Sweep the coupler gap

Analytic calculation of 100% coupling length into two parallel SOI waveguides with a varying gap at different TE wavelengths.

An example refractive index profile for the two waveguides spaced 200nm is shown.

[1]:

import numpy as np
import matplotlib.pyplot as plt
import modes as ms
import opticalmaterialspy as mat
from modes.design import directional_coupler_lc

wavelength_nm  = 1550
width = 0.45
thickness = 0.22
widths = [width]*2
wg_gaps = np.arange(0.15, 0.30, 0.05)
wg_gaps = np.array([0.15, 0.2, 0.25])
dcs = [ms.waveguide_array(widths=widths, wg_gaps=[wg_gap], sub_width=3, thickness=thickness) for wg_gap in wg_gaps]
dcs[0]

[1]:

[0.45, 0.45] x 0.22 um, n_wg = 3.4757, n_clad = [1.444023621703261]
../_images/notebooks_30_sweep_coupler_gap_1_1.png 
[2]:

ms.mode_solver_full(wg=dcs[0], n_modes=2, plot=True, plot_index=True, fields_to_write=('Ex'))

[2]:

<modes._mode_solver_full_vectorial.ModeSolverFullyVectorial at 0x7f358d06a3d0>
../_images/notebooks_30_sweep_coupler_gap_2_1.png
../_images/notebooks_30_sweep_coupler_gap_2_2.png
../_images/notebooks_30_sweep_coupler_gap_2_3.png 
[3]:

n_effs = [ms.mode_solver_full(wg=wg, n_modes=2).results['n_effs'] for wg in dcs]

[4]:

ne = [ n_eff[0].real for n_eff in n_effs]
no = [ n_eff[1].real for n_eff in n_effs]

[5]:

lc = [directional_coupler_lc(wavelength_nm, n_eff_1, n_eff_2) for n_eff_1, n_eff_2 in zip(ne, no)]

[6]:

plt.plot(wg_gaps*1e3, lc, 'o')
plt.xlabel('gap (nm)')
plt.ylabel('100% Coupling length (um)')

[6]:

Text(0, 0.5, '100% Coupling length (um)')
../_images/notebooks_30_sweep_coupler_gap_6_1.png 
[7]:

# to increase reduce the gap step we need to reduce the size of the x_step and y_step computing grid

wg_gaps = np.arange(0.15, 0.30, 0.02)
dcs = [ms.waveguide_array(widths=widths, wg_gaps=[wg_gap], x_step=0.01, y_step=0.01) for wg_gap in wg_gaps]
n_effs = [ms.mode_solver_full(wg=wg, n_modes=2).results['n_effs'] for wg in dcs]
ne = [ n_eff[0].real for n_eff in n_effs]
no = [ n_eff[1].real for n_eff in n_effs]
lc = [directional_coupler_lc(wavelength_nm, n_eff_1, n_eff_2) for n_eff_1, n_eff_2 in zip(ne, no)]

[8]:

plt.plot(wg_gaps*1e3, lc, 'o')
plt.xlabel('gap (nm)')
plt.ylabel('100% Coupling length (um)')

[8]:

Text(0, 0.5, '100% Coupling length (um)')
../_images/notebooks_30_sweep_coupler_gap_8_1.png

Exercise

Design a directional coupler with a gap of 250nm that will tap off 10% of the optical power at a wavelength of 1550nm. What length in microns does the directional coupler have to be?

[9]:

directional_coupler_lc?

[10]:

wavelength_nm  = 1550
width = 0.5
thickness = 0.22
widths = [width]*2
dc = ms.waveguide_array(widths=widths, wg_gaps=[0.25], sub_width=3, thickness=thickness)

[11]:

ms.mode_solver_full(wg=dc, n_modes=2, plot=True, plot_index=True, fields_to_write=('Ex'))

[11]:

<modes._mode_solver_full_vectorial.ModeSolverFullyVectorial at 0x7f358c707be0>
../_images/notebooks_30_sweep_coupler_gap_12_1.png
../_images/notebooks_30_sweep_coupler_gap_12_2.png
../_images/notebooks_30_sweep_coupler_gap_12_3.png 
[12]:

directional_coupler_lc(1550, 2.481, 2.464, power_ratio=0.1)

[12]:

9.337964273048785

Exercise

What is the coupler length (in µm) that corresponds with 100% power transfer from the through port (top) to the cross port (bottom)? Assume 500nm x 220nm Si waveguides in SiO2, 1550 nm wavelength, and a 100 nm coupler gap

[13]:

dc = ms.waveguide_array(widths=widths, wg_gaps=[0.1], sub_width=3, thickness=thickness, x_step=0.01)
m = ms.mode_solver_full(wg=dc, n_modes=2, plot=True, fields_to_write=('Ex'))
../_images/notebooks_30_sweep_coupler_gap_15_0.png
../_images/notebooks_30_sweep_coupler_gap_15_1.png 
[14]:

directional_coupler_lc(1550, np.abs(m.n_effs)[0], np.abs(m.n_effs)[1], power_ratio=1)

[14]:

12.5925379514069

[15]:

directional_coupler_lc(1550, 2.498, 2.437, power_ratio=1)

[15]:

12.704918032786805

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