Abstract

The spin angular momentum of photons offers a robust, scalable and high-bandwidth toolbox for many promising applications based upon spin-controlled manipulations of light. In this work, we develop a method to achieve controllable photonic spin orientation within a diffraction limited optical focal spot produced by a high numerical aperture objective lens. The required pupil field is found analytically through reversing the radiation patterns from two electric dipoles located at the focal point of the lens with orthogonal oscillation directions and quadrature phase. The calculated pupil fields are experimentally generated with a vectorial optical field generator. The produced photonic spin orientations are quantitatively evaluated by their spin densities according to the tightly focused electric fields calculated by Richard-Wolf vectorial diffraction theory to demonstrate the validity and capability of the proposed technique.

© 2017 Optical Society of America

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References

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2017 (4)

J. Chen, C. Wan, L. Kong, and Q. Zhan, “Experimental generation of complex optical fields for diffraction limited optical focus with purely transverse spin angular momentum,” Opt. Express 25(8), 8966–8974 (2017).
[Crossref] [PubMed]

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[Crossref] [PubMed]

Y. Y. Tanaka and T. Shimura, “Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle,” Nano Lett. 17(5), 3165–3170 (2017).
[Crossref] [PubMed]

J. Chen, C. Wan, L. Kong, and Q. Zhan, “Precise transverse alignment of spatial light modulator sections for complex optical field generation,” Appl. Opt. 56(10), 2614–2620 (2017).
[Crossref] [PubMed]

2016 (3)

G. Rui, J. Chen, X. Wang, B. Gu, Y. Cui, and Q. Zhan, “Synthesis of focused beam with controllable arbitrary homogeneous polarization using engineered vectorial optical fields,” Opt. Express 24(21), 23667–23676 (2016).
[Crossref] [PubMed]

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

2015 (8)

F. Cardano and L. Marrucci, “Spin–orbit photonics,” Nat. Photonics 9(12), 776–778 (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]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

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

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

W. Han, W. Cheng, and Q. Zhan, “Design and alignment strategies of 4f systems used in the vectorial optical field generator,” Appl. Opt. 54(9), 2275–2278 (2015).
[Crossref] [PubMed]

2014 (4)

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2014).
[Crossref]

D. Maluenda, R. Martínez-Herrero, I. Juvells, and A. Carnicer, “Synthesis of highly focused fields with circular polarization at any transverse plane,” Opt. Express 22(6), 6859–6867 (2014).
[Crossref] [PubMed]

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

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref] [PubMed]

2013 (7)

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(6130), 328–330 (2013).
[Crossref] [PubMed]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

J. P. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88(12), 121410 (2013).
[Crossref]

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
[Crossref] [PubMed]

D. Maluenda, I. Juvells, R. Martínez-Herrero, and A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21(5), 5432–5439 (2013).
[Crossref] [PubMed]

2010 (3)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express 18(21), 21965–21972 (2010).
[Crossref] [PubMed]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

2006 (1)

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

Alpmann, C.

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

Banzer, P.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

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

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

Bauer, T.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

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

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

Bliokh, K. Y.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[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]

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

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

Bogdanov, A. A.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Bu, J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Burge, R. E.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Capasso, F.

J. P. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88(12), 121410 (2013).
[Crossref]

Cardano, F.

F. Cardano and L. Marrucci, “Spin–orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

Carnicer, A.

Chen, J.

Chen, W.

Cheng, W.

Cui, Y.

Dainty, C.

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

Denz, C.

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

Espinosa-Soria, A.

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[Crossref] [PubMed]

Gao, L.

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

Ginzburg, P.

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(6130), 328–330 (2013).
[Crossref] [PubMed]

Griol, A.

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[Crossref] [PubMed]

Gu, B.

Han, W.

Hasman, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Iorsh, I. V.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Juvells, I.

Karimi, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Kivshar, Y. S.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Kleiner, V.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Kong, L.

Lara, D.

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

Leuchs, G.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

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

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

Lindlein, N.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

Low, D. K. Y.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Maguid, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Maluenda, D.

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(6130), 328–330 (2013).
[Crossref] [PubMed]

Marquardt, C.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

Marrucci, L.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

F. Cardano and L. Marrucci, “Spin–orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2014).
[Crossref]

Martínez, A.

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[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(6130), 328–330 (2013).
[Crossref] [PubMed]

Martínez-Herrero, R.

Moh, K. J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Mueller, J. P. B.

J. P. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88(12), 121410 (2013).
[Crossref]

Neugebauer, M.

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

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

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

Nori, F.

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]

O’Connor, D.

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(6130), 328–330 (2013).
[Crossref] [PubMed]

Orlov, S.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Ostrovskaya, E. A.

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

Otte, E.

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

Ovcharenko, A. I.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Ozeri, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Pan, D.

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

Peschel, U.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref] [PubMed]

Rauschenbeutel, A.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Rodríguez-Fortuño, F. J.

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[Crossref] [PubMed]

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]

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(6130), 328–330 (2013).
[Crossref] [PubMed]

Rodríguez-Herrera, O. G.

