- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Gouy phase-assisted Zeno effect for protecting light structure in random media

Nilo Mata-Cervera1, Anton N. Vetlugin1, Cesare Soci1,2, Miguel A. Porras3,*, and Yijie Shen1,2,†

  • *Contact author: miguelangel.porras@upm.es
  • †Contact author: yijie.shen@ntu.edu.sg
PDF

Phys. Rev. Research 8, 023036 – Published 10 April, 2026

DOI: https://doi.org/10.1103/9yy8-dzcm

Abstract

Identifying physical mechanisms that preserve the integrity of structured waves under propagation through complex environments is one of the central problems in wave physics. Here, we show that the purity of orbital angular momentum (OAM) modes can be protected against degradation in random media by leveraging two fundamental features of their own Schrödinger Hamiltonian dynamics, namely, Zeno effect—frequent observations slow down the evolution—and Gouy phase—the backaction of the observation. Repeated, OAM-dependent Gouy phase kicks imparted along the disturbing path by simple imaging systems trigger the optical Zeno effect that protects the input OAM mode against mode crosstalk that would broaden the OAM spectrum. Given the universality of the mechanism, the Gouy phase-assisted Zeno effect would protect propagation modes other than those of OAM, and the diverse forms of structured light built with them.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. L. G. Gouy, Sur une propriété nouvelle des ondes lumineuses (Mélanges scientifiques) (Gauthier-Villars, Paris, 1890), Vol. 2.
  2. L. G. Gouy, Sur la propagation anomale des ondes, Compt. Rendue Acad. Sci. Paris 111, 33 (1890).
  3. N. C. R. Holme, M. T. Myaing, and T. B. Norris, Gouy phase shift of single-cycle picosecond acoustic pulses, in International Conference on Ultrafast Phenomena (Optica Publishing Group, 2002), p. ThA5.
  4. R. Ducharme and I. G. da Paz, Gouy phase for relativistic quantum particles, Phys. Rev. A 92, 023853 (2015).
  5. M. Hiekkamäki, R. F. Barros, M. Ornigotti, and R. Fickler, Observation of the quantum Gouy phase, Nat. Photonics 16, 828 (2022).
  6. J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, Direct observation of Gouy phase shift in a propagating optical vortex, Opt. Express 14, 8382 (2006).
  7. D. Subbarao, Topological phase in Gaussian beam optics, Opt. Lett. 20, 2162 (1995).
  8. R. W. Boyd, Intuitive explanation of the phase anomaly of focused light beams, J. Opt. Soc. Am. 70, 877 (1980).
  9. S. Feng and H. G. Winful, Physical origin of the Gouy phase shift, Opt. Lett. 26, 485 (2001).
  10. M. Padgett and L. Allen, The Poynting vector in Laguerre-Gaussian laser modes, Opt. Commun. 121, 36 (1995).
  11. J. Chen, X. Shen, Q. Zhan, and C.-W. Qiu, Gouy phase induced optical skyrmion transformation in diffraction limited scale, Laser Photonics Rev. 19, 2400327 (2025).
  12. N. D. Bareza and N. Hermosa, Subluminal group velocity and dispersion of Laguerre Gauss beams in free space, Sci. Rep. 6, 26842 (2016).
  13. D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, Spatially structured photons that travel in free space slower than the speed of light, Science 347, 857 (2015).
  14. B. P. da Silva, V. A. Pinillos, D. S. Tasca, L. E. Oxman, and A. Z. Khoury, Pattern revivals from fractional Gouy phases in structured light, Phys. Rev. Lett. 124, 033902 (2020).
  15. R.-Y. Zhong, Z.-H. Zhu, H.-J. Wu, C. Rosales-Guzmán, S.-W. Song, and B.-S. Shi, Gouy-phase-mediated propagation variations and revivals of transverse structure in vectorially structured light, Phys. Rev. A 103, 053520 (2021).
  16. A. Forbes, M. De Oliveira, and M. R. Dennis, Structured light, Nat. Photonics 15, 253 (2021).
  17. P. Martelli, M. Tacca, A. Gatto, G. Moneta, and M. Martinelli, Gouy phase shift in nondiffracting Bessel beams, Opt. Express 18, 7108 (2010).
  18. A. Volyar, T. Fadeeva, and V. Shvedov, Topological phase in a nonparaxial Gaussian beam, Tech. Phys. Lett. 25, 891 (1999).
  19. S. Cruz y Cruz, Z. Gress, P. Jiménez-Macías, and O. Rosas-Ortiz, Laguerre-Gaussian wave propagation in parabolic media, in Geometric Methods in Physics XXXVIII: Workshop, Białowieża, Poland, 2019 (Springer, 2020), pp. 117–128.
  20. S. Feng, H. G. Winful, and R. W. Hellwarth, Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses, Opt. Lett. 23, 385 (1998).
  21. X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, Gouy phase radial mode sorter for light: Concepts and experiments, Phys. Rev. Lett. 120, 103601 (2018).
  22. D. Hofstadter, Alan Turing: Life and Legacy of a Great Thinker (Springer Science & Business Media, 2013).
  23. B. Misra and E. G. Sudarshan, The Zeno’s paradox in quantum theory, J. Math. Phys. 18, 756 (1977).
