Wannier-function based scattering-matrix formalism for photonic crystal circuitry
D. Hermann, M. Schillinger, S. F. Mingaleev, and K. Busch,
J. Opt. Soc. Am. B 25, 202-209 (2008).
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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.
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