Symmetry between absorption and amplification in disordered media

TL;DR

This paper investigates the relationship between absorption and amplification in disordered media, revealing that the perceived symmetry is an artifact and that above the gain threshold, wave amplitudes grow unboundedly over time.

Contribution

The study clarifies the true behavior of wave amplification versus absorption, challenging previous claims of symmetry and emphasizing the importance of time-dependent analysis.

Findings

Absorption and amplification are not symmetric in wave transmission.

Above the gain threshold, wave amplitudes increase without bound.

Time-dependent solutions show growth in transmitted and reflected waves.

Abstract

We address the issue of whether amplification, like absorption, suppresses wave transmission at large gain, as has been claimed in previous studies of wave propagation in active random media. A closer examination reveals that the paradoxical symmetry between absorption and amplification is an artifact of unphysical solutions from the time-independent wave equation. Solutions from the time-dependent equation demonstrate clearly that when gain is above the threshold, the amplitude of both the transmitted and the reflected wave actually increases with time, apparently without bound. The implications of the current finding is discussed