Abstract

Spin-orbit interactions (SOI) arising due to the propagation of a paraxial light beam, with spin-angular momentum and intrinsic- and extrinsic-orbital angular momentum degrees of freedom, along a curved trajectory and their mutual interactions is investigated due to several fundamental effects of interest. We demonstrate here all six direct and reciprocal SOI effects due to the propagation of light in an inhomogeneous-anisotropic medium, such as a graded-index rod. We show that each of light’s angular momentum component impacts the other in such a way as to have a unique effect, characterized using interferometry, polarimetry, and weak measurement methods. The results are expected to have significant impact on the basic understanding of light-matter interaction and its applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. V. Liberman and B. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
    [Crossref]
  2. K. Bliokh and Y. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
    [Crossref]
  3. K. Bliokh and Y. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
    [Crossref]
  4. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
    [Crossref]
  5. 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(6), 066609 (2007).
    [Crossref]
  6. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
    [Crossref]
  7. K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
    [Crossref]
  8. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref]
  9. L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
    [Crossref]
  10. K. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
    [Crossref]
  11. K. 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(10), 1039–1047 (2016).
    [Crossref]
  12. S. Abdulkareem and N. Kundikova, “Joint effect of polarization and the propagation path of a light beam on its intrinsic structure,” Opt. Express 24(17), 19157–19166 (2016).
    [Crossref]
  13. H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
    [Crossref]
  14. K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A: Pure Appl. Opt. 11(9), 094009 (2009).
    [Crossref]
  15. K.Y. Bliokh, A. Aiello, and M.A. Alonso, “Spin-orbit interactions of light in isotropic media,” in The Angular Momentum of Light, David L. Andrews and Mohamed Babiker, eds. (Cambridge University Press, 2012), chap. 8, pp. 174–245.
  16. K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
    [Crossref]
  17. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
    [Crossref]
  18. K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
    [Crossref]
  19. S. Rytov, “On transition from wave to geometrical optics,” Dokl. Akad. Nauk SSSR 18, 263–266 (1938); Tr. Fiz. Inst. Akad. Nauk SSSR 2, 1 (1940).
  20. V. Vladimirskii, “The rotation of a polarization plane for curved light ray,” Dokl. Akad. Nauk SSSR 21, 222–225 (1941).
  21. F. I. Fedorov, “On the theory of total internal reflection,” Dokl. Akad. Nauk SSSR 105(5), 465–469 (1955).
  22. C. Imbert, “Experimental proof of the photon’s translational inertial spin effect,” Phys. Lett. A 31(6), 337–338 (1970).
    [Crossref]
  23. R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57(8), 933–936 (1986).
    [Crossref]
  24. M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326(6110), 277–278 (1987).
    [Crossref]
  25. A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57(8), 937–940 (1986).
    [Crossref]
  26. A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).
  27. A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
    [Crossref]
  28. N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).
  29. S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
    [Crossref]
  30. Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
    [Crossref]
  31. E. W. Marchand, Gradient index optics (Academic Press, 1978).
  32. C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-index optics: Fundamentals and applications (Springer-Verlag, 2002).
  33. W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC® type,” Proc. SPIE 2169, 156–167 (1994).
    [Crossref]
  34. M. Montoya and D. Malacara, “Polarization effects in interferograms of radial GRIN rods,” Opt. Commun. 175(4-6), 259–263 (2000).
    [Crossref]
  35. J. L. Rouke and D. T. Moore, “Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects,” Appl. Opt. 40(28), 4971–4980 (2001).
    [Crossref]
  36. D. Tentori and J. Camacho, “Conoscopic evaluation of the birefringence of gradient-index lenses: infidelity sources,” Appl. Opt. 41(34), 7218–7228 (2002).
    [Crossref]
  37. S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
    [Crossref]
  38. N. I. Petrov, “Evolution of Berry’s phase in a graded-index medium,” Phys. Lett. A 234(4), 239–250 (1997).
    [Crossref]
  39. N. I. Petrov, “Vector Laguerre–Gauss beams with polarization-orbital angular momentum entanglement in a graded-index medium,” J. Opt. Soc. Am. A 33(7), 1363–1369 (2016).
    [Crossref]
  40. C. T. Samlan, D. N. Naik, and N. K. Viswanathan, “Isogyres–manifestation of spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference,” Sci. Rep. 6(1), 33141 (2016).
    [Crossref]
  41. A. Javier and G. D. Boreman, “On-axis and off-axis propagation of Gaussian beams in gradient index media,” Appl. Opt. 29(19), 2944–2950 (1990).
    [Crossref]
  42. A. Ya Bekshaev, “Spin-orbit interaction of light and diffraction of polarized beams,” J. Opt. 19(8), 085602 (2017).
    [Crossref]
  43. K. Y. Bliokh, “Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect,” Phys. Rev. Lett. 97(4), 043901 (2006).
    [Crossref]
  44. K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
    [Crossref]
  45. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [Crossref]
  46. B. Y. Zel’dovich and V. S. Liberman, “Rotation of the plane of a meridional beam in a graded-index waveguide due to the circular nature of the polarization,” Sov. J. Quantum Electron. 20(4), 427–428 (1990).
    [Crossref]
  47. N. R. Sadykov, “Equation of a ray path with circular polarization,” Quantum Electron. 23(11), 989–990 (1993).
    [Crossref]
  48. N. R. Sadykov, “Influence of the Rytov rotation of the field vectors on the path of a ray,” Quantum Electron. 24(11), 1016–1017 (1994).
    [Crossref]
  49. N. R. Sadykov, “Polarization effects due to the mutual influence of trajectory parameters and polarization,” Theor. Math. Phys. 149(1), 1354–1365 (2006).
    [Crossref]
  50. J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).
  51. A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
    [Crossref]
  52. P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
    [Crossref]
  53. D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
    [Crossref]
  54. 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(2), 026605 (2004).
    [Crossref]
  55. Y. A. Kravtsov, B. Bieg, and K. Y. Bliokh, “Stokes-vector evolution in a weakly anisotropic inhomogeneous medium,” J. Opt. Soc. Am. A 24(10), 3388–3396 (2007).
    [Crossref]
  56. V. Kajorndejnukul, S. Sukhov, D. Haefner, A. Dogariu, and G. S. Agarwal, “Surface induced anisotropy of metal–dielectric composites and the anomalous spin Hall effect,” Opt. Lett. 37(15), 3036–3038 (2012).
    [Crossref]
  57. M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
    [Crossref]
  58. Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
    [Crossref]

