# What is the right theory for Anderson localization of light?

## TL;DR

This paper experimentally tests two competing theories of Anderson localization of light, finding evidence that supports a modulus-type description over the traditional potential-type model, with localization independent of wavelength.

## Contribution

It provides experimental validation favoring the modulus-type theory for light localization, challenging the traditional potential-type analogy used in the field.

## Key findings

- Localization radii do not depend on wavelength.
- The modulus-type theory aligns with experimental data.
- The traditional potential-type wave equation neglects a key term.

## 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 characteristics -- depends 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).