Prime number factorization with light beams carrying orbital angular momentum

GAEA / GAEA-2 Spatial Light Modulators
Deep Learning / Neuronal Network Digital-/ Computer Holography/ CGH Higher Order Modes / Optical Vortex / OAM
Published on:
Authors: Xiaofei Li, Xin Liu, Quanying Wu, Jun Zeng, Yangjian Cai, Sergey A. Ponomarenko, Chunhao Liang
Abstract:

We point out a link between orbital angular momentum (OAM) carrying light beams and number theory. The established link makes it possible to formulate and implement a simple and ultrafast protocol for prime number factorization by employing OAM endowed beams that are modulated by a prime number sieve. We are able to differentiate factors from non-factors of a number by simply measuring the on-axis intensity of light in the rear focal plane of a thin lens focusing on a source beam. The proposed protocol solely relies on the periodicity of the OAM phase distribution, and hence, it is applicable to fully as well as partially coherent fields of any frequency and physical nature—from optical or x-ray to matter waves—endowed with OAM. Our experimental results are in excellent agreement with our theory. We anticipate that our protocol will trigger new developments in optical cryptography and information processing with OAM beams.

Open Access

Publication: APL Photonics
Issue/Year: APL Photonics 1 April 2024; 9 (4): 046107
DOI: 10.1063/5.0192223
Link: https://doi.org/10.1063/5.0192223

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