Optical wave fields with lateral and longitudinal periodicity.

The propagation of stationary wave fields that exhibit simultaneously lateral and longitudinal periodicity is investigated. As a model, we use a Fabry-Perot resonator with periodically structured mirrors under monochromatic plane wave illumination. The resonator leads to a longitudinal periodicity, the grating mirrors to a lateral periodicity. The angular spectrum of the transmitted wave field is given as the product of two terms, one related to the lateral, the other to the longitudinal properties. Its modal structure can vary significantly depending on the ratio of the lateral and longitudinal periods and the reflectivity of the resonator's mirrors. For example, it is possible to generate bandgap behavior despite the fact that the periods may be significantly larger than the wavelength. The results of this investigation apply to the design of phase-coupled array resonators and multiplexers.