Directional Coupler

Two parallel waveguides — coupling coefficient, transfer length, power split.

Wavelength (μm) WG width W (μm) WG height H (μm) Δ (%) Gap (μm) L_DC (μm)

n_core (Sellmeier)

—

n_clad

—

n_eff (total)

—

κ_x, γ_x (slab)

—

κ (coupling)

—

L_c (full transfer)

—

L_50 (3 dB / 50:50)

—

P_cross @ L_DC

—

P_through @ L_DC

—

Top: schematic of the coupler (not to scale). Bottom: power transfer along z.

Equations

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

L_c = π/(2κ), L_50 = π/(4κ)

P_cross(z) = sin²(κz), P_through(z) = cos²(κz)