Abstract

Whispering gallery modes are known for possessing orbital angular momentum, however the interplay of local spin density, orbital angular momentum, and the near-field interaction with quantum emitters is far less explored. Here, we study the spin-orbit interaction of a circularly polarized dipole with the whispering gallery modes (WGMs) of a spherical resonator. Using an exact dyadic Green’s function approach, we show that the near-field interaction between the photonic spin of a circularly polarized dipole and the local electromagnetic spin density of whispering gallery modes gives rise to unidirectional behaviour where modes with either positive or negative orbital angular momentum are excited. We show that this is a manifestation of spin-momentum locking with the whispering gallery modes of the spherical resonator. We also discuss requirements for possible experimental demonstrations using Zeeman transitions in cold atoms or quantum dots, and outline potential applications of these previously overlooked properties. Our work firmly establishes local spin density, momentum and decay as a universal right-handed electromagnetic triplet for near-field light-matter interaction.

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

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  12. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
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  13. B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
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  27. 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).
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    [Crossref]

2018 (5)

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum optics interface,” Science 359, 666–668 (2018).
[Crossref] [PubMed]

S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, “Flying couplers above spinning resonators generate irreversible refraction,” Nature 558, 569–572 (2018).
[Crossref] [PubMed]

M. F. Picardi, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Janus and huygens dipoles: near-field directionality beyond spin-momentum locking,” Phys. Rev. Lett. 120, 117402 (2018).
[Crossref] [PubMed]

M. Picardi, K. Bliokh, F. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, “Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes,” Optica 5, 1016–1026 (2018).
[Crossref]

S. Pendharker, F. Kalhor, T. Van Mechelen, S. Jahani, N. Nazemifard, T. Thundat, and Z. Jacob, “Spin photonic forces in non-reciprocal waveguides,” Opt. Express 26, 23898–23910 (2018).
[Crossref] [PubMed]

2016 (4)

T. Van Mechelen and Z. Jacob, “Universal spin-momentum locking of evanescent waves,” Optica 3, 118–126 (2016).
[Crossref]

F. Kalhor, T. Thundat, and Z. Jacob, “Universal spin-momentum locked optical forces,” Appl. Phys. Lett. 108, 061102 (2016).
[Crossref]

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
[Crossref]

C. Li, O. van’t Erve, Y. Li, L. Li, and B. Jonker, “Electrical detection of the helical spin texture in a p-type topological insulator sb2te3,” Sci. Rep. 6, 29533 (2016).
[Crossref]

2015 (6)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-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]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref] [PubMed]

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

M. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref] [PubMed]

A. Hayat, J. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112, 13190–13194 (2015).
[Crossref] [PubMed]

2014 (6)

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

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] [PubMed]

S. Wang and C. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[Crossref] [PubMed]

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

C. Li, O. van’t Erve, J. Robinson, Y. Liu, L. Li, and B. Jonker, “Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in bi2se3,” Nat. Nanotechnol. 9, 218–224 (2014).
[Crossref] [PubMed]

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

2013 (3)

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] [PubMed]

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] [PubMed]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
[Crossref]

2012 (1)

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

2010 (1)

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

2009 (1)

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

2007 (1)

G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
[Crossref] [PubMed]

2006 (1)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

2002 (3)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
[Crossref]

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32, 377–400 (2002).
[Crossref]

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
[Crossref]

1998 (1)

M. V. Berry, “Paraxial beams of spinning light,” SPIE 3487, 6–11 (1998).

1994 (2)

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

L. W. Li, P. S. Kooi, M. S. Leong, and T. S. Yee, “Electromagnetic dyadic green’s function in spherically multilayered media,” IEEE Trans. Microw. Theory Tech. 42, 2302–2310 (1994).
[Crossref]

Aiello, A.

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103, 100401 (2009).
[Crossref] [PubMed]

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] [PubMed]

Alizadeh, M.

M. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

Allen, L.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

Alpeggiani, F.

Alt, W.

G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
[Crossref] [PubMed]

Androvitsaneas, P.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref] [PubMed]

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] [PubMed]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Arazi, L.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref] [PubMed]

Bai, B.

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
[Crossref]

Barik, S.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum optics interface,” Science 359, 666–668 (2018).
[Crossref] [PubMed]

Barnett, S. M.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994).
[Crossref]

Bayer, M.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
[Crossref]

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref] [PubMed]

Beggs, D. M.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref] [PubMed]

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] [PubMed]

Berry, M. V.

