Refractive index of odd mode:", m2.neff)
# Plot the dielectric, shows index of refraction values in sidebar
m1.plot_eps()
# Plot the Electric field intensity of the modes
m1.plot_ey()
m2.plot_ey()
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Refractive index of even mode: 2.412356873283017
Refractive index of odd mode: 2.3769074396552754
Coupling length vs gap between the waveguides
Using gdsfactory helper function ‘find_coupling_vs_gap’
Source Code
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import meep as mp
coupling_gap = gmode.find_coupling_vs_gap(
gap1=0.1,
gap2=0.15,
steps=11,
nmodes=1,
wavelength=1.55,
parity=mp.EVEN_Y,
core_widths=(0.5, 0.5),
core_material=3.45,
clad_material=1.45,
core_thickness=0.22,
resolution=40,
sz=6,
)
coupling_gap
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| gap | ne | no | lc | dn | |
|---|---|---|---|---|---|
| 0 | 0.100 | 2.428738 | 2.371472 | 13.533461 | 0.057265 |
| 1 | 0.105 | 2.426836 | 2.371885 | 14.103476 | 0.054951 |
| 2 | 0.110 | 2.425519 | 2.372191 | 14.532637 | 0.053328 |
| 3 | 0.115 | 2.423959 | 2.372615 | 15.094336 | 0.051344 |
| 4 | 0.120 | 2.423082 | 2.373316 | 15.572816 | 0.049766 |
| 5 | 0.125 | 2.420206 | 2.373469 | 16.582260 | 0.046737 |
| 6 | 0.130 | 2.417458 | 2.373492 | 17.627312 | 0.043966 |
| 7 | 0.135 | 2.415176 | 2.373758 | 18.711407 | 0.041419 |
| 8 | 0.140 | 2.413491 | 2.374407 | 19.828922 | 0.039084 |
| 9 | 0.145 | 2.412899 | 2.375705 | 20.836274 | 0.037195 |
| 10 | 0.150 | 2.412357 | 2.376907 | 21.862126 | 0.035449 |
Coupling power ratio vs length of the waveguide
$\kappa^2 = sin^2(C.L)$ cross coupling ratio
$t^2 = cos^2(C.L)$ through coupling ratio
$C = \frac{\pi\Delta n}{\lambda}$ Coupling coefficient
$c_{length} = \frac{\lambda}{2*\Delta n}$ Cross-over length
gap = 150 nm, n1 = 2.412, n2=2.377
Source Code
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gap = 0.150 # in um
n1 = 2.412
n2 = 2.375
dn = 2.412 - 2.375
L = np.linspace(0, 40, 50)
C = np.pi * dn / 1.55 # coupling coeff
k_cross = (np.sin(C * L)) ** 2
t_through = (np.cos(C * L)) ** 2
C_len = 1.55 / (2 * dn)
plt.figure()
plt.plot(L, k_cross, label="Cross port")
plt.plot(L, t_through, label="Through port")
plt.axvline(C_len, color="black", linestyle="--")
plt.xlabel("Length of the waveguide (um)")
plt.ylabel("Coupling power ratio")
plt.title("Coupling power vs Length")
plt.legend()
plt.show()
Meep simulation of coupler
No bend simualtion - two straight waveguide seperated by gap=0.15 um, Length=22 um
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import meep as mp
from PIL import Image
import glob
import os
# Define materials
Si = mp.Medium(index=3.45)
SiO2 = mp.Medium(index=1.45)
