modesolverpy

Photonic mode solver with a nice interface and output.

• semi-vectorial and fully vectorial options,
• simple structure drawing,
• automated data saving and plotting via Gnuplot,
• some limited (at this stage) data processing (finding MFD of fundamental mode), and
• easily extensible library

The documentation for this project can be found here.

Examples

• Ex1: Semi-vectorial mode solving of a ridge waveguide
• Ex2: Fully vectorial mode solving of an anisotropic material waveguide
• Ex3: Grating-coupler period
• Ex4: Mode Hybridisation In SOI
• Ex6: Directional Coupler 3dB Length In SOI

Example 1: Semi-vectorial mode solving of a ridge waveguide

The following example finds the first two modes of a waveguide with the following, arbitrary, parameters:

• thin-film thickness: 500nm
• waveguide height: 400nm,
• waveguide width: 500nm,
• refractive index of waveguide: 3,
• refractive index of substrate: 1.4,
• refractive index of cladding: 1, and
• wavelength: 1550nm.

Python script

import modesolverpy.mode_solver as ms
import modesolverpy.structure as st
import numpy as np

# All units are relative.  [um] were chosen in this case.
x_step = 0.02
y_step = 0.02
wg_height = 0.4
wg_width = 0.5
sub_height = 0.5
sub_width = 2.
clad_height = 0.5
n_sub = 1.4
n_wg = 3.
n_clad = 1.
film_thickness = 0.5
wavelength = 1.55
angle = 75.

structure = st.RidgeWaveguide(wavelength,
                              x_step,
                              y_step,
                              wg_height,
                              wg_width,
                              sub_height,
                              sub_width,
                              clad_height,
                              n_sub,
                              n_wg,
                              angle,
                              n_clad,
                              film_thickness)

structure.write_to_file('example_structure_1.dat')

mode_solver = ms.ModeSolverSemiVectorial(2, semi_vectorial_method='Ey')
mode_solver.solve(structure)
mode_solver.write_modes_to_file('example_modes_1.dat')

Structure

Modes

Example 2: Fully vectorial mode solving of an anisotropic material waveguide

The following looks at a contrived ridge waveguide in Z-cut KTP.

The simulation outputs:

• 5 plots for each refractive index axis (n_xx, n_xy, n_yx, n_yy and n_zz),
• 48 plots for Ex, Ey, Ez, Hx, Hy and Hz,
• 8 effective index values, one for each mode,
• a wavelength sweep of the waveguide (plotting n_eff vs wavelength for each mode),
• whether a mode is qTE or qTM and the percentage overlap with TE and TM, and
• the group velocity of the mode.

The waveguide parameters are:

• thin-film thickness: 1.2um,
• waveguide height: 800nm,
• waveguide width: 1.2um,
• refractive index of waveguide: used Sellmeier equations to get n_xx, n_yy, n_zz at 1550nm,
• refractive index of substrate: used Sellmeier equation to get SiO2 at 1550nm,
• refractive index of cladding: 1, and
• wavelength: 1550nm.

Python script

import modesolverpy.mode_solver as ms
import modesolverpy.structure as st
import opticalmaterialspy as mat
import numpy as np

wl = 1.55
x_step = 0.06
y_step = 0.06
wg_height = 0.8
wg_width = 1.8
sub_height = 1.0
sub_width = 4.
clad_height = 1.0
film_thickness = 1.2
angle = 60.

def struct_func(n_sub, n_wg, n_clad):
    return st.RidgeWaveguide(wl, x_step, y_step, wg_height, wg_width,
                             sub_height, sub_width, clad_height,
                             n_sub, n_wg, angle, n_clad, film_thickness)

n_sub = mat.SiO2().n(wl)
n_wg_xx = mat.Ktp('x').n(wl)
n_wg_yy = mat.Ktp('y').n(wl)
n_wg_zz = mat.Ktp('z').n(wl)
n_clad = mat.Air().n()

struct_xx = struct_func(n_sub, n_wg_xx, n_clad)
struct_yy = struct_func(n_sub, n_wg_yy, n_clad)
struct_zz = struct_func(n_sub, n_wg_zz, n_clad)

struct_ani = st.StructureAni(struct_xx, struct_yy, struct_zz)
struct_ani.write_to_file()

solver = ms.ModeSolverFullyVectorial(8)
solver.solve(struct_ani)
solver.write_modes_to_file()

solver.solve_ng(struct_ani, 1.55, 0.01)

solver.solve_sweep_wavelength(struct_ani, np.linspace(1.501, 1.60, 21))