2018 (5)

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
[Crossref]

S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
[Crossref]

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

2017 (2)

A. Ya Bekshaev, “Spin-orbit interaction of light and diffraction of polarized beams,” J. Opt. 19(8), 085602 (2017).
[Crossref]

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

2016 (4)

2015 (2)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

2013 (2)

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (1)

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

2009 (3)

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A: Pure Appl. Opt. 11(9), 094009 (2009).
[Crossref]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
[Crossref]

2008 (2)

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

2007 (3)

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(6), 066609 (2007).
[Crossref]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Y. A. Kravtsov, B. Bieg, and K. Y. Bliokh, “Stokes-vector evolution in a weakly anisotropic inhomogeneous medium,” J. Opt. Soc. Am. A 24(10), 3388–3396 (2007).
[Crossref]

2006 (4)

N. R. Sadykov, “Polarization effects due to the mutual influence of trajectory parameters and polarization,” Theor. Math. Phys. 149(1), 1354–1365 (2006).
[Crossref]

K. Bliokh and Y. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

K. Y. Bliokh, “Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect,” Phys. Rev. Lett. 97(4), 043901 (2006).
[Crossref]

2004 (3)

K. Bliokh and Y. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
[Crossref]

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(2), 026605 (2004).
[Crossref]

2002 (1)

2001 (1)

2000 (1)

M. Montoya and D. Malacara, “Polarization effects in interferograms of radial GRIN rods,” Opt. Commun. 175(4-6), 259–263 (2000).
[Crossref]

1997 (1)

N. I. Petrov, “Evolution of Berry’s phase in a graded-index medium,” Phys. Lett. A 234(4), 239–250 (1997).
[Crossref]

1994 (3)

W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC® type,” Proc. SPIE 2169, 156–167 (1994).
[Crossref]

N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).

