Investigation of Brewster anomalies in one-dimensional disordered media having Lévy-type distribution

Abstract

In this paper, we calculate the localization length of a TM electromagnetic wave in unit of system length versus incident angle in a disordered layered structure where the refractive index of one of its constituents follows a Lévy-type distribution with a power exponent α. The incident angle at which the localization length takes the maximum value is called the generalized Brewster angle as before. However, in contrast to previous works with a weak disorder, the wave incident at generalized Brewster angle is not always in the extended regime. For special values of α and the frequency, the system is in a localized state at this angle. But, the localization length at this Brewster angle is always larger than that at other angles. The effects of α variation on the localization length at this Brewster angle and its position are investigated for different frequencies. The localization at this angle degrades with increasing α for all frequencies. At some working frequencies, the generalized Brewster angle is a decreasing function of α. However, at other frequencies, the dependence of generalized Brewster angle on α is not monotonic. For incident angles smaller than a specific angle, the localization length increases with increasing α. However, for incident angles larger than this specific angle, there are incident angles at which any increase of α leads to the decrease of localization length. In other words, for these incident angles, the improvement of Anderson localization surprisingly happens with decrease of disorder strength and the refractive index contrast.