A spiral sampling method for calculating the complex orbital angular momentum spectrum

TL;DR

This paper introduces a novel spiral sampling method combined with Fourier analysis to efficiently calculate the complex orbital angular momentum spectrum of light fields, overcoming limitations of traditional methods.

Contribution

The proposed approach enables rapid and accurate retrieval of the OAM spectrum without prior knowledge, using spiral sampling and Fourier transform techniques.

Findings

MAE of 0.0221 for amplitude

MAE of 0.0199 for phase

Effective for arbitrary OAM components

Abstract

OAM spectrum reflects the OAM component included in measured light field which is crucial in OAM -based application. However, traditional definition-based OAM spectrum algorithm is extraordinary time-consuming and limited to prior knowledge severely. To overcome it, in this paper, we propose a novel method to calculate the complex spectrum. After spiral sampling and Fourier transform, one can retrieve the radial coefficient of arbitrary OAM component by proper filtering and inverse Fourier transform. The simulation results reveal that the Mean Absolute Error (MAE) between retrieved one and target could reach at 0.0221 and 0.0199 on average for amplitude and phase respectively after normalized. This method could provide a powerful tool for future OAM-based and application.