N. R. Sadykov, “Influence of the Rytov rotation of the field vectors on the path of a ray,” Quantum Electron. 24(11), 1016–1017 (1994).
[Crossref]

1993 (1)

N. R. Sadykov, “Equation of a ray path with circular polarization,” Quantum Electron. 23(11), 989–990 (1993).
[Crossref]

1992 (2)

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

V. Liberman and B. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

1991 (1)

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

1990 (2)

B. Y. Zel’dovich and V. S. Liberman, “Rotation of the plane of a meridional beam in a graded-index waveguide due to the circular nature of the polarization,” Sov. J. Quantum Electron. 20(4), 427–428 (1990).
[Crossref]

A. Javier and G. D. Boreman, “On-axis and off-axis propagation of Gaussian beams in gradient index media,” Appl. Opt. 29(19), 2944–2950 (1990).
[Crossref]

1987 (1)

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326(6110), 277–278 (1987).
[Crossref]

1986 (2)

A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57(8), 937–940 (1986).
[Crossref]

R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57(8), 933–936 (1986).
[Crossref]

1982 (1)

1970 (1)

C. Imbert, “Experimental proof of the photon’s translational inertial spin effect,” Phys. Lett. A 31(6), 337–338 (1970).
[Crossref]

1955 (1)

F. I. Fedorov, “On the theory of total internal reflection,” Dokl. Akad. Nauk SSSR 105(5), 465–469 (1955).

1941 (1)

V. Vladimirskii, “The rotation of a polarization plane for curved light ray,” Dokl. Akad. Nauk SSSR 21, 222–225 (1941).

1938 (1)

S. Rytov, “On transition from wave to geometrical optics,” Dokl. Akad. Nauk SSSR 18, 263–266 (1938); Tr. Fiz. Inst. Akad. Nauk SSSR 2, 1 (1940).

Abdulkareem, S.

Adam, A. J. L.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

Agarwal, G. S.

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

K.Y. Bliokh, A. Aiello, and M.A. Alonso, “Spin-orbit interactions of light in isotropic media,” in The Angular Momentum of Light, David L. Andrews and Mohamed Babiker, eds. (Cambridge University Press, 2012), chap. 8, pp. 174–245.

Alonso, M. A.

Alonso, M.A.

K.Y. Bliokh, A. Aiello, and M.A. Alonso, “Spin-orbit interactions of light in isotropic media,” in The Angular Momentum of Light, David L. Andrews and Mohamed Babiker, eds. (Cambridge University Press, 2012), chap. 8, pp. 174–245.

Banerji, J.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
[Crossref]

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-index optics: Fundamentals and applications (Springer-Verlag, 2002).

Baranova, N. B.

N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).

Bekshaev, A. Y.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
[Crossref]

Bellessa, J.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Berry, M. V.

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326(6110), 277–278 (1987).
[Crossref]

Bieg, B.

Bliokh, K.

K. 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(10), 1039–1047 (2016).
[Crossref]

K. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

K. Bliokh and Y. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

K. Bliokh and Y. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A: Pure Appl. Opt. 11(9), 094009 (2009).
[Crossref]

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

Y. A. Kravtsov, B. Bieg, and K. Y. Bliokh, “Stokes-vector evolution in a weakly anisotropic inhomogeneous medium,” J. Opt. Soc. Am. A 24(10), 3388–3396 (2007).
[Crossref]

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(6), 066609 (2007).
[Crossref]

K. Y. Bliokh, “Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect,” Phys. Rev. Lett. 97(4), 043901 (2006).
[Crossref]

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(2), 026605 (2004).
[Crossref]

Bliokh, K.Y.

K.Y. Bliokh, A. Aiello, and M.A. Alonso, “Spin-orbit interactions of light in isotropic media,” in The Angular Momentum of Light, David L. Andrews and Mohamed Babiker, eds. (Cambridge University Press, 2012), chap. 8, pp. 174–245.

Bliokh, Y.

K. Bliokh and Y. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

K. Bliokh and Y. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

Bliokh, Y. P.

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(6), 066609 (2007).
[Crossref]

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(2), 026605 (2004).
[Crossref]

Boreman, G. D.

Brok, J. M.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

Camacho, J.

Chang, S.

S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
[Crossref]

Chiao, R.

A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57(8), 937–940 (1986).
[Crossref]

R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57(8), 933–936 (1986).
[Crossref]

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Dainty, C.

Desyatnikov, A. S.