# Define wavelength in um
wvl = 1.55
# # Define cell and geometric parameters
resolution = 20
wg_width = 0.5
dpml = 1
pad = 0.5
## CHANGE GAP DISTANCE ##
gap = 0.15
## CHANGE WAVEGUIDE LENGTH ##
Lx = 25
Sx = dpml + Lx + dpml
Sy = dpml + pad + wg_width + gap + wg_width + pad + dpml
wg_center_y = gap / 2 + wg_width / 2
# Add PML (perfectly matched layers)
pml = [mp.PML(dpml)]
# Create 2 infinitely long parallel waveguides
geometry = [
mp.Block(size=mp.Vector3(Sx, Sy, 0), center=mp.Vector3(), material=SiO2),
mp.Block(
size=mp.Vector3(Sx, wg_width, 0),
center=mp.Vector3(0, wg_center_y, 0),
material=Si,
),
mp.Block(
size=mp.Vector3(Sx, wg_width, 0),
center=mp.Vector3(0, -wg_center_y, 0),
material=Si,
),
]
# Put a pulse Eigenmode source at beginning of one waveguide
fcen = 1 / wvl
width = 0.1
fwidth = width * fcen
src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)
source = [
mp.EigenModeSource(
src=src,
eig_band=1,
eig_kpoint=(1, 0, 0),
size=mp.Vector3(0, gap + wg_width),
center=mp.Vector3(-Sx / 2 + dpml + 1, -wg_center_y),
)
]
# Simulation object
sim = mp.Simulation(
cell_size=mp.Vector3(Sx, Sy),
boundary_layers=pml,
geometry=geometry,
sources=source,
default_material=SiO2,
resolution=resolution,
)
# Show simulation set-up
sim.plot2D()
sim.reset_meep()
# Capture electric field intensity over time and output into a gif
sim.run(
mp.at_beginning(mp.output_epsilon),
mp.to_appended("ez_100_DC", mp.at_every(2, mp.output_efield_z)),
until=400,
)
# Since HDf5 was installed locally we need this. For sudo install these steps are not needed
os.environ["PATH"] = os.path.expanduser("~") + "/local/bin:" + os.environ["PATH"]
conda_prefix = os.environ["CONDA_PREFIX"]
os.environ["LD_LIBRARY_PATH"] = (
conda_prefix + "/lib:" + os.environ.get("LD_LIBRARY_PATH", "")
)
os.system(
"h5topng -t 0:99 -R -Zc $HOME/local/share/h5utils/colormaps/RdBu -A eps-000000.00.h5 -a $HOME/local/share/h5utils/colormaps/gray ez_100_DC.h5"
)
# Create a gif from the pngs
frames = []
imgs = glob.glob("ez_100_DC.t*")
imgs.sort()
for i in imgs:
new_frame = Image.open(i)
frames.append(new_frame)
# Save into a GIF file that loops forever
frames[0].save(
"ez_100_DC.gif", format="GIF", append_images=frames[1:], save_all=True, loop=0
)
# Clean up workspace by deleting all generated images
for i in imgs:
os.remove(i)
for f in glob.glob("*.h5"):
os.remove(f)
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FloatProgress(value=0.0, description='0% done ', max=400.0)
Coupler with bends - S-Parameter
Use write_sparameters_meep from gdsfactory plugins gmeep to get the sparameter of 100% coupler
Use get_geomentry from gdsfacotory to calcaulate S paramters and steady state fields.
