- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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

Nonreciprocal Goos-Hänchen and photonic spin Hall shifts driven by incident angle and polarization at a planar interface

Rfaqat Ali1, F. A. Almobi2, and Ying Wu1,2,*

  • *Contact author: ying.wu@kaust.edu.sa
PDF

Phys. Rev. B 113, 075308 – Published 20 February, 2026

DOI: https://doi.org/10.1103/bmp1-dk4z

Abstract

Most studies on Goos-Hänchen and photonic spin Hall beam shifts are focused on reciprocal, or direction-independent, beam shifts. In this work, we present a strategy to induce nonreciprocal beam shifts in the reflected field from a planar heterostructure by exploiting direction- and polarization-dependent coupling between the incident field and the structure. We show that the heterostructure's resonant modes lead to polarization-dependent, nonreciprocal reflection at specific incident angles. This behavior enables controlled tuning of the direction-dependent transformation of optical momentum. Consequently, we observe nonreciprocal Goos-Hänchen and photonic spin Hall shifts in the reflection plane, manifesting as lateral and transverse displacements, respectively. These shifts arise from the conversion of linear momentum and orbital angular momentum into spin angular momentum. The results are verified using three independent approaches—comsol multiphysics simulations, the stationary phase method, and Gaussian beam scattering calculations—with excellent agreement among them.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. F. Goos and H. Hänchen, Ein neuer und fundamentaler versuch zur totalreflexion, Ann. Phys. (NY) 436, 333 (1947).
  2. K. Artmann, Berechnung der seitenversetzung des totalreflektierten strahles, Ann. Phys. (NY) 437, 87 (1948).
  3. C. Imbert, Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam, Phys. Rev. D 5, 787 (1972).
  4. D. Amati, M. E. Rose -Elementary theory of angular momentum, Nuov. Cim. 16, 1160 (1960).
  5. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, Geometrodynamics of spinning light, Nat. Photon. 2, 748 (2008).
  6. T. Požar, J. Laloš, A. Babnik, R. Petkovšek, M. Bethune-Waddell, K. J. Chau, G. V. B. Lukasievicz, and N. G. C. Astrath, Isolated detection of elastic waves driven by the momentum of light, Nat. Commun. 9, 3340 (2018).
  7. M. Onoda, S. Murakami, and N. Nagaosa, Hall effect of light, Phys. Rev. Lett. 93, 083901 (2004).
  8. K. Y. Bliokh and A. Aiello, Goos–Hänchen and Imbert–Fedorov beam shifts: an overview, J. Opt. 15, 014001 (2013).
  9. D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, Enhanced spin Hall effect of light in spheres with dual symmetry, Laser Photon. Rev. 12, 1800130 (2018).
  10. R. Ali, Chirality-assisted spin Hall effect of light in the vicinity of the quasi-antidual symmetry mode of a chiral sphere, Phys. Rev. A 106, 063508 (2022).
  11. Y. Xu, C. T. Chan, and H. Chen, Goos-Hänchen effect in epsilon-near-zero metamaterials, Sci. Rep. 5, 8681 (2015).
  12. J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, Goos-Hänchen shifts in an epsilon-near-zero slab, J. Opt. Soc. Am. B 34, 2310 (2017).
  13. Ziauddin, Y.-L. Chuang, S. Qamar, and R.-K. Lee, Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials, Sci. Rep. 6, 26504 (2016).
  14. L.-G. Wang, H. Chen, and S.-Y. Zhu, Large negative Goos–Hänchen shift from a weakly absorbing dielectric slab, Opt. Lett. 30, 2936 (2005).
  15. W. Zhen and D. Deng, Goos–Hänchen and Imbert–Fedorov shifts in temporally dispersive attenuative materials, J. Phys. D: Appl. Phys. 53, 255104 (2020).
  16. J. Götte, A. Aiello, and J. Woerdman, Loss-induced transition of the Goos-Hänchen effect for metals and dielectrics, Opt. Express 16, 3961 (2008).
  17. L. Lambrechts, V. Ginis, J. Danckaert, and P. Tassin, Transformation optics for surface phenomena: Engineering the Goos-Hänchen effect, Phys. Rev. B 95, 035427 (2017).
  18. G. Wan, Z. Ma, Y. Xue, C. Zhang, Y. Chen, and X. Zhou, Photonic spin Hall effect at an optical bound state in the continuum, Phys. Rev. B 111, 085411 (2025).