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

Dogariu, A.

Dooghin, A. V.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

Drezet, A.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Dugin, A.

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Fedorov, F. I.

F. I. Fedorov, “On the theory of total internal reflection,” Dokl. Akad. Nauk SSSR 105(5), 465–469 (1955).

Ghai, D. P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
[Crossref]

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-index optics: Fundamentals and applications (Springer-Verlag, 2002).

Guo, X.

S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
[Crossref]

Guy, S.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Haefner, D.

Hasman, E.

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Imbert, C.

C. Imbert, “Experimental proof of the photon’s translational inertial spin effect,” Phys. Lett. A 31(6), 337–338 (1970).
[Crossref]

Ina, H.

Javier, A.

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Jiang, Q.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Kajorndejnukul, V.

Karpeev, S. V.

S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
[Crossref]

Ke, Y.

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

Khoninaa, S. N.

S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
[Crossref]

Kleiner, V.

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Kobayashi, S.

Kravtsov, Y. A.

Kundikova, N.

S. Abdulkareem and N. Kundikova, “Joint effect of polarization and the propagation path of a light beam on its intrinsic structure,” Opt. Express 24(17), 19157–19166 (2016).
[Crossref]

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

Kundikova, N. D.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Lai, M.-Y.

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Lara, D.

Laverdant, J.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Leluyer, C.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Li, H.

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

Li, Q.

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

Li, X.

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

Liang, G.-H.

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Liberman, V.

V. Liberman and B. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

Liberman, V. S.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

B. Y. Zel’dovich and V. S. Liberman, “Rotation of the plane of a meridional beam in a graded-index waveguide due to the circular nature of the polarization,” Sov. J. Quantum Electron. 20(4), 427–428 (1990).
[Crossref]

Liu, Y.

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

Luo, H.

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

Malacara, D.

M. Montoya and D. Malacara, “Polarization effects in interferograms of radial GRIN rods,” Opt. Commun. 175(4-6), 259–263 (2000).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Marchand, E. W.

E. W. Marchand, Gradient index optics (Academic Press, 1978).

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Montoya, M.

M. Montoya and D. Malacara, “Polarization effects in interferograms of radial GRIN rods,” Opt. Commun. 175(4-6), 259–263 (2000).
[Crossref]

Moore, D. T.

Naik, D. N.

C. T. Samlan, D. N. Naik, and N. K. Viswanathan, “Isogyres–manifestation of spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference,” Sci. Rep. 6(1), 33141 (2016).
[Crossref]

Ni, X.

S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
[Crossref]

Niv, A.

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Nori, F.

K. 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(10), 1039–1047 (2016).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Ostrovskaya, E. A.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Paranin, V. D.

S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
[Crossref]

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-index optics: Fundamentals and applications (Springer-Verlag, 2002).

Petrov, N. I.

Pham, A.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Planken, P. C. M.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

Prajapati, C.

Puentes, G.

Rodríguez-Fortuño, F. J.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Rodríguez-Herrera, O. G.

Rouke, J. L.

Rytov, S.

S. Rytov, “On transition from wave to geometrical optics,” Dokl. Akad. Nauk SSSR 18, 263–266 (1938); Tr. Fiz. Inst. Akad. Nauk SSSR 2, 1 (1940).

Sadykov, N. R.

N. R. Sadykov, “Polarization effects due to the mutual influence of trajectory parameters and polarization,” Theor. Math. Phys. 149(1), 1354–1365 (2006).
[Crossref]

N. R. Sadykov, “Influence of the Rytov rotation of the field vectors on the path of a ray,” Quantum Electron. 24(11), 1016–1017 (1994).
[Crossref]

N. R. Sadykov, “Equation of a ray path with circular polarization,” Quantum Electron. 23(11), 989–990 (1993).
[Crossref]

Samlan, C. T.

C. T. Samlan, D. N. Naik, and N. K. Viswanathan, “Isogyres–manifestation of spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference,” Sci. Rep. 6(1), 33141 (2016).
[Crossref]

K. 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(10), 1039–1047 (2016).
[Crossref]

Savchenko, A. Y.

N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).

Senthilkumaran, P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
[Crossref]

Singh, R. P.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
[Crossref]

Sirohi, R. S.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
[Crossref]

Soskin, M. S.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
[Crossref]

Sukhov, S.

