Anomalous localization and transport behavior of amplifying periodic-on-average random systems at critical disorder

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Optical amplification in a disordered system leads to modification of the localization properties and the relative fluctuations of transport parameters. Here, we study the effect of gain on the localization properties and transport parameters of Anderson-localized modes at critical disorder in a one-dimensional periodic-on-average random amplifying system. We experimentally measured the inverse participation ratio (IPR) and localization length $\ensuremath{\xi}$ to quantify the localization behavior. At high disorder, IPR and ${\ensuremath{\xi}}^{\ensuremath{-}1}$ exhibit a linear relationship, as expected from theoretical studies. However, it shows an anomalous behavior below a critical disorder and transitions into a near-quadratic relationship at weak disorder. We further study the mesoscopic conductance ${g}^{\ensuremath{'}}$ and statistical distributions of modal and integrated intensities to quantify the transport. The intensity distributions show power-law tails whose exponents show atypical gain dependence across the critical disorder. Motivated by the experimental results, we performed numerical studies using a model based on transfer matrices and laser rate equations which endorses our experimental observations.