Abstract

We show the existence of an inherent property of evanescent electromagnetic waves: spin-momentum locking, where the direction of momentum fundamentally locks the polarization of the wave. We trace the ultimate origin of this phenomenon to complex dispersion and causality requirements on evanescent waves. We demonstrate that every case of evanescent waves in total internal reflection (TIR), surface states, and optical fibers/waveguides possesses this intrinsic spin-momentum locking. We also introduce a universal right-handed triplet consisting of momentum, decay, and spin for evanescent waves. We derive the Stokes parameters for evanescent waves, which reveal an intriguing result—every fast decaying evanescent wave is inherently circularly polarized with its handedness tied to the direction of propagation. We also show the existence of a fundamental angle associated with TIR such that propagating waves locally inherit perfect circular polarized characteristics from the evanescent wave. This circular TIR condition occurs if and only if the ratio of permittivities of the two dielectric media exceeds the golden ratio. Our work leads to a unified understanding of this spin-momentum locking in various nanophotonic experiments and sheds light on the electromagnetic analogy with the quantum spin-Hall state for electrons.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2015 (3)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

2014 (7)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

2013 (5)

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, 328–330 (2013).
[Crossref]

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: helicity, spin, momentum and angular momentum,” New J. Phys. 15, 033026 (2013).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

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 496, 196–200 (2013).
[Crossref]

2012 (4)

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).
[Crossref]

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97, 47004 (2012).
[Crossref]

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801 (2012).
[Crossref]

2011 (1)

J. Maciejko, T. L. Hughes, and S.-C. Zhang, “The quantum spin Hall effect,” Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
[Crossref]

2006 (2)

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314, 1757–1761 (2006).
[Crossref]

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[Crossref]

2005 (1)

C. L. Kane and E. J. Mele, “Quantum spin Hall effect in graphene,” Phys. Rev. Lett. 95, 226801 (2005).
[Crossref]

1988 (1)

M. D’yakonov, “New type of electromagnetic wave propagating at the interface,” Zh. Eksp. Teor. Fiz. 94, 119–123 (1988).

1984 (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

1965 (1)

F. Fedorov, “Covariant description of the properties of light beams,” J. Appl. Spectrosc. 2, 344–351 (1965).
[Crossref]

1961 (1)

W. H. McMaster, “Matrix representation of polarization,” Rev. Mod. Phys. 33, 8–28 (1961).
[Crossref]

Albrecht, B.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Antoniou, N.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Banzer, P.

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
[Crossref]

Barnett, S. M.

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).
[Crossref]

Bauer, T.

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
[Crossref]

Bekshaev, A. Y.

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: helicity, spin, momentum and angular momentum,” New J. Phys. 15, 033026 (2013).
[Crossref]

Belov, P. A.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Béri, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Bernevig, B. A.

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314, 1757–1761 (2006).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: helicity, spin, momentum and angular momentum,” New J. Phys. 15, 033026 (2013).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801 (2012).
[Crossref]

Cameron, R. P.

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).
[Crossref]

Capasso, F.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

D’yakonov, M.

M. D’yakonov, “New type of electromagnetic wave propagating at the interface,” Zh. Eksp. Teor. Fiz. 94, 119–123 (1988).

Dreisow, F.

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 496, 196–200 (2013).
[Crossref]

Ducloy, M.

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97, 47004 (2012).
[Crossref]

Ei-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Fang, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Fedorov, F.

F. Fedorov, “Covariant description of the properties of light beams,” J. Appl. Spectrosc. 2, 344–351 (1965).
[Crossref]

Filonov, D. S.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Gao, W.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Ginzburg, P.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

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, 328–330 (2013).
[Crossref]

Grischkowsky, D.

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[Crossref]

Guzatov, D. V.

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97, 47004 (2012).
[Crossref]

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Hughes, T. L.

J. Maciejko, T. L. Hughes, and S.-C. Zhang, “The quantum spin Hall effect,” Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
[Crossref]

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314, 1757–1761 (2006).
[Crossref]

Javadi, A.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Jeon, T.-I.

