M × N MMI Coupler

Self-imaging design (general interference). Length and width from waveguide spec, ports per side, and gap.

Wavelength (μm) WG width W (μm) WG height H (μm) Δ (%) Inputs M Outputs N Gap (μm)

n_core (Sellmeier)

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n_clad

—

pitch (= W + gap)

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W_MMI

—

W_eff (Goos-Hänchen)

—

L_π (beat length)

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L_MMI

—

Top-down schematic. Length (x) and width (y) use independent scales — actual aspect ratio is L_MMI ≫ W_MMI for low-Δ designs.

Equations

pitch = W + gap, W_MMI = max(M, N) · pitch

W_e = W_MMI + (λ/π) · (n_clad/n_core)^2σ / √(n_core² − n_clad²), σ = 0 (TE)

L_π = 4 · n_core · W_e² / (3 · λ), L_MMI = 3 · L_π / N (general interference)