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
Original Manuscript: September 10, 2007
Manuscript Accepted: November 19, 2007
Published: January 29, 2008
Daniel Hermann, Matthias Schillinger, Sergei F. Mingaleev, and Kurt Busch, "Wannier-function based scattering-matrix formalism for photonic crystal circuitry," J. Opt. Soc. Am. B 25, 202-209 (2008)