Abstract

Polarization oscillating beams, namely, polarization standing waves, commonly formed by a pair of coherent counterpropagating light waves with orthogonal polarizations, oscillate their states of polarization periodically within a wavelength interval, offering conceptual and practical interests in light-matter interactions such as the nonreciprocal magnetoelectric effect, and impressive applications in optical imaging, sensing, and chirality detection. Here, we propose a new class of polarization oscillating beams that longitudinally vary states of polarization with spatial intervals within centimeters via the superposition of two copropagating optical frozen waves with preshaped longitudinal intensity profiles and transverse phase structures. The flexibility and manipulability are demonstrated by creating several polarization oscillating beams with different polarization structures. This work paves a new way to manipulate other waves and may be useful for applications of optical standing waves in optical manipulation, light guiding of atoms, polarization-sensitive sensing, etc.

© 2018 Chinese Laser Press

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References

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2017 (7)

E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
[Crossref]

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[Crossref]

P. Li, Y. Zhang, S. Liu, H. Cheng, L. Han, D. Wu, and J. Zhao, “Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation,” Opt. Express 25, 5821–5831 (2017).
[Crossref]

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5, 15–21 (2017).
[Crossref]

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

W. Shu, X. Ling, X. Fu, Y. Liu, Y. Ke, and H. Luo, “Polarization evolution of vector beams generated by q-plates,” Photon. Res. 5, 64–72 (2017).
[Crossref]

T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
[Crossref]

2016 (11)

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[Crossref]

A. Aleksanyan and E. Brasselet, “Spin-orbit photonic interaction engineering of Bessel beams,” Optica 3, 167–174 (2016).
[Crossref]

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
[Crossref]

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

L. Zhang, S. Mei, K. Huang, and C. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41, 2205–2208 (2016).
[Crossref]

P. Li, Y. Zhang, S. Liu, L. Han, H. Cheng, and J. Zhao, “Quasi-Bessel beams with longitudinally varying polarization state generated by employing spectrum engineering,” Opt. Lett. 41, 4811–4814 (2016).
[Crossref]

J. A. Davis, I. Moreno, K. Badham, M. M. Sánchez-López, and D. M. Cottrell, “Nondiffracting vector beams where the charge and the polarization state vary with propagation distance,” Opt. Lett. 41, 2270–2273 (2016).
[Crossref]

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
[Crossref]

X. Fang, K. F. MacDonald, E. Plum, and N. I. Zheludev, “Coherent control of light-matter interactions in polarization standing waves,” Sci. Rep. 6, 31141 (2016).
[Crossref]

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

2015 (3)

2014 (2)

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113, 033601 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

2013 (2)

2012 (1)

2011 (3)

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

2010 (2)

X. Wang, Y. Li, J. Chen, C. Guo, J. Ding, and H. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
[Crossref]

X. Wang, J. Chen, Y. Li, J. Ding, C. Guo, and H. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

2009 (2)

T. Čižmár and K. Dholakia, “Tunable Bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[Crossref]

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted field,” Nano Today 4, 269–279 (2009).
[Crossref]

2007 (1)

2006 (3)

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[Crossref]

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

G. Biener, Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Manipulation of polarization-dependent multivortices with quasi-periodic subwavelength structures,” Opt. Lett. 31, 1594–1596 (2006).
[Crossref]

2004 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

1972 (1)

L. D. Barron, “Parity and optical activity,” Nature 238, 17–19 (1972).
[Crossref]

Aleksanyan, A.

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

Badham, K.

Barron, L. D.

L. D. Barron, “Parity and optical activity,” Nature 238, 17–19 (1972).
[Crossref]

Belov, P. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

Biener, G.

Bliokh, K. Y.

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

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113, 033601 (2014).
[Crossref]

Brasselet, E.

Brussaard, G. J. H.

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Buchler, B. C.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Campbell, G. T.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Cardano, F.

