The invention is a waveguide structure (10) that includes two waveguides (90, 94) flanking a coupling region (92) whose effective refractive index is less than those of the waveguides. Outboard of the waveguides are bounding regions (88, 96) whose effective refractive indices decrease inwards adiabatically at the proximal and distal ends of the bounding regions. The waveguides are coupled optically by periodic perturbations of the waveguide geometry, or by reversible uniform or periodic perturbations of the effective refractive indices. In an optical switch matrix based on the waveguide structure, all the waveguides are straight and parallel. A second aspect of the invention is a directional coupler comprising mechanisms for reversibly and quasiperiodically perturbing the effective refractive indices of the waveguides. The respective envelope functions vary monotonically in opposite senses. Light propagating in one waveguide, in the direction in which that waveguide's envelope function increases, is coupled into the other waveguide.