M. V. Berry, “Paraxial beams of spinning light,” SPIE 3487, 6–11 (1998).

Bliokh, K.

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] [PubMed]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Cai, T.

S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum optics interface,” Science 359, 666–668 (2018).
[Crossref] [PubMed]

Cameron, R. P.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
[Crossref]

Cao, H.

B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

Capasso, F.

A. Hayat, J. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112, 13190–13194 (2015).
[Crossref] [PubMed]

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] [PubMed]

Carmon, T.

S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, “Flying couplers above spinning resonators generate irreversible refraction,” Nature 558, 569–572 (2018).
[Crossref] [PubMed]

Chan, C.

S. Wang and C. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
[Crossref] [PubMed]

Chen, X.

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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Pelli, S.

A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Pendharker, S.

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] [PubMed]

Picardi, M.

Picardi, M. F.

M. F. Picardi, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Janus and huygens dipoles: near-field directionality beyond spin-momentum locking,” Phys. Rev. Lett. 120, 117402 (2018).
[Crossref] [PubMed]

Pregnolato, T.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-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).
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Rarity, J. G.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref] [PubMed]

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

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).
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G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
[Crossref] [PubMed]

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B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
[Crossref]

Reinhard, B. M.

M. Alizadeh and B. M. Reinhard, “Transverse chiral optical forces by chiral surface plasmon polaritons,” ACS Photonics 2, 1780–1788 (2015).
[Crossref]

Reithmaie, J.

M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
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A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
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C. Li, O. van’t Erve, J. Robinson, Y. Liu, L. Li, and B. Jonker, “Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in bi2se3,” Nat. Nanotechnol. 9, 218–224 (2014).
[Crossref] [PubMed]

Rodríguez-Fortuño, F.

Rodríguez-Fortuño, F. J.

M. F. Picardi, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Janus and huygens dipoles: near-field directionality beyond spin-momentum locking,” Phys. Rev. Lett. 120, 117402 (2018).
[Crossref] [PubMed]

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).
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S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref] [PubMed]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
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B. Le Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
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G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
[Crossref] [PubMed]

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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] [PubMed]

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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
[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).
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T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
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T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
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Shomroni, I.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
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Söllner, I.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-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).
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B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
[Crossref] [PubMed]

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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-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).
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B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
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A. Chiasera, Y. Dumeige, P. Feron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
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S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-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).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
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A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
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Thundat, T.

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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
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C. Li, O. van’t Erve, Y. Li, L. Li, and B. Jonker, “Electrical detection of the helical spin texture in a p-type topological insulator sb2te3,” Sci. Rep. 6, 29533 (2016).
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C. Li, O. van’t Erve, J. Robinson, Y. Liu, L. Li, and B. Jonker, “Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in bi2se3,” Nat. Nanotechnol. 9, 218–224 (2014).
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G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
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S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
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J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
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S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum optics interface,” Science 359, 666–668 (2018).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
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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).
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S. Wang and C. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5, 3307 (2014).
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B. Redding, L. Ge, Q. Song, J. Wiersig, G. S. Solomon, and H. Cao, “Local chirality of optical resonances in ultrasmall resonators,” Phys. Rev. Lett. 108, 253902 (2012).
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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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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).
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S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
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A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
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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).
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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).
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M. F. Picardi, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Janus and huygens dipoles: near-field directionality beyond spin-momentum locking,” Phys. Rev. Lett. 120, 117402 (2018).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
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ACS Photonics (1)

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S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, “On the natures of the spin and orbital parts of optical angular momentum,” J. Opt. 18, 064004 (2016).
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L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light. Sci. Appl. 2, e70 (2013).
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S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
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Nat. Nanotechnol. (2)

C. Li, O. van’t Erve, J. Robinson, Y. Liu, L. Li, and B. Jonker, “Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in bi2se3,” Nat. Nanotechnol. 9, 218–224 (2014).
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Nature (3)

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. Kippenberg, K. Vahala, and H. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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M. Bayer, G. Ortner, O. Stern, A. Kuther, A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. Reinecke, S. Walck, J. Reithmaie, F. Klopf, and F. Schafer, “Fine structure of neutral and charged excitons in self-assembled in (ga) as/(al) gaas quantum dots,” Phys. Rev. B 65, 195315 (2002).
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Phys. Rev. E (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002).
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Phys. Rev. Lett. (5)