  19. Z. Ma, J. Hong, S. Lin, G. Wan, R. Long, J. Wen, X. Zhou, and Y. Chen, Ultrawide and unidirectional enhancements of a photonic spin Hall effect in a tilted uniaxial crystal, Opt. Lett. 48, 5811 (2023).
  20. C. Liang, D. Liu, R. Liu, D. Deng, and G. Wang, Chirality-modulated photonic spin Hall effect in PT-symmetry, Nanophotonics 11, 3475 (2022).
  21. Y. Song, Y. Shu, T. Jiang, J. Liu, and Z. Luo, Enhanced spin Hall effect of light in the PT-symmetric trilayer structure containing epsilon-near-zero materials, J. Phys. D: Appl. Phys. 56, 175102 (2023).
  22. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, A. L. Floch, and L. Dutriaux, Measurement of positive and negative Goos–Hänchen effects for metallic gratings near Wood anomalies, Opt. Lett. 26, 666 (2001).
  23. N. I. Petrov, V. A. Danilov, V. V. Popov, and B. A. Usievich, Large positive and negative Goos-Hänchen shifts near the surface plasmon resonance in subwavelength grating, Opt. Express 28, 7552 (2020).
  24. M. Merano, A. Aiello, G. 't Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, Observation of Goos-Hänchen shifts in metallic reflection, Opt. Express 15, 15928 (2007).
  25. T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, Generalized spatial differentiation from the spin Hall effect of light and its application in image processing of edge detection, Phys. Rev. Appl. 11, 034043 (2019).
  26. M. Mazanov, O. Yermakov, I. Deriy, O. Takayama, A. Bogdanov, and A. V. Lavrinenko, Photonic spin Hall effect: Contribution of polarization mixing caused by anisotropy, Quantum Rep. 2, 489 (2020).
  27. F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, Giant enhancement of the Goos-Hänchen shift assisted by quasibound states in the continuum, Phys. Rev. Appl. 12, 014028 (2019).
  28. M. Wei, Y. Long, F. Wu, G.-G. Liu, and B. Zhang, Abrupt lateral beam shifts from terahertz quasi-bound states in the continuum, Sci. Bull. 70, 882 (2025).
  29. Y.-K. Shi, B.-F. Wan, and H.-F. Zhang, Nonreciprocal Goos–Hänchen effect at the reflection of electromagnetic waves from the one-dimensional magnetized ferrite photonic crystals, J. Opt. 24, 055103 (2022).
  30. H. Ma, C. Ju, X. Xi, and R.-X. Wu, Nonreciprocal Goos-Hänchen shift by topological edge states of a magnetic photonic crystal, Opt. Express 28, 19916 (2020).
  31. R. Wang, J. Zhou, K. Zeng, S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, Ultrasensitive and real-time detection of chemical reaction rate based on the photonic spin Hall effect, APL Photon. 5, 016105 (2020).
  32. X. Zhou, L. Sheng, and X. Ling, Photonic spin Hall effect enabled refractive index sensor using weak measurements, Sci. Rep. 8, 1221 (2018).
  33. S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, Precision measurement of the optical conductivity of atomically thin crystals via the photonic spin Hall effect, Phys. Rev. Appl. 13, 014057 (2020).
  34. J.-M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, Ultrafast optical imaging of the spin Hall effect of light in semiconductors, Phys. Rev. B 82, 045303 (2010).
  35. K. Y. Bliokh and Y. P. Bliokh, Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet, Phys. Rev. Lett. 96, 073903 (2006).
  36. R. Ali, T. P. Mayer Alegre, and G. S. Wiederhecker, Enhancing the Goos-Hänchen and spin-Hall shifts in planar and spherical structures through complex-frequency excitations, Phys. Rev. B 110, 085403 (2024).
  37. H. Luo, X. Ling, X. Zhou, W. Shu, S. Wen, and D. Fan, Enhancing or suppressing the spin Hall effect of light in layered nanostructures, Phys. Rev. A 84, 033801 (2011).
  38. O. Hosten and P. Kwiat, Observation of the spin Hall effect of light via weak measurements, Science 319, 787 (2008).
  39. M. Kim, D. Lee, B. Ko, and J. Rho, Diffraction-induced enhancement of optical spin Hall effect in a dielectric grating, APL Photon. 5, 066106 (2020).
  40. M. Kim, D. Lee, Y. Yang, Y. Kim, and J. Rho, Reaching the highest efficiency of spin Hall effect of light in the near-infrared using all-dielectric metasurfaces, Nat. Commun. 13, 2036 (2022).
