Complexity of 2D random laser modes at the transition from weak scattering to Anderson localization

TL;DR

This paper investigates how the spatial complexity of 2D random laser modes evolves from weak scattering to Anderson localization, revealing multipeaked states at the transition point.

Contribution

It systematically analyzes the eigenfunctions of 2D random systems across different scattering regimes, highlighting the existence of necklace states at the localization transition.

Findings

Eigenfunctions correspond to quasimodes in all regimes

Multipeaked necklace states are observed at the localization transition

Eigenfunction complexity increases with scattering strength

Abstract

The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The eigenfunctions are obtained by introducing gain in the medium and pumping just above threshold. All lasing modes are found to correspond to quasimodes of the passive system, for all regimes of propagation. We demonstrate the existence of multipeaked quasimodes or necklace states in 2D at the transition from localized to diffusive, resulting from the coupling of localized states.