# Superdiffusive random laser

## TL;DR

This paper investigates superdiffusive random lasers using Monte Carlo simulations, revealing that superdiffusion increases threshold energy and enhances spectral fluctuations, making the emission regime difficult to switch off.

## Contribution

It provides a theoretical analysis of superdiffusive random lasers, highlighting the impact of superdiffusion on emission thresholds and spectral fluctuations, which was not previously explored.

## Key findings

- Superdiffusion raises the threshold energy for lasing.
- Spectral fluctuations are more prominent in superdiffusive regimes.
- Superdiffusive regimes are hard to switch off by changing gain and scattering.

## Abstract

The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by L\'evy walks, i.e. with a `heavy-tailed' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium, that can lead to a "superdiffusive random laser." Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on the widespread presence of fluctuation regimes, that, in contrast to a diffusive random laser, appears very hard to switch off by changing the gain and scattering strength. Hence, the superdiffusion appears as a condition that increases the value of the threshold energy and promotes the presence of fluctuations in the emission spectrum.