Lattice Form Filter

Cascaded MZI lattice — N stages tuned for a narrow bandpass response (default: 1550 nm center, 0.2 nm passband).

WG width W (μm) WG height H (μm) Δ (%) DC gap (μm, common)

λ center (nm) Passband Δλ (nm, FWHM) Stages N

Target points (auto-generated) — peak at λ_c, 3 dB at ±Δλ/2, deep stop beyond ±Δλ:

λ (nm)	P_bar target	Weight

L min (μm) L max (μm) ΔL min (μm) ΔL max (μm) Random starts Seed

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Window auto-set to ±5·Δλ around λ_c. Target points marked.

Equations

N-stage lattice: T = K(θ_N)·Φ·K(θ_N−1)·Φ·…·Φ·K(θ₀), where K(θ) = [[cos θ, −j sin θ], [−j sin θ, cos θ]] and Φ = diag(1, exp(−jΔφ)).

θ_k = κ(λ)·L_k, Δφ = (2π·n_eff/λ)·ΔL, FSR = λ²/(n_eff·ΔL).

P_bar(λ) = |T₁₁|², P_cross(λ) = |T₂₁|² = 1 − P_bar.