- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

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

Structured light in Möbius-strip-like fiber resonators

C. N. Alexeyev*, B. P. Lapin, S. A. Palvanova, and M. A. Yavorsky

  • *Contact author: c.alexeyev@yandex.ru
PDF

Phys. Rev. A 113, 053529 – Published 26 May, 2026

DOI: https://doi.org/10.1103/mmd5-lzgb

Abstract

In this paper, we study the propagation of structured light in fiber resonators that in effect are generalizations of the Möbius strip. In particular, we address two examples of such systems: ring resonators based on strongly elliptical twisted two-mode fibers and on bielliptical fibers composed of two consecutive sections of elliptical fibers with different orientations of deformation ellipses. We study formation of whispering gallery modes (WGMs) in such systems. By analyzing orbital Stokes parameters of such WGMs we prove that those modes may form in certain cross-section optical vortices (OVs) with modulus unity topological charges. We demonstrate that the ability of resonators with effective topology of a Möbius strip to possess of vortex WGMs can be used for generation of OV frequency combs from Laguerre-Gaussian modes. We emphasize that to guarantee generation of vortex comb in a Möbius ring resonator parameters should be such as to warrant the existence of vortex WGMs in the resonator. We also study the effect of the spin-orbit interaction (SOI) on generation of OV frequency combs by Möbius-strip-like resonators on base of elliptical twisted fibers. We study the influence of the SOI and show that its presence does not prevent implementation of vortex WGMs in orthogonal polarizations and generation of OV combs in those polarizations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. D. M. Walba, R. M. Richards, and R. C. Haltiwanger, Total synthesis of the first molecular Moebius strip, J. Am. Chem. Soc. 104, 3219 (1982).
  2. S. J. Cooke and J. M. Pond, Modes in a möbius wire-loaded cavity resonator, Microw. Opt. Technol. Lett. 31, 6 (2001).
  3. J. Kreismann and M. Hentschel, The optical Möbius strip cavity: Tailoring geometric phases and far fields, Europhys. Lett. 121, 24001 (2018).
  4. J. Wang, S. Valligatla, Y. Yin, L. Schwarz, M. Medina-Sánchez, S. Baunack, C. Hua Lee, R. Thomale, S. Li, V. M. Fomin, L. Ma, and O. G. Schmidt, Experimental observation of Berry phases in optical Möbius-strip microcavities, Nat. Photon. 17, 120 (2023).
  5. Y. L. Song, Y. Monceaux, S. Bittner, K. M. Chao, H. M. R. de la Cruz, C. Lafargue, D. Decanini, B. Dietz, J. Zyss, A. Grigis, X. Checoury, and M. Lebental, Möbius strip microlasers: A testbed for non-Euclidean photonics, Phys. Rev. Lett. 127, 203901 (2021).
  6. Z. Z. Nie, B. Zuo, M. Wang, S. Huang, X.-M. Chen, Z.-Y. Liu, and H. Yang, Light-driven continuous rotating Möbius strip actuators, Nat. Commun. 12, 2334 (2021).
  7. S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, and N. Hatakenaka, A Möbius strip of single crystals, Nature (Lond.) 417, 397 (2002).
  8. G. R. Schaller, F. Topić, K. Rissanen, Y. Okamoto, J. Shen, and R. Herges, Design and synthesis of the first triply twisted Möbius annulene, Nat. Chem. 6, 608 (2014).
  9. C.-W. Chang, M. Liu, S. Nam, S. Zhang, Y. Liu, G. Bartal, and X. Zhang, Optical Möbius symmetry in metamaterials, Phys. Rev. Lett. 105, 235501 (2010).
  10. H. Zhao, J.-S. B. Tai, J.-S. Wu, and I. I. Smalyukh, Liquid crystal defect structures with Möbius strip topology, Nat. Phys. 19, 451 (2023).
  11. J. Gravesen and M. Willatzen, Eigenstates of Möbius nanostructures including curvature effects, Phys. Rev. A 72, 032108 (2005).
  12. Z. Li and L. R. Ram-Mohan, Quantum mechanics on a Möbius ring: Energy levels, symmetry, optical transitions, and level splitting in a magnetic field, Phys. Rev. B 85, 195438 (2012).
  13. J. Bělín, T. Tyc, and S. A. R. Horsley, Optical simulation of quantum mechanics on the Möbius strip, Klein's bottle and other manifolds, and Talbot effect, New J. Phys. 23, 033003 (2021).
  14. D. J. Ballon and H. U. Voss, Classical Möbius-ring resonators exhibit fermion-boson rotational symmetry, Phys. Rev. Lett. 101, 247701 (2008).
  15. L.-T. Wu, R.-P. Guo, T.-J. Cui, and J. Chen, A photonic analog of Möbius strips using coupled optical ring resonators, J. Opt. 19, 025101 (2017).
  16. R. Chen, P. Zhu, X. Yang, H. Lian, Y. Fan, and Z.-Y. Wang, Eigenmode and eigenpropagation of the electromagnetic waves in Möbius and Klein networks, Opt. Express 32, 38055 (2024).
  17. I. Freund, Multitwist optical Möbius strips, Opt. Lett. 35, 148 (2010).
  18. I. Freund, Optical Möbius strips in three-dimensional ellipse fields: I. Lines of circular polarization, Opt. Commun. 283, 1 (2010).
  19. T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, Observation of optical polarization Möbius strips, Science 347, 964 (2015).
