# Topological transformations of speckles

## TL;DR

This paper explores advanced topological transformations of speckle patterns using spiral wavefront modulation combined with symmetry-based amplitude modulations, enabling enhanced control over speckle features for optical applications.

## Contribution

It introduces novel combinations of spiral phase transforms and symmetry-based amplitude modulations to achieve controlled topological transformations of speckles.

## Key findings

- Permutations of speckle intensity maxima are statistically strengthened.
- Control over the period of transformations is achieved for periods 3 and 4.
- Phase saddle-points complete the transformation cycle.

## Abstract

Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As recently shown, spiral wavefront modulation of the impinging beam allows permuting intensity maxima and intrinsic $\pm 1$-charged optical vortices. Here, we study this cyclic-group algebra when combining spiral phase transforms of charge $n$, with $D_3$- and $D_4$-point-group symmetry star-like amplitude modulations. This combination allows statistical strengthening of permutations and controlling the period to be 3 and 4, respectively. Phase saddle-points are shown to complete the cycle. These results offer new tools to manipulate critical points in speckles.