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Spin-dependent routing of optical beams in the bulk of twisted anisotropic media

Chandroth P. Jisha1,*, Lorenzo Marrucci2, Stefan Nolte1,3, and Alessandro Alberucci1,†

  • *Contact author: jisha.chandroth.pannian@uni-jena.de
  • †Contact author: alessandro.alberucci@uni-jena.de

Phys. Rev. A 112, 043521 – Published 15 October, 2025

DOI: https://doi.org/10.1103/jm7q-nxy1

Abstract

We theoretically discuss a kind of photonic spin-Hall effect (PSHE) for optical beams propagating inside an inhomogeneously twisted anisotropic material. The rotation angle plays the role of an effective gauge field. When the twisting distribution is odd symmetric, the optical beams move along mirror-symmetric trajectories according to their helicity. Connection of this volumetric PSHE with the geometric phase and the Kapitza effect is elucidated.

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References (80)

  1. W. Gerlach and O. Stern, Der experimentelle nachweis der richtungsquantelung im magnetfeld, Z. Phys. 9, 349 (1922).
  2. Hereafter, we will use the term Stern-Gerlach effect to indicate the symmetric spatial separation between beams carrying opposite spins or pseudospins.
  3. J. E. Hirsch, Spin Hall effect, Phys. Rev. Lett. 83, 1834 (1999).
  4. J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015).
  5. J.-Q. Lu, X.-G. Zhang, and S. T. Pantelides, Tunable spin Hall effect by Stern-Gerlach diffraction, Phys. Rev. B 74, 245319 (2006).
  6. T. Sleator, T. Pfau, V. Balykin, O. Carnal, and J. Mlynek, Experimental demonstration of the optical Stern-Gerlach effect, Phys. Rev. Lett. 68, 1996 (1992).
  7. O. Yesharim, A. Karnieli, S. Jackel, G. Di Domenico, S. Trajtenberg-Mills, and A. Arie, Observation of the all-optical Stern–Gerlach effect in nonlinear optics, Nat. Photon. 16, 582 (2022).
  8. S. Longhi, Quantum-optical analogies using photonic structures, Laser Photon. Rev. 3, 243 (2009).
  9. A. Patsyk, U. Sivan, M. Segev, and M. A. Bandres, Observation of branched flow of light, Nature (London) 583, 60 (2020).
  10. A. L. M. Muniz, F. O. Wu, P. S. Jung, M. Khajavikhan, D. N. Christodoulides, and U. Peschel, Observation of photon-photon thermodynamic processes under negative optical temperature conditions, Science 379, 1019 (2023).
  11. A. Paredes, D. N. Olivieri, and H. Michinel, From optics to dark matter: A review on nonlinear Schrödinger–Poisson systems, Physica D 403, 132301 (2020).
  12. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
  13. S. Klembt, T. Harder, O. Egorov, K. Winkler, R. Ge, M. Bandres, M. Emmerling, L. Worschech, T. Liew, M. Segev, C. Scheneider, and S. Höfling, Exciton-polariton topological insulator, Nature (London) 562, 552 (2018).
  14. N. Schine, A. Ryou, A. Gromov, A. Sommer, and J. Simon, Synthetic Landau levels for photons, Nature (London) 534, 671 (2016).
  15. L. W. Clark, N. Schine, C. Baum, N. Jia, and J. Simon, Observation of Laughlin states made of light, Nature (London) 582, 41 (2020).
  16. H. Kuratsuji and S. Kakigi, Maxwell-Schrödinger equation for polarized light and evolution of the Stokes parameters, Phys. Rev. Lett. 80, 1888 (1998).
  17. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, Recent advances in the spin Hall effect of light, Rep. Prog. Phys. 80, 066401 (2017).
  18. Y. Liu, Y. Ke, H. Luo, and S. Wen, Photonic spin Hall effect in metasurfaces: A brief review, Nanophotonics 6, 51 (2017).
  19. M. Kim, Y. Yang, D. Lee, Y. Kim, H. Kim, and J. Rho, Spin Hall effect of light: From fundamentals to recent advancements, Laser Photon. Rev. 17, 2200046 (2023).
  20. C. Zhou, W. Liang, Z. Xie, J. Ma, H. Yang, X. Yang, Y. Hu, H. Duan, and X. Yuan, Optical vectorial-mode parity Hall effect: A case study with cylindrical vector beams, Nat. Commun. 15, 4022 (2024).
  21. F. Cardano and L. Marrucci, Spin-orbit photonics, Nat. Photon. 9, 776 (2015).
  22. K. Y. Bliokh, F. J. Rodríguez-Fortuno, F. Nori, and A. V. Zayats, Spin-orbit interactions of light, Nat. Photon. 9, 796 (2015).
  23. M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett. 93, 083901 (2004).
  24. K. Y. Bliokh and Y. P. Bliokh, Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect, Phys. Rev. E 70, 026605 (2004).
