Transmission and reflection analysis of functional coupled cavity components

This paper contributes to the ongoing discussion within the photonic crystal community by providing essential insight into the limiting conditions of the coupled cavity waveguiding mechanism. A theoretical and numerical description of coupled defects in PBG crystals is applied to quantify the conditions under which reflections occur within coupled cavity photonic crystal systems. We present an analysis of coupled cavity systems that form a straight and bent waveguide, a Y-shaped symmetric power splitter, and a waveguide incorporating two bends. The method is based on a weak interaction approach; the actual configuration of the defects (chain, lattice, bend, splitter, or anything else) enters the equations as a linear coupling between neighboring defects. The strength of this method is that many solutions of this system are known analytically, and that the band structure as well as the transmission and reflection response of the system can be determined.