Glossary entry

Directional coupler

A four-port optical device that transfers power between two parallel waveguides via evanescent-field coupling. Used as a power splitter, combiner, and wavelength-selective filter in integrated photonics.

A directional coupler consists of two waveguides brought close enough together that their evanescent fields overlap. The overlap causes power to oscillate periodically between the two waveguides as it propagates along their length.

For two identical lossless waveguides with coupling coefficient $\kappa$ , light input to waveguide 1 produces power transfer described by

P_1(z) \;=\; P_0 \cos^2(\kappa z), \qquad P_2(z) \;=\; P_0 \sin^2(\kappa z).

Full power transfer occurs at $z = \pi / (2\kappa)$ — the coupling length. The 3 dB (50/50) coupling length is $\pi / (4\kappa)$ , half this value. The coupling coefficient $\kappa$ depends exponentially on the waveguide separation; precise control of the gap and length determines the splitting ratio.

When the two waveguides have different propagation constants (asymmetric coupler), the maximum power transfer is limited and the coupling becomes wavelength-selective. This is the basis for wavelength-division multiplexers and add–drop filters built from directional couplers.

Typical SOI directional couplers (220 nm strip, 1550 nm):

Configuration	Gap	Length	Splitting
50/50 coupler	200 nm	5 – 10 μm	3 dB ± 0.3 dB
90/10 tap	200 nm	$\sim$ 2 μm	10 dB tap
99/1 tap	250 nm	$\sim$ 1 μm	20 dB tap
Variable coupling for ring resonators	100 – 400 nm	gap-dependent	continuous

Compared to MMI couplers:

Property	Directional coupler	MMI coupler
Wavelength range	Narrow ( $\pm$ 5 – 10 nm flat)	Broad ( $\pm$ 30 – 50 nm flat)
Fabrication sensitivity	High (gap width critical)	Lower
Achievable splitting ratios	Continuous (any ratio)	Discrete (set by port positions)
Insertion loss (intrinsic)	$<$ 0.05 dB	0.1 – 0.5 dB
Best use case	Tunable rings, weak taps, narrowband filters	Broadband balanced splitters

Directional couplers are also the standard coupling element for ring resonators (chip-coupled microring): the ring waveguide and the bus waveguide form a short asymmetric directional coupler at their tangent point, transferring a controlled fraction of power per round trip. Tuning this coupling determines whether the ring operates in the under-coupled, critically coupled, or over-coupled regime.