  25. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Geometrodynamics of spinning light, Nat. Photon. 2, 748 (2008).
  26. K. Y. Bliokh and Y. P. Bliokh, Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet, Phys. Rev. E 75, 066609 (2007).
  27. K. Y. Bliokh and A. Aiello, Goos–Hänchen and Imbert–Fedorov beam shifts: An overview, J. Opt. 15, 014001 (2013).
  28. O. Hosten and P. Kwiat, Observation of the spin Hall effect of light via weak measurements, Science 319, 787 (2008).
  29. E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures, Opt. Commun. 209, 45 (2002).
  30. L. Marrucci, C. Manzo, and D. Paparo, Pancharatnam–Berry phase optical elements for wavefront shaping in the visible domain: Switchable helical modes generation, Appl. Phys. Lett. 88, 221102 (2006).
  31. R. Drevinskas, M. Beresna, J. Zhang, A. G. Kazanskii, and P. G. Kazansky, Ultrafast laser-induced metasurfaces for geometric phase manipulation, Adv. Opt. Mater. 5, 1600575 (2017).
  32. X. Zhou, X. Lin, Z. Xiao, T. Low, A. Alù, B. Zhang, and H. Sun, Controlling photonic spin Hall effect via exceptional points, Phys. Rev. B 100, 115429 (2019).
  33. K. Y. Bliokh, D. Smirnova, and F. Nori, Quantum spin Hall effect of light, Science 348, 1448 (2015).
  34. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Observation of the spin-based plasmonic effect in nanoscale structures, Phys. Rev. Lett. 101, 043903 (2008).
  35. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O'Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, Near-field interference for the unidirectional excitation of electromagnetic guided modes, Science 340, 328 (2013).
  36. K. Y. Bliokh, C. T. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, Spin-Hall effect and circular birefringence of a uniaxial crystal plate, Optica 3, 1039 (2016).
  37. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  38. A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Nematicon all-optical control in liquid crystal light valves, Opt. Lett. 35, 390 (2010).
  39. X. Ling, H. Luo, F. Guan, X. Zhou, H. Luo, and L. Zhou, Vortex generation in the spin-orbit interaction of a light beam propagating inside a uniaxial medium: Origin and efficiency, Opt. Express 28, 27258 (2020).
  40. W. Zhu, H. Zheng, Y. Zhong, J. Yu, and Z. Chen, Wave-vector-varying Pancharatnam-Berry phase photonic spin Hall effect, Phys. Rev. Lett. 126, 083901 (2021).
  41. W. Zhu, X. Liang, W. Xie, H. Zheng, Y. Zhong, J. Tang, J. Yu, and Z. Chen, Optical Stern–Gerlach effect in periodically poled electro-optical crystals, Laser Photon. Rev. 18, 2301030 (2024).
  42. G. Liu, Z. Zeng, H. Lin, Y. Hu, Z. Li, Z. Chen, and S. Fu, Electrically engineering synthetic magnetic fields for polarized photons, Optica 11, 980 (2024).
  43. F. Liu and J. Li, Gauge field optics with anisotropic media, Phys. Rev. Lett. 114, 103902 (2015).
  44. K. Rechcińska, M. Król, R. Mazur, P. Morawiak, R. Mirek, K. Łempicka, W. Bardyszewski, M. Matuszewski, P. Kula, W. Piecek, P. G. Lagoudakis, B. Piętka, and J. Szczytko, Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities, Science 366, 727 (2019).
  45. M. Król, K. Rechcińska, H. Sigurdsson, P. Oliwa, R. Mazur, P. Morawiak, W. Piecek, P. Kula, P. G. Lagoudakis, M. Matuszewski, W. Bardyszewski, B. Piętka, and J. Szczytko, Realizing optical persistent spin helix and Stern-Gerlach deflection in an anisotropic liquid crystal microcavity, Phys. Rev. Lett. 127, 190401 (2021).
  46. M. E. Ketara and E. Brasselet, Observation of self-induced optical vortex precession, Phys. Rev. Lett. 110, 233603 (2013).
  47. R. C. Jones, A new calculus for the treatment of optical systems I. Description and discussion of the calculus, J. Opt. Soc. Am. 31, 488 (1941).
  48. R. Bhandari, Polarization of light and topological phases, Phys. Rep. 281, 1 (1997).
  49. Z. Bomzon, V. Kleiner, and E. Hasman, Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings, Opt. Lett. 26, 1424 (2001).
  50. M. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. A 392, 45 (1984).
  51. S. Pancharatnam, Generalized theory of interference, and its applications, Proc. Indian Acad. Sci. A 44, 247 (1956).
