Statistics of Reflected Speckle Intensities Arising from Localized States Inside the GAP of Disordered Photonic Crystals

Abstract

The field distributions of reflected speckles arising from localized states inside the gap of disordered photonic crystals in two dimensions were studied through numerical simulations using the multiple-scattering method. By separating the field into the coherent and diffuse parts, we have studied the statistics of field and phase distributions for both diffuse and total fields as well as their speckle contrasts as a function of the amount of disorder. For the non-Bragg angles, it is found that the intensity distribution crosses over from non-Rayleigh to Rayleigh statistics when disorder is increased. This is similar to the crossover from ballistic to diffusive wave propagation for the transmitted waves and can be described by the random-phasor-sum model (RPS). For the Bragg angle, only non-Rayleigh statistics were found. Both the RPS and K distribution have limited range of validity in this case.