SWG-MMI Mode Demultiplexer — Muhammad Zareii

36 µmDevice Footprint

300 nmBandwidth (1.40–1.70 µm)

EMT + EIMDispersion Model

LumericalFDTD Validation

SOI 220 nmPlatform

Python / NumPy · Lumerical FDTD scripts available on request

github.com/muhammadzareii/swg-mmi-mode-demux

Overview

Mode-division multiplexing (MDM) is a strategy for increasing the data capacity of a photonic interconnect without increasing bandwidth or power — by transmitting independent data streams on orthogonal spatial modes (TE₀, TE₁, TE₂, …) through the same waveguide simultaneously. A mode demultiplexer is the key passive component: it routes each mode to its own port, separating the streams for individual detection.

This project analytically simulates a compact SOI mode demultiplexer based on the González-Andrade 2018 design. The device combines four passive elements — a Y-junction, a differential phase shifter, a sub-wavelength grating (SWG) MMI coupler, and tapered transitions — to convert TE₁ to TE₀ and route TE₀ and TE₁ inputs to separate output ports over a 300 nm wavelength range (1.40–1.70 µm). Total device length is approximately 36 µm on a standard 220 nm SOI platform.

Rather than running a commercial FDTD solver, the simulation implements the full analytical design chain from first principles: Effective Medium Theory extracts the SWG bulk properties, the Effective Index Method with a bisection dispersion solver computes waveguide propagation constants, the MMI self-imaging condition calibrates the beat length, and the 2D field distributions are reconstructed section-by-section using cosine mode superposition with correct excitation amplitudes. The result matches the published paper figures without any numerical integration of Maxwell's equations.

Device Architecture

Fig. S1. Full device top-view schematic. Signal enters at Port 3 (right, single multimode waveguide) and is demultiplexed to Port 1 and Port 2 (left, single-mode wire waveguides). The four sections — Y-junction, phase shifter, and SWG-MMI with tapered stubs — are labelled with their key dimensions.

Section	Function	Key Dimensions
Y-Junction	Splits TE₀ and TE₁ by symmetry — in-phase → stem, anti-phase → branches	W_stem = 1.0 µm, θ/2 = 12°, L = 7.14 µm
Phase Shifter	Adds Δφ = +90° between arms via width mismatch	W_upper = 0.70 µm, W_lower = 0.50 µm, L = 3.41 µm
Input Tapers	Adiabatic transition from wire to MMI port width	L_taper = 5.7 µm per stub
SWG-MMI Coupler	2×2 self-imaging coupler; cross-imaging at 3L_π/2	W = 3.25 µm, L = 14.06 µm, Λ = 190 nm, DC = 50%

Physical Model

Sub-Wavelength Grating — Effective Medium Theory

The SWG inside the MMI coupler has a period Λ = 190 nm, far below the 1.55 µm operating wavelength. At sub-wavelength periods, light cannot diffract off the individual teeth — instead the grating acts as a homogeneous uniaxial anisotropic medium described by zeroth-order EMT:

n_∥² = DC · n_Si² + (1 − DC) · n_SiO₂² → n_∥ = 2.659

1/n_⊥² = DC/n_Si² + (1 − DC)/n_SiO₂² → n_⊥ = 1.891

The lower index contrast of the SWG effective medium compared to solid silicon reduces the sensitivity of the MMI beat length to wavelength — this is the mechanism behind the 300 nm operating bandwidth.

Effective Index Method and Propagation Constants

The SOI waveguide dispersion (220 nm Si core, SiO₂ substrate, air top cladding) is solved with the Effective Index Method. The slab dispersion equation for TE modes is:

tan(κ·d) = κ(γ₁ + γ₂) / (κ² − γ₁γ₂)

where κ² = n_core²k₀² − β² and γ² = β² − n_clad²k₀². Propagation constants β₀ and β₁ for the two lowest MMI modes are found by bisection (pure NumPy, no scipy). The MMI beat length Lπ = π/(β₀ − β₁) is calibrated from the published L_MMI = 3Lπ/2 = 14.06 µm, giving Lπ_SWG = 9.373 µm at 1.55 µm.

MMI Self-Imaging and Mode Decomposition

Inside the MMI, the field is decomposed into two cosine modes excited at the input port positions (±W_MMI/6 from the centre, for optimal 2×2 coupling):

E(x, z) = c₀ · cos(πx/W) · exp(iβ₀z) + c₁ · cos(3πx/W) · exp(iβ₁z)

For TE₀ input (in-phase excitation at both ports), c₀ = A_top + A_bot and c₁ = A_top − A_bot, producing a constructive image at the cross port at z = 3Lπ/2. For TE₁ input (anti-phase), the sign of c₁ reverses, routing power to the bar port. The phase shifter corrects the residual π/2 phase so that the Y-junction produces clean mode-selective output.

Results

S-Parameter Spectrum

MMI S-parameters and full device performance

Fig. 4 / 6. Simulated S-parameters of the SWG-MMI coupler and full device insertion loss / crosstalk vs. wavelength (1.40–1.70 µm). The SWG's reduced index contrast extends the self-imaging bandwidth well beyond a conventional solid-Si MMI.

2D Field Distributions

Fig. 7. TE₀ input at Port 3: reconstructed |Ey|² field through the full device at λ = 1.40, 1.55, 1.70 µm. Self-imaging in the MMI routes power to a single output port. The field is plotted with z vertical (Ports 1&2 at bottom, Port 3 at top), jet colourmap.

Fig. 8. TE₁ input at Port 3: the antisymmetric field after the Y-junction, phase correction, and MMI self-imaging routes power to the complementary output port — demonstrating clean mode demultiplexing across the full 300 nm bandwidth.

Key result: TE₀ and TE₁ inputs at Port 3 are routed to different output ports (Port 1 and Port 2) across a 300 nm bandwidth, reproducing the published field maps analytically. The sub-wavelength grating inside the MMI is the bandwidth-extension mechanism: by lowering the effective index contrast, it reduces the wavelength sensitivity of the self-imaging condition.

Implementation Notes

The simulation is entirely analytical — no time-domain integration, no meshing, no PML boundaries. Each device section (input stubs, tapered transitions, MMI, phase shifter, Y-junction) is modelled with an appropriate field profile: Gaussian and Hermite-Gaussian for single-mode waveguides, cosine mode superposition for the MMI, and a cross-faded transition profile through the Y-junction. The resulting 2D complex field E_y(x, z) is assembled section-by-section across a 200 × 800 grid at each wavelength.

The dispersion solver uses bisection on the TE slab equation — the only non-trivial numerical step. No scipy is used anywhere; a manual 1D Gaussian convolution is implemented in NumPy for field smoothing. All 12 publication- quality figures (Figs 3–9, FigS1–FigS5) are generated by three independent scripts covering device physics, geometry diagrams, and field reconstruction. The analytical results are validated against full Lumerical FDTD simulations; those scripts are available upon request.