Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media

TL;DR

This paper theoretically analyzes how the localization length of TE waves at critical incidence scales in stratified random media with short-range correlated disorder, revealing universal scaling laws and dependencies on disorder parameters.

Contribution

It introduces a universal scaling law for the localization length at critical incidence in correlated random media, extending the invariant embedding method to such systems.

Findings

At critical angle, $k\xi$ depends on $kl_c\sigma^2$ via a universal equation.

The localization length scales as $\lambda^{4/3}$ across all wavelengths.

Strong disorder causes the localization behavior at other angles to converge to that at critical incidence.

Abstract

We theoretically investigate the scaling behavior of the localization length for $s$-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro-Loginov formula of differentiation, we accurately compute the localization length $\xi$ of $s$ waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter $\sigma^2$ and the disorder correlation length $l_c$. Away from the critical angle, $\xi$ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber $k$, $k\xi$ depends on the single parameter $kl_c\sigma^2$, satisfying a universal equation $k\xi\approx 1.3717\left(kl_c\sigma^2\right)^{-1/3}$ across the entire range of parameter values. Additionally, we find that $\xi$ scales as ${\lambda}^{4/3}$ for the entire range of the wavelength $\lambda$, regardless of the values of $\sigma^2$ and $l_c$. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence.