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  • Letter

Axial Correlation Revivals and Number Factorization with Structured Random Waves

Xin Liu1,2,‡, Chunhao Liang1,2,‡, Yangjian Cai1,2,*, and Sergey A. Ponomarenko3,4,†

  • 1Shandong Provincial Engineering and Technical Center of Light Manipulation and Shandong Provincial Key Laboratory of Optics and Photonics Devices, School of Physics and Electronics, Shandong Normal University, Jinan 250014, China
  • 2Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
  • 3Department of Electrical and Computer Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4, Canada
  • 4Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada

  • *yangjian_cai@163.com
  • †serpo@dal.ca
  • ‡These authors contributed equally to this work
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Phys. Rev. Applied 20, L021004 – Published 22 August, 2023

DOI: https://doi.org/10.1103/PhysRevApplied.20.L021004

Abstract

We advance a general theory of field correlation revivals of structured random wave packets, composed of superpositions of propagation invariant modes, at pairs of planes transverse to the packet propagation direction. We derive an elegant analytical relation between the normalized intensity autocorrelation function of the thus structured paraxial light fields at a pair of points on an optical axis of the system and an incomplete Gauss sum, thereby establishing a fundamental link between statistical optics and number theory. We propose and experimentally implement a simple robust analog random wave computer that can efficiently decompose numbers into prime factors.

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Phys. Rev. Applied 20, L021004– Published 22 August, 2023
  • Received 19 March 2023
  • Revised 16 July 2023
  • Accepted 26 July 2023
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