Group Velocity

The group velocity at 1550nm for each mode is:

# modes_full_vec/ng.dat
# Mode idx, Group index
0,1.776
1,1.799
2,1.826
3,1.847
4,1.841
5,1.882
6,1.872
7,1.871

Structure

Modes

Only the first 4 (out of 8) modes are shown, and only the E-fields are shown (not H-fields). For the rest of the images, look in the example folder or run the script.

A_{x,y,z} give the percentage power of that particular E-field component with respect to the total of all components.

Mode types:

# modes_full_vec/mode_info
# Mode idx, Mode type, % in major direction, n_eff
0,qTE,97.39,1.643
1,qTM,92.54,1.640
2,qTE,90.60,1.576
3,qTM,91.41,1.571
4,qTE,89.48,1.497
5,qTM,86.70,1.475
6,qTE,89.47,1.447
7,qTM,68.35,1.437

Wavelength Sweep

Example 3: Grating-coupler period

Analytic calculation of the grating coupler period for various duty-cycles in SOI.

Seems to match well with the periods in Taillaert et al., Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides, IOP Science, 2006.

import modesolverpy.mode_solver as ms
import modesolverpy.structure as st
import modesolverpy.design as de
import opticalmaterialspy as mat
import numpy as np

wls = [1.5, 1.55, 1.6]
x_step = 0.05
y_step = 0.05
etch_depth = 0.07
wg_width = 10
sub_height = 0.5
sub_width = 14.
clad_height = 0.5
film_thickness = 0.22
polarisation = 'TE'
dcs = np.linspace(20, 80, 61) / 100

ed1 = etch_depth
ft1 = film_thickness
ed2 = ft1 - ed1
ft2 = ed2

periods = []
periods.append(dcs)

for wl in wls:
    ngc = []
    for ed, ft in [(ed1, ft1), (ed2, ft2)]:
        def struct_func(n_sub, n_wg, n_clad):
            return st.RidgeWaveguide(wl, x_step, y_step, ed, wg_width,
                                     sub_height, sub_width, clad_height,
                                     n_sub, n_wg, None, n_clad, ft)

        n_sub = mat.SiO2().n(wl)
        n_wg_xx = 3.46
        n_wg_yy = 3.46
        n_wg_zz = 3.46
        n_clad = mat.Air().n()

        struct_xx = struct_func(n_sub, n_wg_xx, n_clad)
        struct_yy = struct_func(n_sub, n_wg_yy, n_clad)
        struct_zz = struct_func(n_sub, n_wg_zz, n_clad)

        struct_ani = st.StructureAni(struct_xx, struct_yy, struct_zz)
        #struct_ani.write_to_file()

        solver = ms.ModeSolverFullyVectorial(4)
        solver.solve(struct_ani)
        #solver.write_modes_to_file()

        if polarisation == 'TE':
            ngc.append(np.round(np.real(solver.n_effs_te), 4)[0])
        elif polarisation == 'TM':
            ngc.append(np.round(np.real(solver.n_effs_tm), 4)[0])

    period = de.grating_coupler_period(wl, dcs*ngc[0]+(1-dcs)*ngc[1], n_clad, 8, 1)
    periods.append(period)

filename = 'dc-sweep-%s-%inm-etch-%i-film.dat' % (polarisation, etch_depth*1000, film_thickness*1000)
np.savetxt(filename, np.array(periods).T, delimiter=',', header=','.join([str(val) for val in wls]))
print(np.c_[periods])

Example 4: Mode Hybridisation In SOI

Simulation of mode hybridisation in 220nm thick fully-etched SOI ridge waveguides.

