Abstract

We demonstrate a method to generate complex optical fields at the pupil plane of a high numerical aperture (NA) objective lens for the creation of diffraction limited optical focus with purely transverse spin angular momentum. The complex optical fields are analytically deduced through reversing the radiated patterns from two electric dipoles, which are located at the focal point of the high NA lens and oscillate respectively in x- and z- directions with phase difference of π/2. The derived fields can be experimentally created with a vectorial optical field generator. Using the Richard-Wolf vectorial diffraction theory, the electric fields within the focal region are calculated to evaluate the intensities and polarization distributions of the tightly focused beams corresponding to both the theoretical and experimentally generated pupil fields and the results clearly demonstrate the validity of the proposed technique.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  5. M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14(5), 2546–2551 (2014).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2016 (1)

2015 (8)

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]

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]

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (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]

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

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

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

2014 (5)

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]

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

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (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]

2013 (5)

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]

R. Martínez-Herrero, I. Juvells, and A. Carnicer, “On the physical realizability of highly focused electromagnetic field distributions,” Opt. Lett. 38(12), 2065–2067 (2013).
[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. Public. 8, 13032 (2013).
[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]

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[Crossref] [PubMed]

2012 (2)

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

2010 (3)

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]

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]

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]

2007 (1)

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

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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 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]

Banzer, P.

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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 8, 13032 (2013).
[Crossref]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

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

Bliokh, K. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

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

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

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[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]

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.

Chiu, D. T.

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

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]

Daley, A. J.

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (2015).
[Crossref]

Edgar, J. S.

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

Gu, B.

Han, W.

Helm, M.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Hubrich, R.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Jeffries, G. D.

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

Junge, C.

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[Crossref] [PubMed]

Juvells, I.

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.

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, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 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.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 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]

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. Public. 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.

F. Cardano and L. Marrucci, “Spin–orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[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(6130), 328–330 (2013).
[Crossref] [PubMed]

Martínez-Herrero, R.

McGloin, D.

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

Mittendorff, M.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[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]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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. Public. 8, 13032 (2013).
[Crossref]

Nori, F.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

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

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

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[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]

O’Shea, D.

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[Crossref] [PubMed]

Orlov, S.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[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]

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]

Pichler, H.

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (2015).
[Crossref]

Ramos, T.

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (2015).
[Crossref]

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]

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[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.

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]

Rui, G.

Schneider, H.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

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]

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[Crossref] [PubMed]

Wang, J.

Wang, X.

Winnerl, S.

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Wolf, E.

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]

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]

Yang, Y.

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.

Zhao, Y.

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

Zoller, P.

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (2015).
[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. (1)

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

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. Commun. (1)

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

Nat. Photonics (3)

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]

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

New J. Phys. (1)

S. Winnerl, R. Hubrich, M. Mittendorff, H. Schneider, and M. Helm, “Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams,” New J. Phys. 14(10), 103049 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rep. (1)

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

Phys. Rev. A (3)

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin Hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, “Quantum optics of chiral spin networks,” Phys. Rev. A 91(4), 042116 (2015).
[Crossref]

Phys. Rev. Lett. (5)

C. Junge, D. O’Shea, J. Volz, and A. Rauschenbeutel, “Strong coupling between single atoms and nontransversal photons,” Phys. Rev. Lett. 110(21), 213604 (2013).
[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]

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]

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]

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

Phys. Rev. X (1)

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

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]

Science (2)

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]

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]

Other (2)

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.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the method of pupil plane field calculation to achieve specific focal field characteristics through reversing the radiation pattern from two electric dipoles.

Fig. 2
Fig. 2

(a) Ideal pupil field for generating the purely transverse spinning focused spot. (b) Projection of the intensity and state of polarization distributions on three orthogonal planes in the focal region. (c) Normalized intensity distributions of the focused beam along x-, y- and z-axis. (d)-(f) Histograms of ellipticity of the state of polarization on the three orthogonal planes in (b).

Fig. 3
Fig. 3

Schematic diagram of the experimental setup. HWP, half wave plate; P, polarizer; L, lens; M, mirror; SF, spatial filter; BS, beam splitter.

Fig. 4
Fig. 4

Experimental results of generating the required pupil field. (a) Intensity distribution with polarization map. Comparison of intensity distribution between the experimental and theoretical pupil field along x-axis (b) and y-axis (c).

Fig. 5
Fig. 5

Focused beam corresponding to the experimentally generated pupil field. (a) Projection of the intensity and state of polarization distributions on three orthogonal planes in the focal region. (b) Normalized intensity distributions of the focused beam along x-, y- and z-axis. (c)-(e) Histograms of ellipticity of the state of polarization on the three orthogonal planes.

Equations (10)

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E 1 ( θ,φ )=jω μ I 0 l e jkf 4πf [ cosθcosφ e θ +sinφ e φ ].
E 2 ( θ,φ )=jω μ I 0 l e jkf 4πf e jπ/2 sinθ e θ .
E t ( θ,φ )= E 1 ( θ,φ )+ E 2 ( θ,φ ) =jω μ I 0 l e jkf 4πf [ ( cosθcosφ+ e jπ/2 sinθ ) e θ +sinφ e φ ].
E i ( r,φ )=[ ( cosθcosφ+ e jπ/2 sinθ ) e r +sinφ e φ ]/ cos( θ ) .
e r =cosφ e x +sinφ e y .
e φ =sinφ e x +cosφ e y .
E i ( r,φ )=[(sinθcosφ e jπ/2 cosθ cos 2 φ sin 2 φ) e x +(sinθsinφ e jπ/2 cosθcosφsinφ+sinφcosφ) e y ]/ cos(θ) .
E o ( θ,φ )={ [ e jπ/2 sinθcosθcosφ cos 2 θ cos 2 φ sin 2 φ ] e x [ e jπ/2 sinθcosθsinφ cos 2 θcosφsinφ+sinφcosφ ] e y [ e jπ/2 sin 2 θcosθsinθcosφ ] e z .
E ( r p ,ϕ, z p )= i λ 0 θ max 0 2π E o ( θ,φ )× e jk r p sinθcos( φϕ )+jk z p cosθ sinθdθdφ = i λ 0 θ max 0 2π [ ( e jπ/2 sinθcosθcosφ cos 2 θ cos 2 φ sin 2 φ ) e x ( e jπ/2 sinθcosθsinφco s 2 θcosφsinφ+sinφcosφ ) e y ( e jπ/2 sin 2 θcosθsinθcosφ ) e z ] × e jk r p sinθcos( φϕ )+jk z p cosθ sinθdθdφ.
{ S 0 =I( 0 , 0 )+I( 90 , 90 ) S 1 =I( 0 , 0 )I( 90 , 90 ) S 2 =I( 45 , 45 )I( 135 , 135 ) S 3 =I( 45 , 0 )I( 135 , 0 ) .