Abstract
A theory is presented for the flow of electromagnetic energy in photonic crystal circuits. Photonic crystal circuits are waveguide networks in photonic crystals. The theory is based on a set of difference equations which describe the propagation of electromagnetic waves in particular types of photonic crystal waveguides. Solutions are given for the transmission and reflection of electromagnetic waves from barriers in an otherwise infinitely long straight photonic crystal waveguide, from a junction of an infinite and a semi-infinite photonic crystal waveguide, and from an optical switching circuit. The theory developed is applicable to extended circuits with complex topologies. It is applicable to circuits in two-dimensional and three-dimensional photonic crystals.
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