Results look the same as those found in Daoxin Dai and Ming Zhang, "Mode hybridization and conversion in silicon-on-insulator nanowires with angled sidewalls," Opt. Express 23, 32452-32464 (2015).

import modesolverpy.mode_solver as ms
import modesolverpy.structure as st
import opticalmaterialspy as mat
import numpy as np

wl = 1.55
x_step = 0.02
y_step = 0.02
etch_depth = 0.22
wg_widths = np.arange(0.3, 2., 0.05)
sub_height = 1.
sub_width = 4.
clad_height = 1.
film_thickness = 0.22

n_sub = mat.SiO2().n(wl)
n_clad = mat.Air().n(wl)
n_wg = mat.RefractiveIndexWeb(
    'https://refractiveindex.info/?shelf=main&book=Si&page=Li-293K').n(wl)

r = []
for w in wg_widths:
    r.append(
        st.RidgeWaveguide(wl, x_step, y_step, etch_depth, w, sub_height,
                          sub_width, clad_height, n_sub, n_wg, None, n_clad,
                          film_thickness))

r[0].write_to_file('start_n_profile.dat')
r[-1].write_to_file('end_n_profile.dat')

solver = ms.ModeSolverFullyVectorial(6)
solver.solve_sweep_structure(r, wg_widths, x_label='Taper width', fraction_mode_list=[1,2])
solver.write_modes_to_file()

Example 5: Directional Coupler 3dB Length In SOI

Analytic calculation of 3dB coupling length into two parallel SOI waveguides with a varying gap at 3 different TE wavelengths.

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

import modesolverpy.mode_solver as ms
import modesolverpy.structure as st
import modesolverpy.design as de
import opticalmaterialspy as mat
import numpy as np
import tqdm

wls = [1.5, 1.55, 1.6]
x_step = 0.02
y_step = 0.02
etch_depth = 0.22
wg_width = 0.44
sub_height = 0.5
sub_width = 2.
clad_height = 0.5
film_thickness = 0.22
gaps = np.linspace(0.1, 0.5, 11)

for wl in wls:
    lengths = []

    n_sub = mat.SiO2().n(wl)
    n_clad = mat.Air().n(wl)
    n_wg = 3.476

    for gap in tqdm.tqdm(gaps):
        r = st.WgArray(wl, x_step, y_step, etch_depth, [wg_width, wg_width], gap,
                       sub_height, sub_width, clad_height, n_sub, n_wg, None)
        #r.write_to_file()

        solver = ms.ModeSolverFullyVectorial(2)
        solver.solve(r)
        n1 = solver.n_effs_te[0]
        n2 = solver.n_effs_te[1]
        lengths.append(de.directional_coupler_lc(wl*1000, n1, n2)/2)

    filename = 'dc-sweep-%inm-%s-%inm-etch-%i-film.dat' % (wl*1000, 'TE', etch_depth*1000, film_thickness*1000)
    np.savetxt(filename, np.c_[gaps, lengths], delimiter=',', header='Coupling lengths (50\%)')

Installation

It is recommend to install modesolverpy either via:

Ubuntu/Mint/Debian:

pip3 install modesolverpy # or pip2 install modesolverpy
apt install gnuplot

Arch Linux:

yaourt -S python-modesolverpy

Dependencies

If installing using the Arch Linux AUR package or pip, dependencies will be automatically downloaded and installed, if not, one should ensure the following dependencies are installed:

Either Gnuplot or Matplotlib can be used for plotting; I am a Gnuplot user to the code was written with it in mind. If both Gnuplot and Matplotlib are installed, the code will default to Gnuplot.

• setuptools,
• numpy,
• scipy,
• tqdm, and
• opticalmaterialspy.

Plotting

EITHER:

• Gnuplot.
• gnuplotpy,

OR:

• matplotlib,

Acknowledgments

This finite difference mode solver is based on a modified version of EMpy.

Thank you to Inna Krasnokutska for testing.