T.-I. Jeon and D. Grischkowsky, “THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet,” Appl. Phys. Lett. 88, 061113 (2006).
[Crossref]

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Kane, C. L.

C. L. Kane and E. J. Mele, “Quantum spin Hall effect in graphene,” Phys. Rev. Lett. 95, 226801 (2005).
[Crossref]

Kapitanova, P. V.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Kim, K.-Y.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Kiršanske, G.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Kivshar, Y. S.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Klimov, V. V.

V. V. Klimov, D. V. Guzatov, and M. Ducloy, “Engineering of radiation of optically active molecules with chiral nano-meta-particles,” Europhys. Lett. 97, 47004 (2012).
[Crossref]

Kuipers, L.

B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

Lawrence, M.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Le Feber, B.

B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

Lee, B.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Lee, E. H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Lee, I.-M.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Lee, S.-Y.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Lee, W.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Leuchs, G.

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
[Crossref]

Li, J.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Lin, J.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Liu, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Livio, M.

M. Livio, The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number (Broadway, 2008).

Lodahl, P.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Lu, L.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Lumer, Y.

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 496, 196–200 (2013).
[Crossref]

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Maciejko, J.

J. Maciejko, T. L. Hughes, and S.-C. Zhang, “The quantum spin Hall effect,” Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
[Crossref]

Mahmoodian, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Marino, G.

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, 328–330 (2013).
[Crossref]

Martínez, A.

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, 328–330 (2013).
[Crossref]

McMaster, W. H.

W. H. McMaster, “Matrix representation of polarization,” Rev. Mod. Phys. 33, 8–28 (1961).
[Crossref]

Mele, E. J.

C. L. Kane and E. J. Mele, “Quantum spin Hall effect in graphene,” Phys. Rev. Lett. 95, 226801 (2005).
[Crossref]

Midolo, L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Mitsch, R.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Mueller, J. B.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Neugebauer, M.

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
[Crossref]

Nolte, S.

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 496, 196–200 (2013).
[Crossref]

Nori, F.

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: helicity, spin, momentum and angular momentum,” New J. Phys. 15, 033026 (2013).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801 (2012).
[Crossref]

O’Connor, D.

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

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, 328–330 (2013).
[Crossref]

Oh, S.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Park, J.

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

Plotnik, Y.

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 496, 196–200 (2013).
[Crossref]

Poddubny, A. N.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Podolsky, D.

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 496, 196–200 (2013).
[Crossref]

Pregnolato, T.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Rauschenbeutel, A.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Rechtsman, M. C.

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 496, 196–200 (2013).
[Crossref]

Rodríguez-Fortuño, F.

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

Rodríguez-Fortuño, F. J.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

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, 328–330 (2013).
[Crossref]

Rotenberg, N.

B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

Sayrin, C.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Schneeweiss, P.

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

Segev, M.

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 496, 196–200 (2013).
[Crossref]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Soljacic, M.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Söllner, I.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Song, J. D.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Stobbe, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Szameit, A.

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 496, 196–200 (2013).
[Crossref]

Tse, W.-K.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Volz, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

Voroshilov, P. M.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

Wang, Q.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Weber, W. H.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Wurtz, G.

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

Wurtz, G. A.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

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, 328–330 (2013).
[Crossref]

Yang, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Yao, A. M.

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).
[Crossref]

Yuan, G.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Yuan, X.-C.

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Zayats, A.

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

Zayats, A. V.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

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, 328–330 (2013).
[Crossref]

Zeuner, J. M.

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 496, 196–200 (2013).
[Crossref]

Zhang, S.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Zhang, S.-C.

