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.
- 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
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.
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')
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.
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))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 
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 
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])
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()
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\%)')
It is recommend to install modesolverpy either via:
pip3 install modesolverpy # or pip2 install modesolverpy apt install gnuplotyaourt -S python-modesolverpyIf 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.
EITHER:
OR:
This finite difference mode solver is based on a modified version of EMpy.
Thank you to Inna Krasnokutska for testing.