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

Rubano, A.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Rui, G.

Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Schlickriede, C.

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

Shimura, T.

Y. Y. Tanaka and T. Shimura, “Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle,” Nano Lett. 17(5), 3165–3170 (2017).
[Crossref] [PubMed]

Shitrit, N.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Tanaka, Y. Y.

Y. Y. Tanaka and T. Shimura, “Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle,” Nano Lett. 17(5), 3165–3170 (2017).
[Crossref] [PubMed]

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

Volz, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref] [PubMed]

Wan, C.

Wang, J.

Wang, X.

Wei, H.

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

Wurtz, G. 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(6130), 328–330 (2013).
[Crossref] [PubMed]

Xu, H.

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

Yang, Y.

Yermakov, O. Y.

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Yuan, X. C.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

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]

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(6130), 328–330 (2013).
[Crossref] [PubMed]

Zhan, Q.

J. Chen, C. Wan, L. Kong, and Q. Zhan, “Precise transverse alignment of spatial light modulator sections for complex optical field generation,” Appl. Opt. 56(10), 2614–2620 (2017).
[Crossref] [PubMed]

J. Chen, C. Wan, L. Kong, and Q. Zhan, “Experimental generation of complex optical fields for diffraction limited optical focus with purely transverse spin angular momentum,” Opt. Express 25(8), 8966–8974 (2017).
[Crossref] [PubMed]

G. Rui, J. Chen, X. Wang, B. Gu, Y. Cui, and Q. Zhan, “Synthesis of focused beam with controllable arbitrary homogeneous polarization using engineered vectorial optical fields,” Opt. Express 24(21), 23667–23676 (2016).
[Crossref] [PubMed]

W. Han, W. Cheng, and Q. Zhan, “Design and alignment strategies of 4f systems used in the vectorial optical field generator,” Appl. Opt. 54(9), 2275–2278 (2015).
[Crossref] [PubMed]

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
[Crossref] [PubMed]

J. Wang, W. Chen, and Q. Zhan, “Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation,” Opt. Express 18(21), 21965–21972 (2010).
[Crossref] [PubMed]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89(25), 251114 (2006).
[Crossref]

J. Europ. Opt. Soc. Rap. Pub. (1)

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, “The photonic wheel - demonstration of a state of light with purely transverse angular momentum,” J. Europ. Opt. Soc. Rap. Pub. 8, 13032 (2013).
[Crossref]

J. Opt. (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Nano Lett. (3)

A. Espinosa-Soria, F. J. Rodríguez-Fortuño, A. Griol, and A. Martínez, “On-Chip optimal stokes nanopolarimetry based on spin–orbit interaction of light,” Nano Lett. 17(5), 3139–3144 (2017).
[Crossref] [PubMed]

Y. Y. Tanaka and T. Shimura, “Tridirectional polarization routing of light by a single triangular plasmonic nanoparticle,” Nano Lett. 17(5), 3165–3170 (2017).
[Crossref] [PubMed]

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

Nat. Photonics (4)

F. Cardano and L. Marrucci, “Spin–orbit photonics,” Nat. Photonics 9(12), 776–778 (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]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2013).
[Crossref]

Nat. Phys. (1)

L. Marrucci, “Quantum optics: spin gives direction,” Nat. Phys. 11(1), 9–10 (2014).
[Crossref]

Opt. Express (6)

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. B (2)

J. P. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88(12), 121410 (2013).
[Crossref]

O. Y. Yermakov, A. I. Ovcharenko, A. A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, “Spin control of light with hyperbolic metasurfaces,” Phys. Rev. B 94(7), 075446 (2016).
[Crossref]

Phys. Rev. Lett. (4)

D. Pan, H. Wei, L. Gao, and H. Xu, “Strong spin-orbit interaction of light in plasmonic nanostructures and nanocircuits,” Phys. Rev. Lett. 117(16), 166803 (2016).
[Crossref] [PubMed]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref] [PubMed]

M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, “Measuring the transverse spin density of light,” Phys. Rev. Lett. 114(6), 063901 (2015).
[Crossref] [PubMed]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

B. Richards and E. Wolf, “Electromagnetic diffraction in optical system II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Proc. SPIE (1)

E. Otte, C. Schlickriede, C. Alpmann, and C. Denz, “Complex light fields enter a new dimension: holographic modulation of polarization in addition to amplitude and phase,” Proc. SPIE 9379, 937908 (2015).
[Crossref]

Science (4)

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref] [PubMed]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[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(6130), 328–330 (2013).
[Crossref] [PubMed]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Other (3)

A. Balanis, Antenna Theory: Analysis and Design (Wiley-Interscience, 2005).

M. Born and E. Wolf, Principles of optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).

M. Gu, Advanced Optical Imaging Theory (Springer, 1999), Chap. 6.

Supplementary Material (2)

NameDescription
» Visualization 1       the theoretical incident pupil fields and corresponding focused beams for the spin axis rotation in Fig. 4.
» Visualization 2       the theoretical incident pupil fields and corresponding focused beams for the spin axis rotation in Fig. 8.

