Quantum like representation of aSpiral Phase Plate

TL;DR

This paper presents a quantum-like two-mode phase operator model for a Spiral Phase Plate, validated by classical and quantum comparisons, offering a novel mathematical framework for analyzing optical elements.

Contribution

It introduces a new quantum-like representation of a Spiral Phase Plate using a two-mode phase operator based on the Newton binomial expansion.

Findings

The representation matches Paul's operator in the single mode limit.

It accurately describes the action on Gaussian and off-axis Gaussian beams.

The model bridges classical and quantum descriptions of optical elements.

Abstract

We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of lowering and raising operators of quantum field. The correctness of this representation is proved by obtaining the same results of the Paul's operator in the single mode limit and comparing the results of two particular problems solved both in the classical and quantum picture: the action of a Spiral Phase Plate on a Gaussian Beam (corresponding to the vacuum state of the two-dimensional harmonic oscillator) and on a off-axis Gaussian Beam (corresponding to the displaced vacuum state in quantum picture).