J. Maciejko, T. L. Hughes, and S.-C. Zhang, “The quantum spin Hall effect,” Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
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B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314, 1757–1761 (2006).
[Crossref]

Annu. Rev. Condens. Matter Phys. (1)

J. Maciejko, T. L. Hughes, and S.-C. Zhang, “The quantum spin Hall effect,” Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
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Nano Lett. (1)

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546–2551 (2014).
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Nat. Commun. (5)

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Commun. 5, 5713 (2014).
[Crossref]

D. O’Connor, P. Ginzburg, F. Rodríguez-Fortuño, G. Wurtz, and A. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5, 5327 (2014).
[Crossref]

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5, 3226 (2014).
[Crossref]

B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

Nat. Mater. (1)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12, 233–239 (2013).
[Crossref]

Nat. Nanotechnol. (1)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanske, T. Pregnolato, H. Ei-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Nat. Photonics (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8, 821–829 (2014).
[Crossref]

Nature (1)

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 496, 196–200 (2013).
[Crossref]

New J. Phys. (2)

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).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Dual electromagnetism: helicity, spin, momentum and angular momentum,” New J. Phys. 15, 033026 (2013).
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Phys. Rep. (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[Crossref]

Phys. Rev. A (1)

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801 (2012).
[Crossref]

Phys. Rev. Lett. (3)

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic induction currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

C. L. Kane and E. J. Mele, “Quantum spin Hall effect in graphene,” Phys. Rev. Lett. 95, 226801 (2005).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114, 037402 (2015).
[Crossref]

Rev. Mod. Phys. (1)

W. H. McMaster, “Matrix representation of polarization,” Rev. Mod. Phys. 33, 8–28 (1961).
[Crossref]

Science (4)

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, 328–330 (2013).
[Crossref]

J. Lin, J. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Quantum spin Hall effect and topological phase transition in HgTe quantum wells,” Science 314, 1757–1761 (2006).
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Zh. Eksp. Teor. Fiz. (1)

M. D’yakonov, “New type of electromagnetic wave propagating at the interface,” Zh. Eksp. Teor. Fiz. 94, 119–123 (1988).

Other (1)

M. Livio, The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number (Broadway, 2008).

Supplementary Material (1)

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Figures (11)

Fig. 1.
Fig. 1.

Our result shows a fundamental right-handed triplet formed by momentum, decay, and spin for evanescent waves. Note the locked triplets for waves propagating in two opposite directions. As we can see, the direction of the spin s^ flips for the two cases. It is important to note that, in general, there are four degenerate solutions, but two of these correspond to growing evanescent waves, which are forbidden due to causality. This explains why the left-handed triplet is not allowed and the phenomenon of spin-momentum locking is universal to evanescent waves.

Fig. 2.
Fig. 2.

Poincaré spheres for propagating waves and evanescent waves. Propagating waves can have any arbitrary polarization state for a given phase velocity. However, all fast decaying evanescent waves are circularly polarized and lie on the south or north pole of the Poincaré sphere (S3=±1). Furthermore, the choice between these two points is locked to the direction of momentum (±κ).

Fig. 3.
Fig. 3.

CTIR at interface between glass with n1=2 and air with n2=1 at the θCTIR condition. For waves traveling in the +x direction, the evanescent wave in region 2 has right-handed spin-momentum locking (inset). Note the wave in medium 1 has perfect circular polarization characteristics close to the interface at this angle of incidence. The overlaid false color plot is the spatial distribution of the normalized Stokes parameter (S3), which characterizes the handedness of the wave (degree of circular polarization) from 1 to 1 at each point.

Fig. 4.
Fig. 4.

CTIR at interface between glass with n1=2 and air with n2=1 at the θCTIR condition. For waves traveling in the x direction, the evanescent wave in region 2 has left-handed spin-momentum locking (inset). The plot illustrates that the evanescent wave spin has the opposite sign as compared to the previous case because the momentum and spin are locked.

Fig. 5.
Fig. 5.

Waveguide mode at interface between glass with n1=4 and air with n2=1. The width of the waveguide is 2k0d=2. For waveguide modes traveling in the +x direction, the evanescent waves in region 2 lock the handedness (locally) to +s^ at k0z=1 and s^ at k0z=1. The false color plot shows the spatial distribution of the normalized Stokes parameter (S3) from 1 to 1 for the waveguide and illustrates the intrinsic handedness of the evanescent waves. Furthermore, on comparison with the counterpropagating waveguide mode, we see that the handedness is reversed.

Fig. 6.
Fig. 6.