Symonds, C.

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Takeda, M.

Tang, M.

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

Tentori, D.

Tomita, A.

A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57(8), 937–940 (1986).
[Crossref]

Urbach, H. P.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

Vaity, P.

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
[Crossref]

Vasnetsov, M. V.

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
[Crossref]

Viswanathan, N. K.

C. T. Samlan, D. N. Naik, and N. K. Viswanathan, “Isogyres–manifestation of spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference,” Sci. Rep. 6(1), 33141 (2016).
[Crossref]

K. 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(10), 1039–1047 (2016).
[Crossref]

Vladimirskii, V.

V. Vladimirskii, “The rotation of a polarization plane for curved light ray,” Dokl. Akad. Nauk SSSR 21, 222–225 (1941).

Vuong, L. T.

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

Wang, C.

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

Wang, F.

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

Wang, J.

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

Wang, Y.-L.

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Wen, S.

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

Wozniak, W. A.

W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC® type,” Proc. SPIE 2169, 156–167 (1994).
[Crossref]

Wu, Y.-S.

R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57(8), 933–936 (1986).
[Crossref]

Ya Bekshaev, A.

A. Ya Bekshaev, “Spin-orbit interaction of light and diffraction of polarized beams,” J. Opt. 19(8), 085602 (2017).
[Crossref]

Zayats, A. V.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Zel’dovich, B.

V. Liberman and B. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

Zel’dovich, B. Y.

N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).

B. Y. Zel’dovich and V. S. Liberman, “Rotation of the plane of a meridional beam in a graded-index waveguide due to the circular nature of the polarization,” Sov. J. Quantum Electron. 20(4), 427–428 (1990).
[Crossref]

Zeldovich, B. Y.

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

Zhang, P.

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

Zhao, Y.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

Zhu, J.

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

Zong, H.-S.

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Annu. Rev. Mater. Res. (1)

S. Chang, X. Guo, and X. Ni, “Optical Metasurfaces: Progress and Applications,” Annu. Rev. Mater. Res. 48(1), 279–302 (2018).
[Crossref]

Appl. Opt. (3)

Dokl. Akad. Nauk SSSR (3)

S. Rytov, “On transition from wave to geometrical optics,” Dokl. Akad. Nauk SSSR 18, 263–266 (1938); Tr. Fiz. Inst. Akad. Nauk SSSR 2, 1 (1940).

V. Vladimirskii, “The rotation of a polarization plane for curved light ray,” Dokl. Akad. Nauk SSSR 21, 222–225 (1941).

F. I. Fedorov, “On the theory of total internal reflection,” Dokl. Akad. Nauk SSSR 105(5), 465–469 (1955).

J. Exp. Theor. Phys. Lett. (1)

A. Dugin, B. Zel’dovich, N. Kundikova, and V. Liberman, “Effect of circular polarization on the propagation of light through an optical fiber,” J. Exp. Theor. Phys. Lett. 53, 197–199 (1991).

J. Opt. (2)

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

A. Ya Bekshaev, “Spin-orbit interaction of light and diffraction of polarized beams,” J. Opt. 19(8), 085602 (2017).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A: Pure Appl. Opt. 11(9), 094009 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

JETP Lett. (1)

N. B. Baranova, A. Y. Savchenko, and B. Y. Zel’dovich, “Transverse shift of a focal spot due to switching of the sign of circular polarization,” JETP Lett. 59, 232–234 (1994).

Nanophotonics (1)

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

Nat. Photonics (2)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Nature (1)

M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature 326(6110), 277–278 (1987).
[Crossref]

Opt. Commun. (2)

M. Montoya and D. Malacara, “Polarization effects in interferograms of radial GRIN rods,” Opt. Commun. 175(4-6), 259–263 (2000).
[Crossref]

A. Y. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241(4-6), 237–247 (2004).
[Crossref]

Opt. Express (2)

Opt. Laser Eng. (1)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single slit diffraction of an optical beam with phase singularity,” Opt. Laser Eng. 47(1), 123–126 (2009).
[Crossref]

Opt. Lett. (1)

Optica (1)

Optik (1)

S. N. Khoninaa, S. V. Karpeev, and V. D. Paranin, “Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam,” Optik 164, 679–685 (2018).
[Crossref]