  41. X. Ling, W. Xiao, S. Chen, X. Zhou, H. Luo, and L. Zhou, Revisiting the anomalous spin-Hall effect of light near the Brewster angle, Phys. Rev. A 103, 033515 (2021).
  42. M. Kim, D. Lee, T. H.-Y. Nguyen, H.-J. Lee, G. Byun, and J. Rho, Total reflection-induced efficiency enhancement of the spin Hall effect of light, ACS Photon. 8, 2705 (2021).
  43. O. J. S. Santana and L. E. E. de Araujo, Direct measurement of the composite Goosänchen shift of an optical beam, Opt. Lett. 43, 4037 (2018).
  44. S.-q. Wu, H. yuan Song, Y.-bo Li, S.-fang Fu, and X.-zhang Wang, Tunable spin Hall effect via hybrid polaritons around epsilon-near-zero on graphene-HBN heterostructures, Results Phys. 35, 105383 (2022).
  45. T. Tang, L. Bi, L. Luo, and J. Li, Imbert-Fedorov effect in Kretschmann configuration with anisotropic metamaterial, Plasmonics 13, 1425 (2018).
  46. F. Wu, T. Liu, Y. Long, S. Xiao, and G. Chen, Giant photonic spin Hall effect empowered by polarization-dependent quasibound states in the continuum in compound grating waveguide structures, Phys. Rev. B 107, 165428 (2023).
  47. H. Da, Q. Song, H. Ye, and X. Yan, Nonreciprocal photonic spin Hall effect of magnetic Weyl semimetals, Appl. Phys. Lett. 119, 081103 (2021).
  48. J. Wang, L. Shi, and J. Zi, Spin Hall effect of light via momentum-space topological vortices around bound states in the continuum, Phys. Rev. Lett. 129, 236101 (2022).
  49. L. Wang, F. J. García de Abajo, and G. T. Papadakis, Maximal violation of Kirchhoff's law in planar heterostructures, Phys. Rev. Res. 5, L022051 (2023).
  50. W. Yang, J. Qin, J. Long, W. Yan, Y. Yang, C. Li, E. Li, J. Hu, L. Deng, Q. Du, and L. Bi, A self-biased non-reciprocal magnetic metasurface for bidirectional phase modulation, Nat. Electron. 6, 225 (2023).
  51. A. M. Mahmoud, A. R. Davoyan, and N. Engheta, All-passive nonreciprocal metastructure, Nat. Commun. 6, 8359 (2015).
  52. S. Buddhiraju, A. Song, G. T. Papadakis, and S. Fan, Nonreciprocal metamaterial obeying time-reversal symmetry, Phys. Rev. Lett. 124, 257403 (2020).
  53. S. V. Kutsaev, A. Krasnok, S. N. Romanenko, A. Y. Smirnov, K. Taletski, and V. P. Yakovlev, Up-and-coming advances in optical and microwave nonreciprocity: From classical to quantum realm, Adv. Photon. Res. 2, 2000104 (2021).
  54. K. J. Shayegan, B. Zhao, Y. Kim, S. Fan, and H. A. Atwater, Nonreciprocal infrared absorption via resonant magneto-optical coupling to InAs, Sci. Adv. 8, eabm4308 (2022).
  55. N. Kumar, Y. Sun, N. Xu, K. Manna, M. Yao, V. Süss, I. Leermakers, O. Young, T. Förster, M. Schmidt, H. Borrmann, B. Yan, U. Zeitler, M. Shi, C. Felser, and C. Shekhar, Extremely high magnetoresistance and conductivity in the Type-II Weyl semimetals WP2 and MoP2, Nat. Commun. 8, 1642 (2017).
  56. G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4, Phys. Rev. Lett. 107, 186806 (2011).
  57. X. Wen, H. K. Yip, C. Cho, J. Li, and N. Park, Acoustic amplifying diode using nonreciprocal Willis coupling, Phys. Rev. Lett. 130, 176101 (2023).
  58. J. Qin, S. Xia, W. Yang, H. Wang, W. Yan, Y. Yang, Z. Wei, W. Liu, Y. Luo, L. Deng, and L. Bi, Nanophotonic devices based on magneto-optical materials: Recent developments and applications, Nanophotonics 11, 2639 (2022).
  59. J. Lee, J. Kim, S. Shim, Y. Yang, J. Choi, J. Rho, D. Lee, and M. Kim, Real-time observation of the spin Hall effect of light using metasurface-enabled single-shot weak measurements, Nat. Commun. 16, 2699 (2025).
  60. G. D. Landry and T. A. Maldonado, Gaussian beam transmission and reflection from a general anisotropic multilayer structure, Appl. Opt. 35, 5870 (1996).

Outline

Information

Phys. Rev. B 113, 075308– Published 20 February, 2026
  • Received 28 August 2025
  • Revised 14 December 2025
  • Accepted 2 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. Open access publication funded by King Abdullah University of Science and Technology (KAUST).

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation