Optics Letters

Prime number factorization and degree of coherence of speckled light beams

Tianyu Cao, Xin Liu, Qian Chen, Sergey A. Ponomarenko, Yangjian Cai, Chunhao Liang

Published Sep 3, 2024• 5 citations

Abstract

We discover a connection between a Gauss sum of number theory and the degree of coherence (DOC) of the field in a transverse plane of structured speckled light beams. We theoretically demonstrate and experimentally validate that prime number factorization can be achieved by manipulating the source beam's DOC in Young's double-slit experiment. The determination of whether a number can be factored is based solely on the visibility of the resulting interference patterns. Our findings offer new insights into information encryption and decryption, data compression, etc.

DOI: 10.1364/ol.537537

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