Phys. Lett. A (4)

N. I. Petrov, “Evolution of Berry’s phase in a graded-index medium,” Phys. Lett. A 234(4), 239–250 (1997).
[Crossref]

C. Imbert, “Experimental proof of the photon’s translational inertial spin effect,” Phys. Lett. A 31(6), 337–338 (1970).
[Crossref]

K. Bliokh and Y. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

P. Vaity, J. Banerji, and R. P. Singh, “Measuring the topological charge of an optical vortex by using a tilted convex lens,” Phys. Lett. A 377(15), 1154–1156 (2013).
[Crossref]

Phys. Rep. (1)

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

Phys. Rev. A (5)

H. Li, J. Wang, M. Tang, and X. Li, “Changes of phase structure of a paraxial beam due to spin-orbit coupling,” Phys. Rev. A 97(5), 053843 (2018).
[Crossref]

V. Liberman and B. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46(8), 5199–5207 (1992).
[Crossref]

A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zeldovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992).
[Crossref]

K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009).
[Crossref]

M.-Y. Lai, Y.-L. Wang, G.-H. Liang, F. Wang, and H.-S. Zong, “Electromagnetic wave propagating along a space curve,” Phys. Rev. A 97(3), 033843 (2018).
[Crossref]

Phys. Rev. Appl. (1)

Q. Jiang, J. Laverdant, C. Symonds, A. Pham, C. Leluyer, S. Guy, A. Drezet, and J. Bellessa, “Metasurface for reciprocal spin-orbit coupling of light on waveguiding structures,” Phys. Rev. Appl. 10(1), 014014 (2018).
[Crossref]

Phys. Rev. E (2)

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(2), 026605 (2004).
[Crossref]

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(6), 066609 (2007).
[Crossref]

Phys. Rev. Lett. (7)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett. 99(7), 073901 (2007).
[Crossref]

K. Bliokh and Y. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

L. T. Vuong, A. J. L. Adam, J. M. Brok, P. C. M. Planken, and H. P. Urbach, “Electromagnetic spin-orbit interactions via scattering of subwavelength apertures,” Phys. Rev. Lett. 104(8), 083903 (2010).
[Crossref]

A. Tomita and R. Chiao, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57(8), 937–940 (1986).
[Crossref]

R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57(8), 933–936 (1986).
[Crossref]

K. Y. Bliokh, “Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect,” Phys. Rev. Lett. 97(4), 043901 (2006).
[Crossref]

Proc. SPIE (1)

W. A. Wozniak, “Birefringence of gradient-index lenses of SELFOC® type,” Proc. SPIE 2169, 156–167 (1994).
[Crossref]

Quantum Electron. (2)

N. R. Sadykov, “Equation of a ray path with circular polarization,” Quantum Electron. 23(11), 989–990 (1993).
[Crossref]

N. R. Sadykov, “Influence of the Rytov rotation of the field vectors on the path of a ray,” Quantum Electron. 24(11), 1016–1017 (1994).
[Crossref]

Sci. Rep. (1)

C. T. Samlan, D. N. Naik, and N. K. Viswanathan, “Isogyres–manifestation of spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference,” Sci. Rep. 6(1), 33141 (2016).
[Crossref]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Sov. J. Quantum Electron. (1)

B. Y. Zel’dovich and V. S. Liberman, “Rotation of the plane of a meridional beam in a graded-index waveguide due to the circular nature of the polarization,” Sov. J. Quantum Electron. 20(4), 427–428 (1990).
[Crossref]

Theor. Math. Phys. (1)

N. R. Sadykov, “Polarization effects due to the mutual influence of trajectory parameters and polarization,” Theor. Math. Phys. 149(1), 1354–1365 (2006).
[Crossref]

Other (4)

J. Zhu, P. Zhang, Q. Li, F. Wang, and C. Wang, “An experimental measurement of the topological charge of orbital angular momentum beams through weak measurement,” ArXiv 1801.07341 (2018).

K.Y. Bliokh, A. Aiello, and M.A. Alonso, “Spin-orbit interactions of light in isotropic media,” in The Angular Momentum of Light, David L. Andrews and Mohamed Babiker, eds. (Cambridge University Press, 2012), chap. 8, pp. 174–245.

