Wannier-Function Based Scattering-Matrix Formalism For Photonic Crystal Circuitry

A guided-mode scattering matrix approach to photonic crystal integrated devices, based on the expansion of the electromagnetic field in Wannier functions is presented and its applicability to large-scale photonic circuits is demonstrated. In particular, we design two components typically used in wavelength division multi/demultiplexing applications, namely, a directional coupler and a Mach-Zehnder interferometer, and we analyze the transmission spectra as a function of the coupler length and/ or delay line length, respectively. These examples demonstrate that by cascading basic functional elements, large-scale circuits can be accurately described and efficiently designed with minimal numerical effort. © 2008 Optical Society of America