G. Sagué, E. Vetsch, W. Alt, D. Meschede, and A. Rauschenbeutel, “Cold-atom physics using ultrathin optical fibers: Light-induced dipole forces and surface interactions,” Phys. Rev. Lett. 99, 163602 (2007).
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[Crossref] [PubMed]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115, 153901 (2015).
[Crossref] [PubMed]

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Science (5)

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
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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).
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S. Barik, A. Karasahin, C. Flower, T. Cai, H. Miyake, W. DeGottardi, M. Hafezi, and E. Waks, “A topological quantum optics interface,” Science 359, 666–668 (2018).
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Supplementary Material (2)

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» Visualization 1       Electromagnetic field animation of circularly polarized dipole interacting with a whispering gallery mode resonator
» Visualization 2       Electromagnetic field animation of circularly polarized dipole interacting with a whispering gallery mode resonator

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Figures (5)

Fig. 1
Fig. 1 Schematic of the proposed experiment to study spin photonics in WGMs. The unique proposed effect due to the locked electromagnetic triplet consisting of spin, momentum, and decay. (a) A quantum source with circularly polarized emission (σ± transitions) is placed in the vicinity of a spherical resonator. The near-field interaction between the source and TM WGMs of the sphere results in excitation of WGM with only spin polarized, positive OAM along z direction. This unidirectional behaviour is a manifestation of spin-momentum locking in a 3D structure. Spin, linear momentum, and decay are along θ̂, ϕ̂, and r̂, respectively, and form a triplet for the TE and TM modes. (b) General form of Zeeman transitions in a cold atom [22] or quantum dot [23]. For σ± and π transitions, ΔmF = ±1 and ΔmF = 0, respectively, where mF is the quantum number pertinent to the total angular momentum of the source (nucleous and electrons). These transitions can be modeled by dipole sources with the electric dipole moment given by Eq. (7) [27].

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Fig. 2
Fig. 2 Proposed experimental setup for the spin photonics in WGMs. By exciting the resonator using a σ− transition of a quantum source, WGMs with positive orbital angular momentum are excited stronger. This can be observed by proximity coupling of a tapered optical fiber to the spherical resonator. As a result of coupling between the WGMs with positive OAM and the fiber, modes propagate only in one particular direction in the fiber [13, 24]. Switching to a σ+ transition instead, would also reverse the propagation direction inside the fiber. The source can be Zeeman transitions in cold Caesium atom prepared in the excited state using a excitation signal [22].

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Fig. 3
Fig. 3 Electromagnetic spin in TE and TM whispering galley modes. The color plot shows the field intensity of Hr (Er) component of the TE (TM) mode for l = 16 and m = 16 on the surface of the resonator. The blue arrows show the direction of spin on the surface of the sphere. Modes with positive m, orbit the z axis counter-clockwise (+ϕ̂) while those with negative m orbit the z axis clock-wise (−ϕ̂). With linear momentum along +ϕ̂, Momentum, decay, and spin form a triplet. Spin direction follows the spin-momentum locking property for both TE and TM modes. This means that by changing the direction of OAM (changing the sign of m), the direction of the spin (blue arrows) reverses for both TE and TM modes. This behaviour inspires unidirectional coupling of a circularly polarized dipole to the WGMs.

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Fig. 4
Fig. 4 Plots of normalized scattered electromagnetic fields due to the right-handed circularly polarized dipole (σ+ transition). (a) Er, (b) Eϕ, and (c) Hθ in the x − y plane. All components of the fields orbit along −ϕ direction as a result of the circularly polarized dipole located at xd = a +10nm and yd = zd = 0 with the dipole moment d + = d 0 2 ( x ^ + i y ^ ) = d 0 e ^ +. The circularly polarized dipole couples unidirectionally to the orbit of the fields in the spherical resonator as a result of spin-momentum locking. One important consequence of this is that the photonic spin of the source is opposite to the OAM of the WGMs. Additional videos in supplementary information show the spin-momentum locking (see Visualization 1 and Visualization 2).

