Evanescent-Field Coupling
When two optical waveguides are brought close together, the exponentially decaying evanescent fields of their guided modes overlap. This overlap creates a periodic exchange of optical power between the waveguides, described by coupled-mode theory. The coupling coefficient kappa depends exponentially on the gap between the waveguides.
Coupled-Mode Theory
The coupled-mode equations describe how the complex amplitudes in each waveguide evolve along the propagation direction. For identical waveguides (zero phase mismatch), power transfers sinusoidally with a period of 2L_c, where L_c = pi/(2kappa) is the complete coupling length. The device length determines the splitting ratio.
Phase Mismatch Effects
When the waveguides have different widths, materials, or effective indices, a phase mismatch delta-beta arises. This mismatch reduces the maximum achievable coupling below unity and increases the oscillation frequency. The modified coupling behavior follows a generalized sinusoidal expression involving both kappa and delta-beta.
Integrated Photonic Applications
Directional couplers are fundamental building blocks of photonic integrated circuits. By controlling the coupling length and gap, designers create 3 dB splitters for interferometers, wavelength demultiplexers that exploit the wavelength dependence of kappa, and electro-optic switches that modulate delta-beta. Modern silicon photonics achieves sub-micron gaps with lithographic precision.