Anderson localization of electromagnetic waves in randomly-stratified magnetodielectric media with uniform impedance

Abstract

The propagation and the Anderson localization of electromagnetic waves in a randomly-stratified slab, where both the dielectric permittivity and the magnetic permeability depend on one spatial coordinate in a random manner, is theoretically studied. The case where the wave impedance is uniform, while the refractive index is random, is considered in detail. The localization length and the disorder-averaged transmittance of s and p waves incident obliquely on the slab are calculated as a function of the incident angle θ and the strength of randomness in a numerically precise manner, using the invariant imbedding method. It is found that the waves incident perpendicularly on the slab are delocalized, while those incident obliquely are localized. As the incident angle increases from zero, the localization length decreases from infinity monotonically to some finite value. The localization length is found to depend on the incident angle as θ^-4 and a simple analytical formula, which works quite well for weak disorder and small incident angles, is derived. The localization length does not depend on the wave polarization, but the disorder-averaged transmittance generally does.

Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

“…The value of the slope suggests an exponent v′ 2, i.e., ξ ∝ sin −2 θ 0 . This result is distinctly different from those found in Hermitian impedance-matched 1D random systems [31] and pseudospin-1 system [32], in which the exponents found are both v′ 4 rather than v′ 2.…”

“…In both scenarios, it is expected that the presence of coherent backscattering can lead to the Anderson localization of waves, i.e., the transmission will decay exponentially to zero when the sample is sufficiently large. Our results will be compared with the Anderson localization behaviors found in some special Hermitian random systems, where localization length is also known to be infinite at normal incidence such as random layered media with the same impedance in all layers [31] and pseudospin-1 systems in 1D random potential [32,33].…”

Anderson localization and delocalization of massless two-dimensional Dirac electrons in random one-dimensional scalar and vector potentials

“…Similar methods have been applied in previous studies of the localization of electromagnetic waves in random dielectric media. 41,[47][48][49] We assume that an electron plane wave is incident from a uniform region (x > L) onto the random region (0 ≤ x ≤ L) obliquely at an angle θ and transmitted to another uniform region (x < 0). The wave function ψ A (or equivalently ψ B ) in the incident and transmitted regions can be expressed in terms of the reflection coefficient r and the transmission coefficient t:…”

Quasi-resonant diffusion of wave packets in one-dimensional disordered mosaic lattices

“…However, it has been found that this conclusion is not always true in more general random systems and there exist various situations where some states are not exponentially localized, but are either extended or critically localized. Representative examples include the cases where distinct kinds of impedance matching phenomena such as the Brewster anomaly [15][16][17][18][19][20] and the Klein effect [21][22][23][24] happen or the random potential is spatially correlated with short-or long-range correlations [25][26][27][28][29][30][31][32][33]. For instance, it has been demonstrated both theoretically and experimentally that there exist extended states at two energy values in the 1D random dimer model which contains a special type of shortrange correlated disorder [25,26].…”