Waveguide mode at interface between glass with n1=4 and air with n2=1. The width of the waveguide is 2k0d=2. For waveguide modes traveling in the x direction, the evanescent waves in region 2 lock the handedness (locally) to s^ at k0z=1 and +s^ at k0z=1.

Fig. 7.
Fig. 7.

Evolution of the polarization vector as it propagates in an optical fiber with V=1.5 and Δ=0.1. We display the electric field at a single point at r=a in the m=+1 HE11 mode to demonstrate the transverse spin near the core–cladding region. As we can see, the electric field rotates in the z plane as well as in the xy plane, hence, there is a spin component directed around φ^ (inset). Out of four possible degenerate solutions, only two are allowed because of the decaying condition on evanescent waves outside the core. Consequently, the HE11 mode of the optical fiber has spin-momentum locking.

Fig. 8.
Fig. 8.

Normalized HE11 polarization intensities (I/IE(0)) for an optical fiber of V=1.5 and Δ=0.1. We see that the majority of the field is concentrated in the IAM angular momentum component, but there is a significant component of spin intensity (IS) in the φ^ direction near the core–cladding interface at r=a.

Fig. 9.
Fig. 9.

Chiral emitter placed at r0=0 and transverse emitter placed at r0=ax^ inside the optical fiber. The intrinsic chirality of the HE11 mode opens possibilities for spin-controlled quantum photonics. We emphasize that this intrinsic chirality is universal and arises from the evanescent waves outside the core.

Fig. 10.
Fig. 10.

All electromagnetic surface waves will show spin-momentum locking. We depict here an SPP excitation between metal with ε1=2 and air with ε2=1 propagating in the +x direction. The vector plot overlaid on the spatial distribution of the Stokes parameter (S3) illustrates the inherent handedness of the two evanescent waves and how they couple with counter-rotating spins.

Fig. 11.
Fig. 11.

SPP dispersion relation that also includes the handedness of the evanescent spin (in the dielectric region). As the momentum κ increases, the SPP spin approaches perfect circular polarization (SPP resonance).

Equations (31)

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k·k=k02,
κ2η2=k02,
κ·η=0.
s^=κ×η|κ×η|=ik×k*|k×k*|,
p^=k×s^|k|=ik×(k×k*)|k||k×k*|,
k·s^=k·p^=s^·p^=0,
p^=i[η|k|(κκ)+iκ|k|(ηη)],
S0=p^|1|p^=1,
S1=p^|σz|p^=k02|k|2,
S2=p^|σx|p^=0,
S3±=p^|σy|p^=±2κη|k|2.
p^i2[(κκ)+i(ηη)],
S10,
S3±±1,
[EE]1=±iε2ε1[κη]2at  interface,
ε1ε2=[κη]2.
κ2=ε1ε2ε12ε22k0,
η2=ε2ε2ε12ε22k0.
sin(θCTIR)=1/ε1/ε2ε2/ε1.
[ε1ε2]GR=12(1+5)1.618,
E[kz{sin(kzz)cos(kzz)}x^+ikx{cos(kzz)sin(kzz)}z^]eikxx,
Em=E0[2βJ0(Xr/a)e^m+iXJ1(Xr/a)z^]eimφ,
Hm=imH0[2(σ1)2J0(Xr/a)e^m+iβXJ1(Xr/a)z^]eimφ
Em=NE0[2βK0(Yr/a)e^m+iYK1(Yr/a)z^]eimφ,
Hm=imNH0[2(σ2)2K0(Yr/a)e^m+iβYK1(Yr/a)z^]eimφ
(IAM)m=m2|E0|2β2J02(Xr/a),
(IS)m=sign(β)2|E0|2|β|XJ0(Xr/a)J1(Xr/a),
[JE(r)JH(r)]±=iωδ3(rr0)[pm]=iωδ3(rr0)[p0im0]e^±e±iφ,
|Am|2=C1|sign(β)|β|ωp0+m(σ1)2m0μ0a|2,
|Am|2=C2ω2|sign(β)|β|J0(X)px+XJ1(X)pz|2,
(S3)1=(S3)2=2|ε1|ε2|ε1|+ε2,

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