Mach-Zehnder Interferometer

Two identical DCs with arm path difference ΔL → wavelength filter (FSR = λ²/(n_eff·ΔL)).

WG width W (μm) WG height H (μm) Δ (%) DC1 gap (μm) DC1 L (μm) DC2 gap (μm) DC2 L (μm) ΔL (path diff) (μm) λ start (μm) λ end (μm) Samples

λ_center

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n_eff (at center)

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κ₁ · L₁ (DC1 split angle)

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κ₂ · L₂ (DC2 split angle)

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FSR (theory) λ²/(n_eff·ΔL)

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Bar peaks (P_bar≈1) at λ ≈

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Cross peaks (P_cross≈1) at λ ≈

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Top: schematic. Bottom: spectrum (P_bar blue, P_cross red).

Equations

Each DC: T = [[cos(κL), −j sin(κL)], [−j sin(κL), cos(κL)]]

Phase shift in arms: Δφ = β·ΔL = (2π·n_eff/λ)·ΔL

P_bar = |cos(κL₁)cos(κL₂) − sin(κL₁)sin(κL₂)·exp(−jΔφ)|², P_cross = 1 − P_bar

FSR ≈ λ² / (n_eff · ΔL) — channel spacing in WDM