Directional Coupler II — WDM Spectrum

Wavelength-dependent power split. κ(λ) varies via Sellmeier and slab modes — fixed geometry produces a wavelength filter.

WG width W (μm) WG height H (μm) Δ (%) Gap (μm) L_DC (μm) λ start (μm) λ end (μm) Samples

λ_center (range mid)

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κ at λ_center

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L_c at λ_center

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P_cross at λ_center

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Cross peaks (P=1) at λ ≈

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Bar peaks (P_through=1) at λ ≈

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Approx FSR (peak spacing)

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Spectrum: P_through (blue) and P_cross (red) vs wavelength. Vertical lines mark the cross peaks and through peaks.

Equations

κ(λ) = 2·κ_x²·γ_x·exp(−γ_x·gap) / [β·(κ_x²+γ_x²)·(1+γ_x·a)], recomputed at every λ

P_cross(λ) = sin²(κ(λ)·L_DC), P_through(λ) = cos²(κ(λ)·L_DC)