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Fig. 5
Fig. 5 Normalized Poynting vector along ϕ direction, Pϕ, for the three cases of (a) σ+ transitions (RH circularly polarized dipole), (b) σ− transitions (LH circularly polarized dipole), and (c) π transitions (linearly polarized dipole along x), in the x − y plane for the source located at xd = a + 10nm and yd = zd = 0, and with the dipole moments given by Eq. (7). The negative value of Pϕ in (a) and postive value of Pϕ in (b) indicate that, for the RH and LH circularly polarized dipoles as the source, the WGMs of the spherical resonator orbit clockwise (along −ϕ̂) and counter-clockwise (along +ϕ̂), respectively. For the linearly polarized dipole in (c), however, the WGMs inside the sphere are a mixture of clockwise and counter-clockwise fields which eventually cancel out each other to give a net-zero OAM. Therefore, coupling the WGMs to an optical fiber, for instance, on the other side from the source, would result in an equal wave propagation in both directions inside the fiber. However, for a circularly polarized source, the modes would only propagate along one direction inside the fiber, depending on the handedness of source. This figure clearly shows the unidirectional behaviour of spin interaction of the source and WGMs, as a result of the spin-momentum locking.

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Tables (1)

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Table 1 Summary of the properties of the WGMs

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Equations (13)

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s = p × γ
S lm , θ TM = S lm , θ TE = − m μ 0 2 ω l ( l + 1 ) | k 1 | 2 a 2 g ( θ ) [ ℛ { k 1 a j l * ( k 1 a ) j l + 1 ( k 1 a ) } − ( l + 1 ) | j l ( k 1 a ) | 2 ] ,
G ¯ e ( r , r ′ ) = G ¯ 0 e ( r , r ′ ) + G ¯ es ( r , r ′ ) ,
G ¯ 0 e ( r , r ′ ) = r ^ r ^ k 0 2 δ ( r − r ′ ) + i k 0 4 π ∑ l = 0 ∞ ∑ m = 0 l C l m { M l m ( 1 ) ( k 0 ) M l m ′ ( k 0 ) + N l m ( 1 ) ( k 0 ) N l m ′ ( k 0 ) r ≥ r ′ M lm ( k 0 ) M l m ′ ( 1 ) ( k 0 ) + N lm ( k 0 ) N l m ′ ( 1 ) ( k 0 ) r ≤ r ′ ,
G ¯ es ( 11 ) ( r , r ′ ) = i k 0 4 π ∑ l = 0 ∞ ∑ m = 0 l C l m [ ℬ M M l m ( 1 ) ( k 0 ) M l m ′ ( 1 ) ( k 0 ) + ℬ N N l m ( 1 ) ( k 0 ) N l m ′ ( 1 ) ( k 0 ) ] ,
G ¯ es ( 21 ) ( r , r ′ ) = i k 0 4 π ∑ l = 0 ∞ ∑ m = 0 l C l m [ 𝒟 M M lm ( k 1 ) M l m ′ ( 1 ) ( k 0 ) + 𝒟 N N lm ( k 1 ) N l m ′ ( 1 ) ( k 0 ) ] .
d + = d 0 e ^ ± = d 0 2 ( r ^ ± i ϕ ^ ) ,         d π = d 0 x ^
𝒲 lm TM = 1 2 ℛ { E lm TM ⋅ d ± * } .
E lm TM = E lm , + e ^ + + E lm , − e ^ − + E lm , θ θ ^
E lm , ± = − 1 2 μ 0 ∊ 0 [ l + 1 k 0 r d f l ( k 0 r d ) ( l ± m ) ∓ f l + 1 ( k 0 r d ) ] Y lm ( θ d , ϕ d )
E lm , θ = − μ 0 ∊ 0 [ l + 1 k 0 r d f l ( k 0 r d ) − f l + 1 ( k 0 r d ) ] ∂ Y lm ( θ d , ϕ d ) ∂ θ
E lm , + E lm , − = l ( l + 1 ) f l ( k 0 r d ) − m [ k 0 r d f l + 1 ( k 0 r d ) − ( l + 1 ) f l ( k 0 r d ) ] l ( l + 1 ) f l ( k 0 r d ) + m [ k 0 r d f l + 1 ( k 0 r d ) − ( l + 1 ) f l ( k 0 r d ) ] .
E lm , + E lm , − ≤ 1 ,                 m ≥ 0 E lm , + E lm , − > 1 ,                 m < 0 .

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