What is the Right Theory for Anderson Localization of Light? An Experimental Test

Abstract

Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description the disorder strength -and hence the localization characteristicsdepends strongly on the wavelength of the incident light. In an alternative description in analogy to sound waves in a material with spatially fluctuating elastic moduli this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using transverse-localized optical devices. We do not find any dependence of the observed localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional, potential-type theory a term in the wave equation has been tacititly neglected. In our new modulus-type theory the wave equation is exact. We check the consistency of the new theory with our data using a field-theoretical approach (nonlinear sigma model).

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“…The acceleration of the process of thermalization reported in this work is also relevant to the notion of prethermalization to out of equilibrium states [23,[112][113][114][115], which is attracting a growing interest in different research communities, including long range interacting systems with fast relaxation towards quasi-stationary states [116][117][118], or one dimensional (nearly) integrable (quantum) systems [119][120][121][122][123]. From a broader perspective, the present work can contribute to the challenging question of spontaneous organization of coherent states in nonlinear disordered (turbulent) systems [84,85,[124][125][126][127][128], in relation with the paradigm of statistical lightmode dynamics (glassy behaviors) and complexity in random lasers [129,130].…”

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