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- ItemSensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method(Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Goray, Leonid; Schmidt, GuntherThe conical boundary integral equation method has been proposed to calculate the sensitive optical response of 2D photonic band gaps (PBGs), including dielectric, absorbing, and highconductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a 2×2 system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equations system and the factorization of the discrete matrices, which takes the major computing time, are carried out only once for a boundary. It turned out that a small number of collocation points per boundary combined with a high convergence rate can provide adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs. array cell geometry parameters was found to vary from a few percent up to a few hundred percent. The influence of other types of anomalies (i.e. waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc), conductivity, and polarization states on the optical response has been demonstrated.