Abstract

We extend the fictitious source superposition method in order to model linear defects in photonic woodpiles, and we use the method to model a waveguide that is created by changing either the radius or refractive index of a single rod of an infinite woodpile composed of chalcogenide glass cylinders. In one instance, a nearly constant dispersion was observed over a sizable $k_x$ interval, where $k_x$ is the Bloch vector in the waveguiding direction, making this a compelling geometry for slow-light waveguides. The principal advantage of the method is that it does not rely on a supercell, thus avoiding what is possibly the greatest source of inefficiency present in most of the other methods that are used for modeling these structures. Instead, the method proceeds by placing an artificial source inside each rod of the defect layer and then subsequently taking an appropriate field superposition to remove all but one of these sources. The remaining source can then be used to mimic the fields that would be produced by a defect rod.

© 2011 Optical Society of America

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