Transverse Light Localization in waveguide arrays with random absorption or amplification

We investigate the possibility to induce transverse localization of light in an array of waveguides with randomness pertaining to the imaginary part of the dielectric constant. Although this new set-up is distinct from the traditional Anderson scenario, where localization emerges due to multiple scattering from a real random potential, we find that disordered amplification/attenuation can also lead to exponential localization. We quantify the degree of localization of the Floquet-Bloch modes of our system via their participation number, which is shown to satisfy a one-parameter scaling theory. The effects of this transverse localization of the normal modes in the paraxial beam propagation are theoretically predicted and confirmed by numerical experiments.