Exact modelling of generalised defect modes in photonic crystal structures

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.