Photonic Waveguide Directional Coupler

Input Port

Chip Parameters

Waveguide gap 1.20 μm

Phase mismatch Δβ 0.00 mm⁻¹

Chip length L 4.0 mm

Output Power Split

Bar 100%Cross 0%

Coupling κ

— mm⁻¹

Coupling length L_c

— mm

How it works

Two single-mode waveguides brought close together on a photonic chip share overlapping evanescent fields. Their amplitudes a(z), b(z) obey the coupled-mode equations:

i da/dz = β₁a + κb
i db/dz = β₂b + κa

With light launched into waveguide A only, and δ = (β₁−β₂)/2 the propagation-constant mismatch, κ_eff = √(κ²+δ²) gives the exact solution:

P_A(z) = cos²(κ_eff z) + (δ/κ_eff)² sin²(κ_eff z)
P_B(z) = (κ/κ_eff)² sin²(κ_eff z)

Waveguide gap — the coupling coefficient falls off exponentially with separation, κ(g) = κ₀·exp(−g/d), so a wider gap slows the power exchange.
Phase mismatch Δβ — identical (phase-matched) waveguides allow 100% power transfer at the coupling length L_c = π/(2κ); detuned waveguides (different widths) never fully transfer, capping the cross-coupled power at κ²/(κ²+δ²).
Chip length L — the physical propagation distance; the output split is read off wherever the light exits the coupler region.

This exact mechanism is the workhorse building block of integrated photonic circuits — directional couplers act as on-chip beamsplitters for Mach-Zehnder interferometers, ring-resonator add-drop filters, and the linear-optical networks used in photonic quantum computing.

Waveguide A (input) Waveguide B (coupled)

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