Resonances in 1D disordered systems: localization of energy and resonant transmission

TL;DR

This paper investigates localized states in 1D disordered systems, revealing their connection to internal sample structures and how certain localized modes lead to high transmission and energy concentration.

Contribution

It introduces a mapping of the stochastic scattering problem to a deterministic quantum problem and proposes an algorithm to locate resonant cavities within disordered samples.

Findings

Localized states are linked to transparent segments within the sample.

Only a subset of localized modes achieve near-perfect transmission.

Maximal transmission occurs in modes localized at the center, while energy concentrates near the input.

Abstract

Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with these states are due to the existence inside the sample of a transparent (for a given resonant frequency) segment with the minimal size of order of the localization length. A mapping of the stochastic scattering problem in hand onto a deterministic quantum problem is developed. It is shown that there is no one-to-one correspondence between the localization and high transparency: only small part of localized modes provides the transmission coefficient close to one. The maximal transmission is provided by the modes that are localized in the center, while the highest energy concentration takes place in cavities shifted towards the input. An algorithm is proposed to estimate the position of an effective resonant cavity and its pumping rate by measuring the resonant transmission coefficient. The validity of the analytical results have been checked by extensive numerical simulations and wavelet analysis.