Substructuring approach to optimization of matching structures for photonic crystal waveguides

Micro-cavities formed by local defects within an otherwise perfect photonic crystal can trap light and resonate at wavelengths within the stop-band of the background crystal. An array of equally spaced identical micro-cavities forms the coupled cavity waveguide (CCW), a narrow band waveguide whose central frequency and bandwidth are determined by the form of the micro-cavities and their inter-spacing. Such devices can be used as optical or millimeter wave filters, routers, and (de)multiplexers. We develop a method for matching these devices to external structures. We formulate an optimization problem in which one seeks for the minimum of a properly defined standing wave ratio (SWR), with respect to limited variations of the dielectric structure in the neighborhood of the interface between the sub-system (micro-cavity, CCW) and the external structure. A novel numerical approach to solve this problem is developed and tested on a few examples.