# Phenomenology of complex structured light in turbulent air

## TL;DR

This paper investigates how atmospheric turbulence affects complex structured light, specifically Ince-Gauss modes, revealing basis-dependent propagation effects that could guide future experimental and theoretical research.

## Contribution

It provides the first detailed analysis of atmospheric turbulence effects on different spatial bases of complex light, especially Ince-Gauss modes, bridging a gap between theory and experiment.

## Key findings

- Eigenstate basis light is more affected by turbulence.
- Turbulence influence varies with the spatial basis.
- Results suggest basis choice is crucial for robust complex light transmission.

## Abstract

The study of light propagation has been a cornerstone of progress in physics and technology. Recently, advances in control and shaping of light have created significant interest in the propagation of complex structures of light -- particularly under realistic terrestrial conditions. While theoretical understanding of this research question has significantly grown over the last two decades, outdoor-experiments with complex light structures are rare, and comparisons with theory have been nearly lacking. Such situations show a significant gap between theoretical models of atmospheric light behaviour and current experimental effort. Here, in an attempt to reduce this gap, we describe an interesting result of atmospheric models which are feasible for empirical observation. We analyze in detail light propagation in different spatial bases and present results of the theory that the influence of atmospheric turbulence is basis-dependent. Concretely, light propagating as eigenstate in one complete basis is stronger influenced by atmosphere than light propagating in a different, complete basis. We obtain these results by exploiting a family of the continuously adjustable, complete basis of spatial modes -- the Ince-Gauss modes. Our concrete numerical results will hopefully inspire experimental efforts and bring the theoretical and empirical study of complex light patterns in realistic scenarios closer together.