E. W. Marchand, Gradient index optics (Academic Press, 1978).

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-index optics: Fundamentals and applications (Springer-Verlag, 2002).

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Figures (8)

Fig. 1.
Fig. 1. (a) Calculated output beam intensity pattern for orthogonal (H-) polarization projection for V- polarized input Gaussian beam into the GRIN rod, (b) residual phase gradient due to rotation of the propagation vector as a function of input position that results in parallel transport of SoP. Overall size of each image is (1.8 × 1.8) mm.
Fig. 2.
Fig. 2. Schematic of the experimental setup to investigate all the SOI effects due to propagation of polarized Gaussian and LG beams through the GRIN rod. BS: 50-50 Beam splitter, M: Mirror, SLM: Spatial light modulator, MO: Microscope objective lens, O/p: Output measurements, CCD: camera. Cross-section of the GRIN shows the location where the input beam is incident. Insets (i) and (ii) correspond to polarimetry and projection / weak measurement setup and interferometry setup.
Fig. 3.
Fig. 3. Orthogonal SoP projection of output beam field, after passing through the GRIN rod, for input (a) RCP and (f) LCP Gaussian beam. On-axis (b) and (g) and off-axis (c) and (h) interferograms of the orthogonally projected beams. Extracted phase from the interferograms for (d,e) RCP and (i,j) LCP input beams.
Fig. 4.
Fig. 4. Experimentally measured S3 Stokes parameter for different IOAM values (l = ±1, ±2 and ± 3) of input beam with vertical SoP, corresponding to σ = 0. Red and blue color correspond to left and right circular SoP components in the output beam.
Fig. 5.
Fig. 5. (a) Experimentally measured output beam intensity due to spin-Hall effect in the GRIN rod, for vertically polarized input Gaussian beam, shifted by 0.7 mm from on-axis. The transverse shift of the beam centroid and projected at angles, ɛ = (a) - 9°, (b) 0° and (c) +9° of the analyzer, (d) S3 Stokes parameter of the output beam and (e) calculated beam shift as a function of analyzer rotation angle.
Fig. 6.
Fig. 6. Experimental measurement to demonstrate the effect of trajectory curvature on SHE of light. (a) – (h) shows the S3 parameter as a function of the input beam position (indicated in the bottom left side of each, in mm) from close to on-axis (0.07 mm) to off-axis (0.7 mm). Graphs (i) and (j) are the data extracted from the S3 Stokes measurement and beam shift from weak measurement, as a function of input beam position.
Fig. 7.
Fig. 7. Experimentally measured transverse IOAM-dependent CoI shift due to OHE for beams with intrinsic OAM with different (+) and (-) topological charges (a) to (e) and (f) to (j) respectively. The solid (white color) horizontal lines in the figures represent the CoI of reference Gaussian beam and dashed lines are the CoI of corresponding to + l and -l IOAM input beams. The green ellipse indicates the high intensity areas of shifted output OAM beams. (k) transverse OHE beam shift increases linearly with l.
Fig. 8.
Fig. 8. Experimentally measured output beam intensity for + 45° and -45° oriented input HG beam, after propagating through the GRIN rod, as a function of input beam position y. (a) Rotation of output beam intensity as a function of input position, (b) collimated output beam for fixed input beam position of y = -0.56 mm and the corresponding single slit diffraction pattern confirming the presence of phase dislocation and (c) plot of rotation angle as a function of input beam position along ± y direction for two different intensity distribution and phase structure.

Equations (4)

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E out = A ( θ c ) cos θ c [ a b e i 2 φ b e i 2 φ a ] [ E r i E l i ]
E vo = i A ( θ c ) cos θ c [ ( a E r i + b e i 2 φ E l i ) r ( b e i 2 φ E r i a E l i ) l ] E ho = i A ( θ c ) cos θ c [ ( b e i 2 φ E l i ) r ( b e i 2 φ E r i ) l ]
E out = { A ( θ c ) cos θ c [ a b e i 2 φ b e i 2 φ a ] + i B ( θ c ) sin θ 2 cos θ c [ r s e i φ r s e i φ r s e i φ r s e i φ ] } [ E r i E l i ]
Y = 0 , X = σ f y s 3 B sin 4 θ c 2 A ( 4 3 cos θ c cos 3 θ c )

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