Get Field animations
Couplers from gdsfactory component
Source Code
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import gdsfactory as gf
gf.clear_cache()
dir_coupler_100 = gf.Component("100% coupler")
gap = 0.15
length_100 = 22
dir_100_ref = dir_coupler_100.add_ref(gf.components.coupler(gap=gap, length=length_100))
dir_coupler_100.add_ports(dir_100_ref.ports)
dir_coupler_100.draw_ports()
dir_coupler_100.plot()
Effective index calcaution for 2.5D simulations (Not accurate like 3D simualtion but close enough and way faster)
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import gplugins
core_material = gplugins.get_effective_indices(
core_material=3.45,
clad_materialding=1.44,
nsubstrate=1.44,
thickness=0.22,
wavelength=1.55,
polarization="te",
)[0]
core_material
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2.8217018611269684
Using write_sparameters_meep function
Source Code
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import meep as mp
import matplotlib.pyplot as plt
import gplugins.gmeep as gm
mp.verbosity(0)
# Define materials
Si = mp.Medium(index=3.45)
SiO2 = mp.Medium(index=1.45)
resolution = 20
dpml = 1
pad = 1
sx = dpml + -(dir_coupler_100.ports["o1"].x) + (dir_coupler_100.ports["o4"].x) + dpml
sy = (
dpml
+ pad
+ -(dir_coupler_100.ports["o1"].y)
+ (dir_coupler_100.ports["o4"].y)
+ pad
+ dpml
)
port_symmetries_crossing = {
"o1@0,o1@0": ["o2@0,o2@0", "o3@0,o3@0", "o4@0,o4@0"],
"o2@0,o1@0": ["o1@0,o2@0", "o3@0,o4@0", "o4@0,o3@0"],
"o3@0,o1@0": ["o1@0,o3@0", "o2@0,o4@0", "o4@0,o2@0"],
"o4@0,o1@0": ["o1@0,o4@0", "o2@0,o3@0", "o3@0,o2@0"],
}
# plotting the meep geomentry
gm.write_sparameters_meep(
dir_coupler_100,
xmargin_left=1,
xmargin_right=1,
ymargin_top=1,
ymargin_bot=1,
resolution=resolution,
wavelength_start=1.54,
wavelength_stop=1.56,
wavelength_points=100,
tpml=dpml,
port_source_offset=0.2,
port_monitor_offset=-0.1,
port_symmetries=port_symmetries_crossing,
distance_source_to_monitors=0.3,
material_name_to_meep=dict(si=3.45),
run=False,
)
# Running the simulations
sp = gm.write_sparameters_meep(
dir_coupler_100,
xmargin_left=1,
xmargin_right=1,
ymargin_top=1,
ymargin_bot=1,
wavelength_start=1.54,
wavelength_stop=1.56,
wavelength_points=100,
resolution=resolution,
tpml=dpml,
port_source_offset=0.2,
port_monitor_offset=-0.1,
distance_source_to_monitors=0.3,
port_symmetries=port_symmetries_crossing,
material_name_to_meep=dict(si=3.45),
run=True,
)
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/home/ramprakash/anaconda3/envs/si_photo/lib/python3.13/site-packages/meep/visualization.py:966: UserWarning: plot_eps_flag is deprecated. Use show_epsilon instead.
warnings.warn("plot_eps_flag is deprecated. Use show_epsilon instead.")
/home/ramprakash/anaconda3/envs/si_photo/lib/python3.13/site-packages/meep/__init__.py:4446: ComplexWarning: Casting complex values to real discards the imaginary part
return _meep._get_epsilon_grid(gobj_list, mlist, _default_material, _ensure_periodicity, gv, cell_size, cell_center, nx, xtics, ny, ytics, nz, ztics, grid_vals, frequency)
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/home/ramprakash/anaconda3/envs/si_photo/lib/python3.13/site-packages/meep/__init__.py:4440: ComplexWarning: Casting complex values to real discards the imaginary part
return _meep.create_structure(cell_size, dft_data_list_, pml_1d_vols_, pml_2d_vols_, pml_3d_vols_, absorber_vols_, gv, br, sym, num_chunks, Courant, use_anisotropic_averaging, tol, maxeval, gobj_list, center, _ensure_periodicity, _default_material, alist, extra_materials, split_chunks_evenly, set_materials, existing_s, output_chunk_costs, my_bp)
/home/ramprakash/anaconda3/envs/si_photo/lib/python3.13/site-packages/meep/__init__.py:4443: ComplexWarning: Casting complex values to real discards the imaginary part
return _meep._set_materials(s, cell_size, gv, use_anisotropic_averaging, tol, maxeval, gobj_list, center, _ensure_periodicity, _default_material, alist, extra_materials, split_chunks_evenly, set_materials, existing_geps, output_chunk_costs, my_bp)
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gm.plot.plot_sparameters(
sp,
keys=(
"o3@0,o1@0",
"o4@0,o1@0",
),
logscale=False,
)
Using meep 2D simualtion vary length
calculating the s_parameter and the steady state fields for varying length
Length = [10, 15, 22, 30, 40], gap = 0.15
Source Code
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from gdsfactory.technology import LayerLevel, LayerStack
mp.verbosity(0)
# Set up frequency points for simulation
npoints = 100
lcen = 1.55
dlam = 0.02
wl = np.linspace(lcen - dlam / 2, lcen + dlam / 2, npoints)
fcen = 1 / lcen
fwidth = 3 * dlam / lcen**2
fpoints = 1 / wl # Center frequency
mode_parity = mp.EVEN_Y + mp.ODD_Z
# Define simulation parameters
gap = 0.15 # Choosen a small value to reduce the coupling length for faster simualtion
lengths = [10, 15, 22, 30, 40]
t_Si = 0.220
resolution = 20 # resoultion (using low value for faster simualtion)
dpml = 1
dpad = 1
# Define materials
Si = mp.Medium(index=3.45)
SiO2 = mp.Medium(index=1.45)
s_cross = [] # to save the S parameter for the cross port
s_through = [] # to save the S parameter for the through port
for length in lengths:
dir_coupler = gf.components.coupler(gap=gap, length=length)
cell_size = mp.Vector3(
dir_coupler.xsize + 2 * dpml, dir_coupler.ysize + 2 * dpml + 2 * dpad, 0
)
layers = dict(
core=LayerLevel(
layer=(1, 0),
thickness=t_Si,
zmin=-t_Si / 2,
material="si",
mesh_order=2,
sidewall_angle=0,
width_to_z=0.5,
orientation="100",
)
)
layer_stack = LayerStack(layers=layers)
dir_coupler = gf.components.extend_ports(
dir_coupler, port_names=["o1", "o2", "o3", "o4"], length=1
)
dir_coupler = dir_coupler.copy()
dir_coupler.flatten()
dir_coupler.center = (0, 0) # unsure why centering is needed
geometry = gm.get_meep_geometry.get_meep_geometry_from_component(
dir_coupler, layer_stack=layer_stack
)
geometry = [
mp.Prism(geom.vertices, geom.height, geom.axis, geom.center, material=Si)
for geom in geometry
]
src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)
source = [
mp.EigenModeSource(
src=src,
eig_band=1,
eig_parity=mode_parity,
size=mp.Vector3(0, 1),
center=mp.Vector3(
dir_coupler.ports["o1"].x + dpml + 1, dir_coupler["o1"].y
),
)
]
sim = mp.Simulation(
resolution=resolution,
cell_size=cell_size,
boundary_layers=[
mp.PML(dpml)
], # the boundary layers to absorb fields that leave the simulation
sources=source, # The sources
geometry=geometry, # The geometry
default_material=SiO2,
)
m1 = mp.Volume(
center=mp.Vector3(
dir_coupler.ports["o1"].x + dpml + 1 + 0.5, dir_coupler["o1"].y
),
size=mp.Vector3(0, 1),
)
m2 = mp.Volume(
center=mp.Vector3(
dir_coupler.ports["o2"].x + dpml + 1 + 0.5, dir_coupler["o2"].y
),
size=mp.Vector3(0, 1),
)
m3 = mp.Volume(
center=mp.Vector3(
dir_coupler.ports["o3"].x - dpml - 1 - 0.5, dir_coupler["o3"].y
),
size=mp.Vector3(0, 1),
)
m4 = mp.Volume(
center=mp.Vector3(
dir_coupler.ports["o4"].x - dpml - 1 - 0.5, dir_coupler["o4"].y
),
size=mp.Vector3(0, 1),
)
mode_monitor_1 = sim.add_mode_monitor(fpoints, mp.ModeRegion(volume=m1))
mode_monitor_2 = sim.add_mode_monitor(fpoints, mp.ModeRegion(volume=m2))
mode_monitor_3 = sim.add_mode_monitor(fpoints, mp.ModeRegion(volume=m3))
mode_monitor_4 = sim.add_mode_monitor(fpoints, mp.ModeRegion(volume=m4))
whole_dft = sim.add_dft_fields(
[mp.Ez], fcen, 0, 1, center=mp.Vector3(), size=cell_size
)
if length == 10:
sim.plot2D(labels=False)
# Runs the simulation
sim.run(until_after_sources=mp.stop_when_dft_decayed(tol=1e-4))
# Finds the S parameters
norm_mode_coeff = sim.get_eigenmode_coefficients(
mode_monitor_1, [1], eig_parity=mode_parity
).alpha[0, :, 0]
port1_coeff = (
sim.get_eigenmode_coefficients(
mode_monitor_1, [1], eig_parity=mode_parity
).alpha[0, :, 1]
/ norm_mode_coeff
)
port2_coeff = (
sim.get_eigenmode_coefficients(
mode_monitor_2, [1], eig_parity=mode_parity
).alpha[0, :, 1]
/ norm_mode_coeff
)
port3_coeff = (
sim.get_eigenmode_coefficients(
mode_monitor_3, [1], eig_parity=mode_parity
).alpha[0, :, 0]
/ norm_mode_coeff
)
port4_coeff = (
sim.get_eigenmode_coefficients(
mode_monitor_4, [1], eig_parity=mode_parity
).alpha[0, :, 0]
/ norm_mode_coeff
)
# Calculates the transmittance based off of the S parameters
port1_trans = abs(port1_coeff) ** 2
port2_trans = abs(port2_coeff) ** 2
port3_trans = abs(port3_coeff) ** 2
port4_trans = abs(port4_coeff) ** 2
val = 1.55
idx = (np.abs(wl - val)).argmin()
s_cross.append(port3_trans[idx])
s_through.append(port4_trans[idx])
fig = plt.figure(figsize=(15, 4))
fig.suptitle(f"Results for length = {length} µm", fontsize=16)
ax_trans1 = fig.add_subplot(1, 3, 1)
ax_trans1.set_title("Transmission per Port")
ax_trans1.plot(wl, port1_trans, label=r"s11^2")
ax_trans1.plot(wl, port2_trans, label=r"s21^2")
ax_trans1.plot(wl, port3_trans, label=r"s31^2")
ax_trans1.plot(wl, port4_trans, label=r"s41^2")
ax_trans1.set_xlabel(r"Wavelength (\mu m)")
ax_trans1.set_ylabel(r"Transmission")
ax_trans1.legend()
ax_phase1 = fig.add_subplot(1, 3, 2)
ax_phase1.set_title("Phase per Port")
ax_phase1.plot(
wl, np.unwrap(np.angle(port1_coeff) * 180 / np.pi), label=r"phase of s11"
)
ax_phase1.plot(
wl, np.unwrap(np.angle(port2_coeff) * 180 / np.pi), label=r"phase of s21"
)
ax_phase1.plot(
wl, np.unwrap(np.angle(port3_coeff) * 180 / np.pi), label=r"phase of s31"
)
ax_phase1.plot(
wl, np.unwrap(np.angle(port4_coeff) * 180 / np.pi), label=r"phase of s41"
)
ax_phase1.set_xlabel(r"Wavelength (\mu m)")
ax_phase1.set_ylabel("Angle (deg)")
ax_phase1.legend()
# sim.reset_meep()
# sim.run(until_after_sources=mp.stop_when_dft_decayed(tol=1e-4))
eps_data = (
sim.get_epsilon()
) # Epsilon Data / The Geometry / An array that holds what materials are where
ez_data = sim.get_dft_array(
whole_dft, mp.Ez, 0
) # Values for the component of the E-field in the z direction (in/out of screen)
# Creates the plot
ax_field = fig.add_subplot(1, 3, 3)
ax_field.set_title("Steady State Fields")
