# Squeeze operators in classical scenarios

## TL;DR

This paper explores how classical optics field propagation can be described using fractional Fourier transforms and squeeze operators, revealing new insights into wavelet transforms as displacement and squeeze operations.

## Contribution

It demonstrates that paraxial propagation and wavelet transforms can be modeled with fractional Fourier and squeeze operators, offering a novel perspective in classical optics analysis.

## Key findings

- Paraxial field propagation is equivalent to fractional Fourier transform followed by a squeeze operator.
- Wavelet transform can be interpreted as a displacement and squeeze operator acting on the mother wavelet.
- Provides a unified operator framework for classical optics and wavelet analysis.

## Abstract

We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field. Secondly, we show that a wavelet transform may be viewed as the application of a displacement and squeeze operator onto the mother wavelet function.