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Figures (8)

Fig. 1
Fig. 1 Calculation of the pupil field to obtain focused beam with specific spin axis orientation through coherently superposition of the radiation pattern from two electric dipoles.
Fig. 2
Fig. 2 (a) Ideal incident pupil field with polarization map corresponding to θ 1 = π / 6 . (b) Projection of the intensity and state of polarization distributions of the focused beam onto three orthogonal planes in the focal region. (c) Normalized intensity distributions of the focused beam along x-, y- and z-axis.
Fig. 3
Fig. 3 Spin density and direction angles of the focused beam in the xz plane of Fig. 2(b). (a)-(c) x-, y- and z-component of the spin density. (d)-(f) The direction angles formed between the spin axis of the focused field and the positive direction of the x-, y- and z-axis.
Fig. 4
Fig. 4 (a) Evolution of the direction angles of the spin axis for focused beams corresponding to ideal pupil fields. (b) 3D demonstration of the two dimensional rotation of the spin axis. (c) Evolution of the spot size of the focused beam. (For the incident pupil fields and corresponding focused beams, see Visualization 1).
Fig. 5
Fig. 5 Schematic diagram of the experimental setup. HWP, half wave plate; P, polarizer; L, lens; M, mirror; SF, spatial filter; BS, beam splitter.
Fig. 6
Fig. 6 (a) Experimentally generated incident pupil field with polarization map corresponding to θ 1 = π / 6 . (b) Projection of the intensity and state of polarization distributions of the focused beam onto three orthogonal planes in the focal region. (c) Normalized intensity distributions of the focused beam along x-, y- and z-axis.
Fig. 7
Fig. 7 Spin density and direction angles of the focused beam in the xz plane of Fig. 6(b). (a)-(c) x-, y- and z-component of the spin density. (d)-(f) The direction angles formed between the spin axis of the focused field and the positive direction of the x-, y- and z-axis.
Fig. 8
Fig. 8 (a) Evolution of the direction angles of the spin axis for focused beams corresponding to experimentally generated pupil fields. (b) 3D demonstration of the two dimensional rotation of the spin axis. (c) Evolution of the spot size of the focused beam. (For the incident pupil fields and corresponding focused beams, see Visualization 2).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

{ α = π / 2 β = θ 1 γ = π / 2 θ 1 ,
E 1 ( θ , φ ) = C e j π / 2 [ ( cos θ 1 sin θ sin θ 1 cos θ sin φ ) e θ sin θ 1 cos φ e φ ] ,
E 2 ( θ , φ ) = C [ cos θ cos φ e θ + sin φ e φ ] .
E A ( θ , φ ) = E 1 ( θ , φ ) + E 2 ( θ , φ ) = C { [ cos θ cos φ + e j π / 2 ( cos θ 1 sin θ sin θ 1 cos θ sin φ ) ] e θ + ( sin φ e j π / 2 sin θ 1 cos φ ) e φ } .
E i ( r , φ ) = C { [ cos θ cos φ + e j π / 2 ( cos θ 1 sin θ sin θ 1 cos θ sin φ ) ] e r + ( sin φ e j π / 2 sin θ 1 cos φ ) e φ } / cos θ ,
E i ( r , φ ) = C cos θ [ A e x + B e y ] , A = e j π / 2 ( cos θ 1 sin θ cos φ + sin θ 1 cos φ sin φ sin θ 1 cos θ sin φ cos φ ) cos θ cos 2 φ sin 2 φ , B = e j π / 2 ( cos θ 1 sin θ sin φ sin θ 1 cos 2 φ sin θ 1 cos θ sin 2 φ ) cos θ cos φ sin φ + sin φ cos φ ,
E o ( θ , φ ) = C [ X e x + Y e y + Z e z ] , X = e j π / 2 ( cos θ 1 sin θ cos θ cos φ sin θ 1 cos 2 θ sin φ cos φ + sin θ 1 cos φ sin φ ) cos 2 θ cos 2 φ sin 2 φ , Y = e j π / 2 ( cos θ 1 sin θ cos θ sin φ sin θ 1 cos 2 θ sin 2 φ sin θ 1 cos 2 φ ) + sin 2 θ c o s φ sin φ , Z = e j π / 2 ( cos θ 1 sin 2 θ sin θ 1 cos θ sin φ sin θ ) cos θ sin θ cos φ ,
E ( r p , ϕ , z p ) = i λ 0 θ max 0 2 π E o ( θ , φ ) × e j k r p sin θ cos ( φ ϕ ) + j k z p cos θ sin θ d θ d φ = i C λ 0 θ max 0 2 π [ X e x + Y e y + Z e z ] × e j k r p sin θ cos ( φ ϕ ) + j k z p cos θ sin θ d θ d φ ,
S Im ( E × E ) .
{ α = cos 1 ( S x / S x 2 + S y 2 + S z 2 ) β = cos 1 ( S y / S x 2 + S y 2 + S z 2 ) γ = cos 1 ( S z / S x 2 + S y 2 + S z 2 ) .

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