ax_field.imshow(np.transpose(eps_data), interpolation="spline36", cmap="binary")
ax_field.imshow(
np.flipud(np.transpose(np.real(ez_data))),
interpolation="spline36",
cmap="RdBu",
alpha=0.9,
)
ax_field.axis("off")
plt.show()
Power Coupling Comparsion between the FDTD and mode solver approach
Source Code
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plt.figure()
plt.plot(L, k_cross, label="Cross port")
plt.plot(L, t_through, label="Through port")
plt.scatter(lengths, s_cross, label="FDTD Cross port")
plt.scatter(lengths, s_through, label="FDTD Through port")
plt.axvline(C_len, color="black", linestyle="--")
plt.xlabel("Length of the waveguide (um)")
plt.ylabel("Coupling power ratio")
plt.title("Coupling power vs Length")
plt.legend()
plt.show()
Field animation
Animating the fields for visualization. Using gmeep plugings in gdsfactory
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mp.verbosity(0)
wvl = 1.55
resolution = 20
dpml = 1
pad = 1
sx = dpml + -(dir_coupler_100.ports["o1"].x) + (dir_coupler_100.ports["o4"].x) + dpml
sy = (
dpml
+ pad
+ -(dir_coupler_100.ports["o1"].y)
+ (dir_coupler_100.ports["o4"].y)
+ pad
+ dpml
)
cell_size = mp.Vector3(sx, sy)
dir_coupler_100 = gf.components.extend_ports(
dir_coupler_100, port_names=["o1", "o2", "o3", "o4"], length=1
)
geometry_100 = gm.get_meep_geometry.get_meep_geometry_from_component(
dir_coupler_100.copy()
)
fcen = 1 / wvl
width = 0.1
fwidth = width * fcen
src = mp.GaussianSource(frequency=fcen, fwidth=fwidth)
source = [
mp.EigenModeSource(
src=src,
eig_band=1,
eig_kpoint=(1, 0),
size=mp.Vector3(0, 1),
center=mp.Vector3(
-dir_coupler_100.ports["o1"].x + dpml + 1, -dir_coupler_100["o1"].y / 2
),
)
]
sim = gm.get_simulation(
dir_coupler_100,
resolution=resolution,
tpml=1,
port_source_offset=0.2,
port_monitor_offset=-0.1,
distance_source_to_monitors=0.3,
)
sim["sim"].sources = sim["sources"]
sim["sim"].cell_size.y = sy + 3
sim["sim"].cell_size.x = sx + 4
sim["sim"].plot2D(labels=True)
sim["sim"].reset_meep()
# Capture electric field intensity over time and output into a gif
sim["sim"].run(
mp.at_beginning(mp.output_epsilon),
mp.to_appended("ez", mp.at_every(2, mp.output_efield_z)),
until=200,
)
os.environ["PATH"] = os.path.expanduser("~") + "/local/bin:" + os.environ["PATH"]
conda_prefix = os.environ["CONDA_PREFIX"]
os.environ["LD_LIBRARY_PATH"] = (
conda_prefix + "/lib:" + os.environ.get("LD_LIBRARY_PATH", "")
)
os.system(
"h5topng -t 0:99 -R -Zc $HOME/local/share/h5utils/colormaps/RdBu -A eps-000000.00.h5 -a $HOME/local/share/h5utils/colormaps/gray ez.h5"
)
# Create a gif from the pngs
frames = []
imgs = glob.glob("ez.t*")
imgs.sort()
for i in imgs:
new_frame = Image.open(i)
frames.append(new_frame)
# Save into a GIF file that loops forever
frames[0].save(
"ez_100_DC.gif", format="GIF", append_images=frames[1:], save_all=True, loop=0
)
# Clean up workspace by deleting all generated images
for i in imgs:
os.remove(i)
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Warning: grid volume is not an integer number of pixels; cell size will be rounded to nearest pixel.
Warning: grid volume is not an integer number of pixels; cell size will be rounded to nearest pixel.
FloatProgress(value=0.0, description='0% done ', max=200.0)
This post is licensed under CC BY 4.0 by the author.