  20. T. Bauer, M. Neugebauer, G. Leuchs, and P. Banzer, Optical polarization Möbius strips and points of purely transverse spin density, Phys. Rev. Lett. 117, 013601 (2016).
  21. L. Su, X. Meng, Y. Xiao, C. Wan, and Q. Zhan, Generation of transversely oriented optical polarization Möbius strips, Opt. Express 29, 25535 (2021).
  22. K. S. Grigoriev and V. A. Makarov, Indices of polarization Möbius strips surrounding lines of circular polarization in nonparaxial optical fields, Opt. Lett. 48, 4420 (2023).
  23. K. S. Grigoriev and V. A. Makarov, Determining triple half-twist of optical Möbius strips in electromagnetic fields with a non-planar structure, Opt. Lett. 49, 2133 (2024).
  24. M. Wang, F. Zhou, X. Lu, A. McClung, M. Davanco, V. A. Aksyuk, and K. Srinivasan, Fractional optical angular momentum and multi-defect-mediated mode renormalization and orientation control in photonic crystal microring resonators, Phys. Rev. Lett. 129, 186101 (2022).
  25. S. Li, X. Zeng, J. Zhou, Z. Cheng, and Y. Feng, Polarization and longitudinal modes of Möbius fiber ring lasers, Optica 9, 1394 (2022).
  26. S. Sun, Z. Shi, Q. Wang, Z. Wang, Y.-G. Liu, D. Xiang, and P. Wang, Position-modulated pulse train generation based on Möbius mode-locked fiber laser: Theory, J. Lightwave Technol. 42, 8383 (2024).
  27. Y. Chen, J. Hou, G. Zhao, X. Chen, and W. Wan, Topological resonances in a Möbius ring resonator, Commun. Phys. 6, 84 (2023).
  28. A. Forbes, M. de Oliveira, and M. R. Dennis, Structured light, Nat. Photon. 15, 253 (2021).
  29. C. N. Alexeyev and M. A. Yavorsky, Topological phase evolving from the orbital angular momentum of “coiled” quantum vortices, J. Opt. A Pure Appl. Opt. 8, 752 (2006).
  30. K. Yu. Bliokh, Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect, Phys. Rev. Lett. 97, 043901 (2006).
  31. C. N. Alexeyev and M. A. Yavorsky, Berry's phase for optical vortices in coiled optical fibres, J. Opt. A Pure Appl. Opt. 9, 6 (2007).
  32. C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Whispering gallery vortex modes of Möbius fiber-ring resonators, Opt. Lett. 50, 5334 (2025).
  33. X. Wang, Z. Wu, J. Wang, L. Shi, and J. Zi, Vectorial lasing with designable topological charges based on Möbius-like correspondence in quasi-BICs, Light: Sci. Appl. 15, 184 (2026).
  34. C. N. Alexeyev and M. A. Yavorsky, Optical vortices and the higher order modes of twisted strongly elliptical optical fibres, J. Opt. A Pure Appl. Opt. 6, 824 (2004).
  35. C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, Transformation of optical vortices in elliptical and anisotropic optical fibres, J. Opt. A Pure Appl. Opt. 9, 387 (2007).
  36. M. J. Padgett and J. Courtial, Poincaré-sphere equivalent for light beams containing orbital angular momentum, Opt. Lett. 24, 430 (1999).
  37. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light, Phys. Rev. Lett. 107, 053601 (2011).
  38. X.-B. Xu, L. Shi, G.-C. Guo, C.-H. Dong, and C.-L. Zou, Möbius” microring resonator, Appl. Phys. Lett. 114, 101106 (2019).
  39. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  40. C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Transmission of optical vortices through fiber loop resonators, Opt. Lett. 44, 4044 (2019).
  41. B. Chen, Y. Zhou, Y. Liu, C. Ye, Q. Cao, P. Huang, C. Kim, Y. Zheng, L. K. Oxenløwe, K. Yvind, J. Li, J. Li, Y. Zhang, C. Dong, S. Fu, Q. Zhan, X. Wang, M. Pu, and J. Liu, Integrated optical vortex microcomb, Nat. Photon. 18, 625 (2024).
  42. C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Vortex-frequency-comb generation assisted by PT-symmetric ring resonators, Phys. Rev. A 107, 023522 (2023).
  43. C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Structured light routing in CROW-endowed add-drop filters, J. Opt. Soc. Am. B 41, 1863 (2024).
  44. B. P. Lapin, S. S. Aliyeva, M. A. Yavorsky, and C. N. Alexeyev, Optical vortices in add-drop filters, Comput. Opt. 49, 378 (2025).
  45. G. Milione, E. Ip, M. J. Li, J. Stone, G. Peng, and T. Wang, Mode crosstalk matrix measurement of a 1  km elliptical core few-mode optical fiber, Opt. Lett. 41, 2755 (2016).
  46. A. P. Porfirev, A. A. Kuchmizhak, S. O. Gurbatov, S. Juodkazis, S. N. Khonina, and Yu. N. Kulchin, Phase singularities and optical vortices in photonics, Phys.–Usp. 65, 789 (2022).
  47. J. Liu, Z. Ma, J. Liu, J. Dong, H. Zhou, S. Mo, L. Wu, S. Li, Y. Chen, L. Rusch, S. Larochelle, S. Ramachandran, and S. Yu, Optical fiber communications using orbital angular momentum modes, Optica 13, 602 (2026).
  48. I. Coddington, N. Newbury, and W. Swann, Dual-comb spectroscopy, Optica 3, 414 (2016).
  49. Y. Ma, Y. Gu, S. Zhou, L. Shi, Y. Xie, and G. Wu, Dual-comb absolute ranging reaches orbit, Light: Sci. Appl. 15, 206 (2026).

Outline

Information

Phys. Rev. A 113, 053529– Published 26 May, 2026
  • Received 6 February 2026
  • Accepted 8 May 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