  24. P. Facchi, V. Gorini, G. Marmo, S. Pascazio, and E. Sudarshan, Quantum Zeno dynamics, Phys. Lett. A 275, 12 (2000).
  25. F. Schäfer, I. Herrera, S. Cherukattil, C. Lovecchio, F. S. Cataliotti, F. Caruso, and A. Smerzi, Experimental realization of quantum Zeno dynamics, Nat. Commun. 5, 3194 (2014).
  26. Q. Liu, W. Liu, K. Ziegler, and F. Chen, Engineering of Zeno dynamics in integrated photonics, Phys. Rev. Lett. 130, 103801 (2023).
  27. P. Blanchard and A. Jadczyk, Strongly coupled quantum and classical systems and Zeno’s effect, Phys. Lett. A 183, 272 (1993).
  28. F. Benatti and R. Floreanini, Irreversible Quantum Dynamics, Lecture Notes in Physics (Springer Berlin, Heidelberg, 2003), Vol. 622.
  29. P. Facchi and S. Pascazio, Quantum Zeno dynamics: Mathematical and physical aspects, J. Phys. A: Math. Theor. 41, 493001 (2008).
  30. P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Duo, P. Laporta, and S. Longhi, Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy, Opt. Express 16, 3762 (2008).
  31. S.-J. Gu, L.-G. Wang, Z.-G. Wang, and H.-Q. Lin, Repeater-assisted Zeno effect in classical stochastic processes, Chin. Phys. Lett. 29, 010303 (2012).
  32. M. A. Porras, A. Luis, I. Gonzalo, and A. S. Sanz, Zeno dynamics in wave-packet diffraction spreading, Phys. Rev. A 84, 052109 (2011).
  33. M. A. Porras, A. Luis, and I. Gonzalo, Classical Zeno dynamics in the light emitted by an extended, partially coherent source, Phys. Rev. A 88, 052101 (2013).
  34. M. Malik, M. O'Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. Lavery, M. J. Padgett, and R. W. Boyd, Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding, Opt. Express 20, 13195 (2012).
  35. M. A. Cox, N. Mphuthi, I. Nape, N. Mashaba, L. Cheng, and A. Forbes, Structured light in turbulence, IEEE J. Sel. Top. Quantum Electron. 27, 1 (2020).
  36. A. Klug, I. Nape, and A. Forbes, The orbital angular momentum of a turbulent atmosphere and its impact on propagating structured light fields, New J. Phys. 23, 093012 (2021).
  37. D. Bachmann, A. Klug, M. Isoard, V. Shatokhin, G. Sorelli, A. Buchleitner, and A. Forbes, Universal crosstalk of twisted light in random media, Phys. Rev. Lett. 132, 063801 (2024).
  38. F. Roddier, The Effects of Atmospheric Turbulence in Optical Astronomy, in Progress in Optics (Elsevier, 1981), Chap. 5, Vol. 19, pp. 281–376.
  39. R. Lane, A. Glindemann, and J. Dainty, Simulation of a Kolmogorov phase screen, Waves Random Media 2, 209 (1992).
  40. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proc. R. Soc. London Ser. A 434, 9 (1991).
  41. M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC Press, 2018).
  42. C. Peters, V. Cocotos, and A. Forbes, Structured light in atmospheric turbulence—A guide to its digital implementation: Tutorial, Adv. Opt. Photonics 17, 113 (2025).
  43. E. Hussey (ed.), Aristotle's Physics, books III and IV (Oxford University Press, 1983), p. 239b10.
  44. R. Gagliardi, Optical Communications, 2nd ed. (Wiley, 1976).
  45. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Free-space information transfer using light beams carrying orbital angular momentum, Opt. Express 12, 5448 (2004).
  46. Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, et al., High-capacity millimetre-wave communications with orbital angular momentum multiplexing, Nat. Commun. 5, 4876 (2014).
  47. D. Dhar, L. K. Grover, and S. M. Roy, Preserving quantum states using inverting pulses: A super-Zeno effect, Phys. Rev. Lett. 96, 100405 (2006).
  48. P. Facchi, D. A. Lidar, and S. Pascazio, Unification of dynamical decoupling and the quantum Zeno effect, Phys. Rev. A 69, 032314 (2004).
  49. P. Facchi and S. Pascazio, Kick and fix: The roots of quantum control, in Proceedings 12, 30 (2019).
  50. H. Nakazato, M. Namiki, and S. Pascazio, Temporal behavior of quantum mechanical systems, Int. J. Mod. Phys. B 10, 247 (1996).
  51. S. R. Wilkinson, C. F. Bharucha, M. C. Fischer, K. W. Madison, P. R. Morrow, Q. Niu, B. Sundaram, and M. G. Raizen, Experimental evidence for non-exponential decay in quantum tunnelling, Nature (London) 387, 575 (1997).
  52. C. Anastopoulos, Decays of unstable quantum systems, Int. J. Theor. Phys. 58, 890 (2019).
  53. https://doi.org/10.21979/N9/C3FOYV.
  54. T. R. Taha and M. I. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation, J. Comput. Phys. 55, 203 (1984).
  55. A. Klug, C. Peters, and A. Forbes, Robust structured light in atmospheric turbulence, Adv. Photonics 5, 016006 (2023).

Outline

Information

Phys. Rev. Research 8, 023036– Published 10 April, 2026
  • Received 18 June 2025
  • Revised 30 September 2025
  • Accepted 20 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation