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  • Letter
  • Open Access

Electromagnetic symmetry dislocations

Alex J. Vernon*, Sebastian Golat, and Francisco J. Rodríguez-Fortuño†

  • *Contact author: alex.vernon@dipc.org
  • †Contact author: francisco.rodriguez_fortuno@kcl.ac.uk
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Phys. Rev. A 112, L021504 – Published 27 August, 2025

DOI: https://doi.org/10.1103/9z11-fw8m

Abstract

Singular optics studies light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. General electromagnetic waves, however, are described by three-dimensional vectors making scalar phase vortices, which depend on the choice of coordinate basis, less meaningful. Polarization singularities instead capture the vector texture of nonparaxial light with separate descriptions for the electric and magnetic fields. But these polarization textures cannot be fundamental because electromagnetic laws can be expressed not only by separate electric and magnetic fields, but by linear combinations of the two. We propose fundamental, basis-independent topological features generic in electromagnetic fields: one- and two-dimensional structures that relate to time-averaged symmetries held locally by the combined electric- and magnetic-field polarization geometry.

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References (47)

  1. J. F. Nye and M. V. Berry, Dislocations in wave trains, Proc. R. Soc. London A 336, 165 (1974).
  2. M. R. Dennis, Topological singularities in wave fields, Ph.D. thesis, University of Bristol, 2001.
  3. J. Nye, Lines of circular polarization in electromagnetic wave fields, Proc. R. Soc. London A 389, 21 (1983).
  4. J. F. Nye and H. J. V, The wave structure of monochromatic electromagnetic radiation, Proc. R. Soc. London A 409, 21 (1987).
  5. M. V. Berry and M. R. Dennis, Polarization singularities in isotropic random vector waves, Proc. R. Soc. London A 457, 141 (2001).
  6. M. R. Dennis, Polarization singularities in paraxial vector fields: morphology and statistics, Opt. Commun. 213, 201 (2002).
  7. O. V. Angelsky, I. I. Mokhun, A. Ya. Bekshaev, C. Yu. Zenkova, and J. Zheng, Polarization singularities: Topological and dynamical aspects, Front. Phys. 11, 1147788 (2023).
  8. S. M. Barnett, F. C. Speirits, and J. B. Götte, On lines of constant polarisation in structured light beams, Europhys. Lett. 143, 35002 (2023).
  9. A. Garcia-Etxarri, Optical polarization möbius strips on all-dielectric optical scatterers, ACS Photon. 4, 1159 (2017).
  10. A. J. Vernon, M. R. Dennis, and F. J. Rodríguez-Fortuño, 3D zeros in electromagnetic fields, Optica 10, 1231 (2023).
  11. J. Peng, R.-Y. Zhang, S. Jia, W. Liu, and S. Wang, Topological near fields generated by topological structures, Sci. Adv. 8, 1231 (2022).
  12. T. Fu, R.-Y. Zhang, S. Jia, C. T. Chan, and S. Wang, Near-field spin chern number quantized by real-space topology of optical structures, Phys. Rev. Lett. 132, 233801 (2024).
  13. M. V. Berry, Optical currents, J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).
  14. K. Y. Bliokh, Y. S. Kivshar, and F. Nori, Magnetoelectric effects in local light-matter interactions, Phys. Rev. Lett. 113, 033601 (2014).
  15. S. M. Barnett, Optical dirac equation, New J. Phys. 16, 093008 (2014).
  16. M. R. Dennis, T. Tijssen, and M. A. Morgan, On the majorana representation of the optical dirac equation, J. Phys. A: Math. Theor. 56, 024004 (2023).
  17. S. Golat, A. J. Vernon, and F. J. Rodríguez-Fortuño, The electromagnetic symmetry sphere a framework for energy, momentum, spin and other electromagnetic quantities, arXiv:2405.15718.
  18. I. Fernandez-Corbaton, X. Zambrana-Puyalto, N. Tischler, X. Vidal, M. L. Juan, and G. Molina-Terriza, Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell's equations, Phys. Rev. Lett. 111, 060401 (2013).
  19. A. Aiello and M. V. Berry, Note on the helicity decomposition of spin and orbital optical currents, J. Opt. 17, 062001 (2015).
  20. M. V. Berry and P. Shukla, Geometry of 3D monochromatic light: local wavevectors, phases, curl forces, and superoscillations, J. Opt. 21 (2019).
  21. I. Białynicki-Birula, On the wave function of the photon, Acta Phys. Pol. A 86, 97 (1994).
  22. I. Bialynicki-Birula, Photon wave function, Prog. Opt. 36, 245 (1996).
  23. I. Bialynicki-Birula and Z. Bialynicka-Birula, The role of the Riemann–Silberstein vector in classical and quantum theories of electromagnetism, J. Phys. A: Math. Theor. 46, 053001 (2013).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9z11-fw8m for a basis-independent formulation of the time-dependent, macroscopic Maxwell's equations, for details of the polarization singularities of the F fields in different bispinor bases, for further information on the time-dependent definitions in Table  1, and for the behavior of time-dependent symmetry dislocations under Lorentz transformations.
  25. I. Bialynicki-Birula and Z. Bialynicki-Birula, Vortex lines of the electromagnetic field, Phys. Rev. A 67, 062114 (2003).
  26. M. V. Berry, Riemann–Silberstein vortices for paraxial waves, J. Opt. A: Pure Appl. Opt. 6, S175 (2004).
  27. G. Kaiser, Helicity, polarization and Riemann–Silberstein vortices, J. Opt. A: Pure Appl. Opt. 6, S243 (2004).
  28. J. F. Nye, Perturbing the polarisation of Riemann–Silberstein electromagnetic vortices, J. Opt. 21, 015002 (2019).
  29. R. P. Cameron, S. M. Barnett, and A. M. Yao, Optical helicity, optical spin and related quantities in electromagnetic theory, New J. Phys. 14, 053050 (2012).
  30. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Dual electromagnetism: helicity, spin, momentum and angular momentum, New J. Phys. 15 (2013).
  31. M. Nieto-Vesperinas and X. Xu, Reactive helicity and reactive power in nanoscale optics: Evanescent waves. Kerker conditions. optical theorems and reactive dichroism, Phys. Rev. Res. 3, 043080 (2021).
  32. L. D. Barron, True and false chirality and absolute asymmetric synthesis, J. Am. Chem. Soc. 108, 5539 (1986).
  33. J. F. Nye, The life-cycle of Riemann–Silberstein electromagnetic vortices, J. Opt. 19, 115002 (2017).
  34. M. Nieto-Vesperinas and X. Xu, The complex Maxwell stress tensor theorem: The imaginary stress tensor and the reactive strength of orbital momentum. a novel scenery underlying electromagnetic optical forces, Light Sci. Appl. 11, 297 (2022).
  35. M. R. Dennis, R. P. King, B. Jack, K. O'Holleran, and M. J. Padgett, Isolated optical vortex knots, Nat. Phys. 6, 118 (2010).
  36. H. Larocque, D. Sugic, D. Mortimer, A. J. Taylor, R. Fickler, R. W. Boyd, M. R. Dennis, and E. Karimi, Reconstructing the topology of optical polarization knots, Nat. Phys. 14, 1079 (2018).
  37. D. Sugic, R. Droop, E. Otte, D. Ehrmanntraut, F. Nori, J. Ruostekoski, C. Denz, and M. R. Dennis, Particle-like topologies in light, Nat. Commun. 12, 6785 (2021).
  38. Y. Shen, E. C. Martínez, and C. Rosales-Guzmán, Generation of optical skyrmions with tunable topological textures, ACS Photon. 9, 296 (2022).
  39. C. M. Spaegele, M. Tamagnone, S. W. D. Lim, M. Ossiander, M. L. Meretska, and F. Capasso, Topologically protected optical polarization singularities in four-dimensional space, Sci. Adv. 9, eadh0369 (2023).
  40. S. Golat, J. J. Kingsley-Smith, I. Diez, J. Martinez-Romeu, A. Martínez, and F. J. Rodríguez-Fortuño, Optical dipolar chiral sorting forces and their manifestation in evanescent waves and nanofibers, Phys. Rev. Res. 6, 023079 (2024).
  41. R. D. Muelas-Hurtado, K. Volke-Sepúlveda, J. L. Ealo, F. Nori, M. A. Alonso, K. Y. Bliokh, and E. Brasselet, Observation of polarization singularities and topological textures in sound waves, Phys. Rev. Lett. 129, 204301 (2022).
  42. A. Kille and A. Afanasev, Nondivergent spinning substructures near acoustic field nodes, Phys. Rev. B 109, 184305 (2024).
  43. D. A. Smirnova, F. Nori, and K. Y. Bliokh, Water-wave vortices and skyrmions, Phys. Rev. Lett. 132, 054003 (2024).
  44. S. Golat, E. A. Lim, and F. J. Rodríguez-Fortuño, Evanescent gravitational waves, Phys. Rev. D 101, 084046 (2020).
  45. S. Čopar, M. R. Dennis, R. D. Kamien, and S. Žumer, Singular values, nematic disclinations, and emergent biaxiality, Phys. Rev. E 87, 050504(R) (2013).
  46. T. Machon and G. P. Alexander, Knotted defects in nematic liquid crystals, Phys. Rev. Lett. 113, 027801 (2014).
  47. J. Binysh, J. Pollard, and G. P. Alexander, Geometry of bend: Singular lines and defects in twist-bend nematics, Phys. Rev. Lett. 125, 047801 (2020).

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Information

Phys. Rev. A 112, L021504– Published 27 August, 2025
  • Received 19 May 2025
  • Accepted 17 July 2025
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