3D TE/TM Mode Source

[601t]

Eigenmode sources in 2D simulations are available for MEEP. But can this be used for 3D simulations as well?

[601t]

I made the following drawing in RSoft and simulated it with FullWAVE FDTD. The excitation light is in TE mode.


A similar drawing was made in KLayout and simulated in MEEP as shown in the code below.

import meep as mp
import time
import numpy as np
import math
import matplotlib.pyplot as plt
import argparse

resolution = 16 # [pixels/um]
C0 = 1
wavelength = 1.55
wavelength_start = 0.55
wavelength_stop = 2.55
freq = C0/wavelength
freq_start = C0/wavelength_stop
freq_stop = C0/wavelength_start
df = 0.5*(freq_stop - freq_start)
TE_mode = mp.ODD_Y + mp.EVEN_Z
TM_mode = mp.EVEN_Y + mp.ODD_Z

# Si
refractive_index_Si = 3.48
material_Si = mp.Medium(index=refractive_index_Si)
# SiO2
refractive_index_SiO2 = 1.44428
material_SiO2 = mp.Medium(index=refractive_index_SiO2)

gds_file = 'layout.gds'
CELL_LAYER = 2 # Domain
PORT1_LAYER = 4 # Bar_in
PORT2_LAYER = 5 # Cross_in
PORT3_LAYER = 6 # Bar_out
PORT4_LAYER = 7 # Cross_out
SOURCE_LAYER = 3 # Input
BAR_LAYER = 0 # Bar
CROSS_LAYER = 1 # Cross
height_core = 0.22
height_rib = 0.18
height_slab = 0.04
SiO2_sub = 10
pml_thickness = 1

def main(args):
    cell_zmax =  1.2 if args.three_d else 0
    cell_zmin = -1.2 if args.three_d else 0
    Si_zmax = 0.5*height_core
    Si_zmin = -0.5*height_core+height_slab
    
    bar_wvg = mp.get_GDSII_prisms(material_Si, gds_file, BAR_LAYER, Si_zmin, Si_zmax)
    cross_wvg = mp.get_GDSII_prisms(material_Si, gds_file, CROSS_LAYER, Si_zmin, Si_zmax)
    base = [# Si_base
        mp.Block(mp.Vector3(mp.inf,mp.inf,height_slab),
                 center=mp.Vector3(0,0,-0.5*(height_rib)),
                 material=material_Si,
                 ),
        mp.Block(mp.Vector3(mp.inf,mp.inf,SiO2_sub),
                 center=mp.Vector3(0,0,-0.5*(SiO2_sub+height_core)),
                 material=material_SiO2,
                 ),
    ]

    cell = mp.GDSII_vol(gds_file, CELL_LAYER, cell_zmin, cell_zmax)
    b_in = mp.GDSII_vol(gds_file, PORT1_LAYER, -0.5*height_core, Si_zmax)
    c_in = mp.GDSII_vol(gds_file, PORT2_LAYER, -0.5*height_core, Si_zmax)
    b_out = mp.GDSII_vol(gds_file, PORT3_LAYER, -0.5*height_core, Si_zmax)
    c_out = mp.GDSII_vol(gds_file, PORT4_LAYER, -0.5*height_core, Si_zmax)
    src_vol = mp.GDSII_vol(gds_file, SOURCE_LAYER, -0.5*height_core, Si_zmax)

    geometry = bar_wvg+cross_wvg+base

    sources = [#mp.Source(mp.GaussianSource(freq,fwidth=df),
               mp.EigenModeSource(mp.GaussianSource(freq,fwidth=df),
                                  #mp.ContinuousSource(freq,),
                                  direction=mp.X,
                                  volume=src_vol,
                                  eig_parity=TE_mode,
                                  ),
    ]

    pml_layers = [mp.PML(pml_thickness)]

    nfreq = 2001

    sim = mp.Simulation(cell_size=cell.size,
                        boundary_layers=pml_layers,
                        geometry=geometry,
                        sources=sources,
                        default_material=material_SiO2,
                        resolution=resolution,
                        )
    
    pt = mp.Vector3(35, 30.35, 0)

