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Nonlinear optical correlator in 4f configuration exploiting Kerr effect for optical processing and matrix multiplication

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Abstract

This paper focuses on the implementation of a nonlinear optical correlator in a 4f configuration. The system exploits the Kerr effect, specifically four-wave mixing, to enable the correlation and convolution of multiple optical fields composed of different objects in a single clock cycle. This approach offers a simpler implementation than other correlation systems, eliminating the need for counterpropagating waves and complex phase matching conditions. It exhibits both low-intensity correlation operations and high-intensity geometric images in its image plane, requiring the use of obstruction masks for optimal contrast. Experimental results confirm the feasibility of the concept, especially for applications in matrix multiplication and instantaneous optical processing operations.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

  1. A. Vander Lugt, Signal detection by complex spatial filtering. IEEE Trans. Inform. Theory 10, 139–145 (1964)

    Article  Google Scholar 

  2. C.S. Weaver, J.W. Goodman, A technique for optically convolving two functions. Appl. Opt. 5(7), 1248–1249 (1966)

    Article  ADS  Google Scholar 

  3. J.P. Huignard, A. Marrakchi, Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis. Opt. Lett. 6, 622–624 (1981)

    Article  ADS  Google Scholar 

  4. M. Cronin-Golomb, A.M. Biernacki, C. Lin, H. Kong, Photorefractive time differentiation of coherent optical images. Opt. Lett. 12(12), 1029–1031 (1987)

    Article  ADS  Google Scholar 

  5. P. Yeh, T.Y. Chang, P.H. Beckwith, Real-time optical image subtraction using dynamic holographic interference in photorefractive media. Opt. Lett. 13(7), 586–588 (1988)

    Article  ADS  Google Scholar 

  6. D.Z. Anderson, J. Feinberg, Optical novelty filters. IEEE J. Quantum Electron. 25(3), 635–647 (1989)

    Article  ADS  Google Scholar 

  7. D.M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Spatial convolution and correlation of optical fields via degenerate four-wave mixing. Opt. Lett. 3(1), 7–9 (1978)

    Article  ADS  Google Scholar 

  8. C.W. Thiel, Four-wave mixing and its applications (Faculty of Washington, Washington DC, 2008)

    Google Scholar 

  9. M. Cronin-Golomb, B. Fischer, J.O. White, A. Yariv, Theory and applications of four-wave mixing in photorefractive media. IEEE J. Quantum Electron. 20(1), 12–30 (1984)

    Article  ADS  Google Scholar 

  10. J.O. White, A. Yariv, Real-time image processing via four-wave mixing in a photorefractive medium. Appl. Phys. Lett. 37(1), 5–7 (1980)

    Article  ADS  Google Scholar 

  11. S.H. Lee, Mathematical operations by optical processing. Opt. Eng. 13(3), 196–207 (1974)

    Article  ADS  Google Scholar 

  12. S. H. Lee. Optical processing with nonlinearity and feedback. Proc. 1975 Electro-Optical Syst. Design co, 29 (1975).

  13. K. Fedus, G. Boudebs, H. Leblond, Degenerate multi-wave mixing inside a 4f imaging system in presence of nonlinear absorption. Appl. Phys. B 100(4), 827–831 (2010)

    Article  ADS  Google Scholar 

  14. K. Fedus, & G. Boudebs. Degenerate multi-wave mixing inside the 4f coherent imaging system. In The European Conference on Lasers and Electro-Optics (Optica Publishing Group, 2009) (p. CD_P17).

  15. W.T. Rhodes, Optical matrix-vector processors: basic concepts. High. Para. Signal. Process. Archit. 614, 146–152 (1986)

    Google Scholar 

  16. D.E. Tamir, N.T. Shaked, P.J. Wilson, S. Dolev, High-speed and low-power electro-optical DSP coprocessor. JOSA A 26(8), A11–A20 (2009)

    Article  ADS  Google Scholar 

  17. F. Wang, L. Liu, Y. Yin, Optical matrix-matrix multiplication by the use of fixed holographic multi-gratings in a photorefractive crystal. Opt. Commun. 125(1–3), 21–26 (1996)

    Article  ADS  Google Scholar 

  18. R.A. Athale, W.C. Collins, Optical matrix–matrix multiplier based on outer product decomposition. Appl. Opt. 21(12), 2089–2090 (1982)

    Article  ADS  Google Scholar 

  19. D. Psaltis, D. Casasent, M. Carlotto, Iterative color-multiplexed, electro-optical processor. Opt. Lett. 4(11), 348–350 (1979)

    Article  ADS  Google Scholar 

  20. D. Manzani, C.B. De Araújo, G. Boudebs, Y. Messaddeq, S.J. Ribeiro, The role of Bi2O3 on the thermal, structural, and optical properties of tungsten-phosphate glasses. J. Phys. Chem. B 117(1), 408–414 (2013)

    Article  Google Scholar 

  21. C.B. de Araújo, E.L. Falcão-Filho, A. Humeau, D. Guichaoua, G. Boudebs, L.R. Kassab, Picosecond third-order nonlinearity of lead-oxide glasses in the infrared. Appl. Phys. Lett. 87(22), 221904 (2005)

    Article  ADS  Google Scholar 

  22. K. Fedus, G. Boudebs, Q. Coulombier, J. Troles, X.H. Zhang, Nonlinear characterization of GeS2–Sb2S3–CsI glass system. J. Appl. Phys. 107(2), 023108 (2010)

    Article  ADS  Google Scholar 

  23. E.L. Falcão-Filho, C.B. de Araújo, C.A.C. Bosco, L.H. Acioli, G. Poirier, Y. Messaddeq, G. Boudebs, M. Poulain, Nonlinear optical properties of tungstate fluorophosphate glasses. J. Appl. Phys. 96(5), 2525–2529 (2004)

    Article  ADS  Google Scholar 

  24. G. Boudebs, M. Chis, A. Monteil, Contrast increasing by third-order nonlinear image processing: a numerical study for microscopic rectangular objects. Optics. Commun. 150(1–6), 287–296 (1998)

    Article  ADS  Google Scholar 

  25. G. Boudebs, S. Cherukulappurath, Nonlinear refraction measurements in presence of nonlinear absorption using phase object in a 4f system. Opt. Commun. 250(4–6), 416–420 (2005)

    Article  ADS  Google Scholar 

  26. S. Cherukulappurath, G. Boudebs, A. Monteil, 4f coherent imager system and its application to nonlinear optical measurements. JOSA B 21(2), 273–279 (2004)

    Article  ADS  Google Scholar 

  27. C. Schnebelin, C. Cassagne, C.B. de Araújo, G. Boudebs, Measurements of the third-and fifth-order optical nonlinearities of water at 532 and 1064 nm using the D4σ method. Opt. Lett. 39(17), 5046–5049 (2014)

    Article  ADS  Google Scholar 

  28. K. Fedus, G. Boudebs, C.B. de Araujo, M. Cathelinaud, F. Charpentier, V. Nazabal, Photoinduced effects in thin films of Te20As30Se50 glass with nonlinear characterization. Appl. Phys. Lett. 94(6), 061122 (2009)

    Article  ADS  Google Scholar 

  29. G. Boudebs, K. Fedus, C. Cassagne, H. Leblond, Degenerate multiwave mixing using Z-scan technique. Appl. Phys. Lett. 93(2), 021118 (2008)

    Article  ADS  Google Scholar 

  30. J. B. Zinoune, M. Chis, & G. Boudebs, Third order nonlinear optical correlators in a 4f Configuration. In 2023 23rd International Conference on Transparent Optical Networks (ICTON) (IEEE, 2023) (pp. 1–4).

  31. G.N. Henderson, J.F. Walkup, E.J. Bochove, Optical quadratic processor using four-wave mixing in BaTiO3. Opt. Lett. 14(15), 770–772 (1989)

    Article  ADS  Google Scholar 

  32. P. Yeh, A.E. Chiou, Optical matrix–vector multiplication through four-wave mixing in photorefractive media. Opt. Lett. 12(2), 138–140 (1987)

    Article  ADS  Google Scholar 

  33. R.A. Heinz, J.O. Artman, S.H. Lee, Matrix multiplication by optical methods. Appl. Opt. 9(9), 2161–2168 (1970)

    Article  ADS  Google Scholar 

  34. M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan, E.W. Van Stryland, Sensitive measurement of optical nonlinearities using a single beam. IEEE J. Quantum Electron. 26(4), 760–769 (1990)

    Article  ADS  Google Scholar 

  35. C.B. De Araújo, A.S. Gomes, G. Boudebs, Techniques for nonlinear optical characterization of materials: a review. Rep. Prog. Phys. 79(3), 036401 (2016)

    Article  ADS  Google Scholar 

  36. A. E. Chiou, M. Khoshnevisan, & P. Yeh, Optical matrix-matrix multiplication using multi-color four-wave mixing. In optical computing and nonlinear materials (Vol. 881, pp. 250–257) (1988). SPIE.

  37. M. Honari, B. Park, Y. Kim, & M. G. Suh, Matrix-vector multiplication using mixed space-frequency multiplexing of optical frequency combs. In Nonlinear Optics. (2023). (pp. Tu3B-3). Optica Publishing Group.

  38. S. Mukhopadhyay, D.N. Das, P.P. Das, P. Ghosh, Implementation of all-optical digital matrix multiplication scheme with nonlinear material. Opt. Eng. 40, 1998–2002 (2001)

    Article  ADS  Google Scholar 

  39. H.H. Zhu, J. Zou, H. Zhang, Y.Z. Shi, S.B. Luo, N. Wang, N. Wang, H. Cai, L.X. Wan, B. Wang, X.D. Jiang, J. Thompson, A.Q. Liu, Space-efficient optical computing with an integrated chip diffractive neural network. Nat. Commun. 13(1), 1044 (2022)

    Article  ADS  Google Scholar 

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Funding

Univ Angers. Laboratoire de Photonique d’Angers (LPHIA, EA 4464). SFR MATRIX. This research was funded through a doctoral contract awarded by the University of Angers and supplemented by financial support from ESAIP, covering half of the total expenses.

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Authors and Affiliations

  1. Univ Angers, LPHIA, SFR MATRIX, F-49000, Angers, France

    Julien-Bilal Zinoune, Christophe Cassagne, Mihaela Chis & Georges Boudebs

  2. ESAIP, CERADE, 18, rue du 8 mai 1945, 49180, St-Barthélemy d’Anjou Cedex, France

    Julien-Bilal Zinoune & Mihaela Chis

Authors
  1. Julien-Bilal Zinoune
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  2. Christophe Cassagne
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  3. Mihaela Chis
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  4. Georges Boudebs
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Contributions

Conceptualization: [G. B.]; Methodology: [G. B.]; Formal analysis and investigation: [J. B. Z.; C. C., G. B.]; Writing - original draft preparation: [J. B. Z.]; Writing - review and editing: [J. B. Z., G. B.; C. C.; M. C.]; Funding acquisition: [G. B., M. C.]; Supervision: [G. B.; C. C.; M. C.]

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Correspondence to Julien-Bilal Zinoune.

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Zinoune, JB., Cassagne, C., Chis, M. et al. Nonlinear optical correlator in 4f configuration exploiting Kerr effect for optical processing and matrix multiplication. Appl. Phys. B 130, 50 (2024). https://doi.org/10.1007/s00340-024-08176-2

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