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

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.