    fr_b_in = sim.add_flux(freq, df, nfreq, mp.FluxRegion(volume=b_in))
    fr_c_in = sim.add_flux(freq, df, nfreq, mp.FluxRegion(volume=c_in))
    fr_b_out = sim.add_flux(freq, df, nfreq, mp.FluxRegion(volume=b_out))
    fr_c_out = sim.add_flux(freq, df, nfreq, mp.FluxRegion(volume=c_out))

    start_time = time.time()
    sim.run(
            until_after_sources=mp.stop_when_fields_decayed(233, mp.Hy, pt, 1e-3)
            )
    finish_time = time.time()
    sim_time = finish_time - start_time
    print(f"Time: {sim_time}[sec]")

    b_in_flux = mp.get_fluxes(fr_b_in)
    b_out_flux = mp.get_fluxes(fr_b_out)
    c_in_flux = mp.get_fluxes(fr_c_in)
    c_out_flux = mp.get_fluxes(fr_c_out)
    flux_freqs = mp.get_flux_freqs(fr_b_in)

    wl = []
    flux_b_out_trans = []
    flux_c_out_trans = []
    flux_coupling = []
    
    for i in range(nfreq):
        wl = np.append(wl, 1000 / flux_freqs[i])
        flux_b_out_trans = np.append(flux_b_out_trans, 10*np.log10(b_out_flux[i]/b_in_flux[i]))
        flux_c_out_trans = np.append(flux_c_out_trans, 10*np.log10(c_out_flux[i]/b_in_flux[i]))
        flux_coupling = np.append(flux_coupling, 100*c_out_flux[i]/(b_out_flux[i]+c_out_flux[i]))

    if mp.am_master():
        plt.figure()
        plt.plot(wl, flux_b_out_trans, "ro-", label="Bar", marker=None,)
        plt.plot(wl, flux_c_out_trans, "bo-", label="Cross", marker=None,)
        plt.axis([1500, 1600, -60, 0.25])
        plt.title("DC, Lc=10[um], Gap=200[nm], R=15[um], Rθ=90[deg], TE, SiO2 covered")
        plt.xlabel("Wavelength [nm]")
        plt.ylabel("Transmittance [dB]")
        plt.legend(loc="best")
        plt.show()

        plt.figure()
        plt.plot(wl, flux_coupling, "go-", label="Coupling ratio", marker=None,)
        plt.axis([1500, 1600, 0, 100])
        plt.title("DC, Lc=10[um], Gap=200[nm], R=15[um], Rθ=90[deg], TE, SiO2 covered")
        plt.xlabel("Wavelength [nm]")
        plt.ylabel("Coupling ratio [%]")
        plt.legend(loc="best")
        plt.show()
        
if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument('--three_d', action='store_true', default=False, help='3D calculation? (default: False)')
    args = parser.parse_args()
    main(args)

But the results were as follows.

Is there something else that needs to be changed?
Or does MEEP not yet support 3D simulation with TE/TM polarization?

[stevengj]

Meep supports eigenmode sources in 3d. However, realized that in a 3d waveguide like this there is no true "TE" or "TM" polarized mode, so passing TE will be a mistake.

What TE and TM correspond to mathematically in Meep are even and odd solutions, respectively, with respect to a $z=0$ mirror-symmetry plane.

But if you have a waveguide on a substrate, then you don't have a $z=0$ mirror plane. If your waveguide is propagating in the $x$ direction, you may have a $y=0$ mirror symmetry plane and use that.

Or you can just not specify the symmetry of the mode, but just specify the correct mode index of the mode you want. Probably the mode that is mostly polarized in-plane is the lower-frequency solution, so that will be mode 1 and the other mode will be mode 2, but you should look at the dispersion relation/eigenmodes (e.g. in MPB) to be sure.

[stevengj]

Aside from that, the usual question is whether you've checked convergence, etcetera.

[601t]

So sorry to change the question, but is it possible to excite light in any direction without using EigenModeSource?
I would like to avoid that the excitation light is circular or spherical in normal Source.

[stevengj]

You can use a gaussian beam source, for example, or an oblique planewave source. Or you can use eigenmode sources for waveguides in oblique directions.

[601t]

Thanks for the reply. I'll try to use it through trial and error.