We present an exact theory for modeling defect modes in two-dimensional photonic crystals having an infinite cladding. The method is based on three key concepts, namely, the use of fictitious sources to modify response fields that allow defects to be introduced, the representation of the defect mode field as a superposition of solutions of quasiperiodic field problems, and the simplification of the two-dimensional superposition to a more efficient, one-dimensional average using Bloch mode methods. We demonstrate the accuracy and efficiency of the method, comparing results obtained using alternative techniques, and then concentrate on its strengths, particularly in handling difficult problems, such as where a mode is highly extended near cutoff, that cannot be dealt with in other ways.

An exact theory for modelling modes of generalised defects in 2D photonic crystals (PCs) with a genuinely infinite cladding is presented. The approach builds on our fictitious source superposition method for simple defects and permits an elegant extension allowing the modelling of arbitrary defects. Numerical results that demonstrate the accuracy and efficiency of the extended method are presented. We also use the method to study the evolution of the mode generated by varying the refractive index of a single defect cylinder and find significant differences between the behaviour of defects in rod-type and hole-type PCs.

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