  52. F. Gori, Measuring Stokes parameters by means of a polarization grating, Opt. Lett. 24, 584 (1999).
  53. C. Provenzano, P. Pagliusi, and G. Cipparrone, Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces, Appl. Phys. Lett. 89, 121105 (2006).
  54. X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence, Light Sci. Appl. 4, e290 (2015).
  55. M. V. Berry, Pancharatnam, virtuoso of the Poincaré sphere: An appreciation, Curr. Sci. 67, 220 (1994).
  56. C. P. Jisha, S. Nolte, and A. Alberucci, Polarization-insensitive wavefront shaping using the Pancharatnam–Berry phase, Opt. Lett. 44, 5517 (2019).
  57. C. P. Jisha, A. Alberucci, L. Marrucci, and G. Assanto, Interplay between diffraction and the Pancharatnam–Berry phase in inhomogeneously twisted anisotropic media, Phys. Rev. A 95, 023823 (2017).
  58. P. L. Kapitza, Dynamic stability of a pendulum when its point of suspension vibrates, Sov. Phys. JETP 21, 588 (1951).
  59. C. P. Jisha, S. V. Arumugam, L. Marrucci, S. Nolte, and A. Alberucci, Waveguiding driven by the Pancharatnam-Berry phase, Phys. Rev. A 107, 013523 (2023).
  60. E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface, Light Sci. Appl. 3, e167 (2014).
  61. S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, A review of dielectric optical metasurfaces for wavefront control, Nanophotonics 7, 1041 (2018).
  62. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, Fabrication of ideal geometric-phase holograms with arbitrary wavefronts, Optica 2, 958 (2015).
  63. A. Rubano, F. Cardano, B. Piccirillo, and L. Marrucci, Q-plate technology: A progress review, J. Opt. Soc. Am. B 36, D70 (2019).
  64. R. Drevinskas and P. G. Kazansky, High-performance geometric phase elements in silica glass, APL Photon. 2, 066104 (2017).
  65. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method, Comput. Phys. Commun. 181, 687 (2010).
  66. F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, Singapore, 1997).
  67. K. Fang and S. Fan, Controlling the flow of light using the inhomogeneous effective gauge field that emerges from dynamic modulation, Phys. Rev. Lett. 111, 203901 (2013).
  68. M. C. Rechtsman, J. M. Zeuner, A. Tünnermann, S. Nolte, M. Segev, and A. Szameit, Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures, Nat. Photon. 7, 153 (2013).
  69. C. V. Sukumar and D. M. Brink, Spin-flip transitions in a magnetic trap, Phys. Rev. A 56, 2451 (1997).
  70. S. Slussarenko, A. Alberucci, C. P. Jisha, B. Piccirillo, E. Santamato, G. Assanto, and L. Marrucci, Guiding light via geometric phases, Nat. Photon. 10, 571 (2016).
  71. C. P. Jisha and A. Alberucci, Paraxial light beams in structured anisotropic media, J. Opt. Soc. Am. A 34, 2019 (2017).
  72. E. Karimi, L. Marrucci, V. Grillo, and E. Santamato, Spin-to-orbital angular momentum conversion and spin-polarization filtering in electron beams, Phys. Rev. Lett. 108, 044801 (2012).
  73. Q. Lin and S. Fan, Light guiding by effective gauge field for photons, Phys. Rev. X 4, 031031 (2014).
  74. H. Abbaszadeh, M. Fruchart, W. van Saarloos, and V. Vitelli, Liquid-crystal-based topological photonics, Proc. Natl. Acad. Sci. USA 118, e2020525118 (2021).
  75. L. Marrucci, C. Manzo, and D. Paparo, Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media, Phys. Rev. Lett. 96, 163905 (2006).
  76. M. Sakakura, Y. Lei, L. Wang, Y.-H. Yu, and P. G. Kazansky, Ultralow-loss geometric phase and polarization shaping by ultrafast laser writing in silica glass, Light Sci. Appl. 9, 15 (2020).
  77. Y. Jin, S. J. Elston, J. A. J. Fells, M. J. Booth, C. Welch, G. H. Mehl, and S. M. Morris, Millisecond optical phase modulation using multipass configurations with liquid-crystal devices, Phys. Rev. Appl. 14, 024007 (2020).
  78. N. F. Mott, The scattering of fast electrons by atomic nuclei, Proc. R. Soc. A 124, 425 (1929).
  79. H. Batelaan, T. J. Gay, and J. J. Schwendiman, Stern-Gerlach effect for electron beams, Phys. Rev. Lett. 79, 4517 (1997).
  80. M. Kohda, S. Nakamura, Y. Nishihara, K. Kobayashi, T. Ono, J.-I. Ohe, Y. Tokura, T. Mineno, and J. Nitta, Spin–orbit induced electronic spin separation in semiconductor nanostructures, Nat. Commun. 3, 1082 (2012).

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