WIAS Preprint No. 1684, (2012)

Sensitivity analysis of 2D photonic band gaps of any rod shape and conductivity using a very fast conical integral equation method


  • Goray, Leonid
  • Schmidt, Gunther

2008 Physics and Astronomy Classification Scheme

  • 02.60.Nm 02.70.Pt 71.36.+c


  • Diffraction, multilayer periodic structure, integral method, oblique incidence, photonic crystal grating, S-matrix method




The conical boundary integral equation method has been proposedto calculate the sensitive optical response of 2D photonic band gaps (PBGs),including dielectric, absorbing, and high-conductive 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 gratingboundary profile. The computation of the matrices is based on the solution of a 2 x 2system 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 oncefor 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. Thenumerical 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 fillingratios. 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.

Appeared in

  • Phys. Rev. E (3), 85 (2012) pp. 036701/1--036701/12 under the new title ``Analysis of two-dimensional photonic band gaps of any rod shape and conductivity using a conical-integral-equation method''.

Download Documents