Chen, J.

X. Wang, Y. Li, J. Chen, C. Guo, J. Ding, and H. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
[Crossref]

X. Wang, J. Chen, Y. Li, J. Ding, C. Guo, and H. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

Chen, P.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Cheng, H.

Cho, Y.-W.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Cižmár, T.

Cohen, A. E.

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted field,” Nano Today 4, 269–279 (2009).
[Crossref]

Cottrell, D. M.

Cui, G.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Davis, J. A.

de Lisio, C.

Dholakia, K.

Ding, J.

Duan, W.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Everett, J. L.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Faccio, D.

E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
[Crossref]

Fang, X.

E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
[Crossref]

X. Fang, K. F. MacDonald, E. Plum, and N. I. Zheludev, “Coherent control of light-matter interactions in polarization standing waves,” Sci. Rep. 6, 31141 (2016).
[Crossref]

Fu, S.

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
[Crossref]

Fu, X.

Gan, X.

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[Crossref]

Gao, C.

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
[Crossref]

Ge, S.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Gesualdi, M. R. R.

Glybovski, S. B.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

Gorodetski, Y.

Guo, C.

Han, L.

Hasman, E.

Higginbottom, D. B.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Hu, W.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Huang, K.

L. Zhang, S. Mei, K. Huang, and C. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Kamp, L. P. J.

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Kang, L.

L. Kang, Q. Ren, and D. H. Werner, “Leveraging superchiral light for manipulation of optical chirality in the near-field of plasmonic metamaterials,” ACS Photon. 4, 1298–1305 (2017).
[Crossref]

Kanters, J. H. M.

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Karimi, E.

Ke, Y.

Kivshar, Y. S.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113, 033601 (2014).
[Crossref]

Kleiner, V.

Lam, P. K.

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
[Crossref]

Lassise, A.

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Li, P.

Li, Y.

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Lim, C. T.

T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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Ling, X.

Liu, S.

Liu, Y.

T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5, 15–21 (2017).
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Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
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Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
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Liu, Z.

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P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
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P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
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E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
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T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
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L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
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J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
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K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113, 033601 (2014).
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L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in imhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
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E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
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T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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L. Zhang, S. Mei, K. Huang, and C. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
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L. Kang, Q. Ren, and D. H. Werner, “Leveraging superchiral light for manipulation of optical chirality in the near-field of plasmonic metamaterials,” ACS Photon. 4, 1298–1305 (2017).
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J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
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P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

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G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

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Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
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N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted field,” Nano Today 4, 269–279 (2009).
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T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
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J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
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Vieira, T. A.

Wang, H.

Wang, M.

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
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S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
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Wang, Z.

T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
[Crossref]

Wei, B.

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

Wen, S.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photon. Res. 5, 15–21 (2017).
[Crossref]

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
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L. Kang, Q. Ren, and D. H. Werner, “Leveraging superchiral light for manipulation of optical chirality in the near-field of plasmonic metamaterials,” ACS Photon. 4, 1298–1305 (2017).
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Yang, N.

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted field,” Nano Today 4, 269–279 (2009).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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Zamnoni-Rached, M.

Zhang, L.

L. Zhang, S. Mei, K. Huang, and C. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
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Zhang, P.

Zhang, S.

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
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T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
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Zhao, J.

Zheludev, N. I.

E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
[Crossref]

X. Fang, K. F. MacDonald, E. Plum, and N. I. Zheludev, “Coherent control of light-matter interactions in polarization standing waves,” Sci. Rep. 6, 31141 (2016).
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Zhou, J.

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
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ACS Nano (1)

T. Zhang, M. R. C. Mahdy, Y. Liu, J. H. Teng, C. T. Lim, Z. Wang, and C. Qiu, “All-optical chirality-sensitive sorting via reversible lateral forces in interference fields,” ACS Nano 11, 4292–4300 (2017).
[Crossref]

ACS Photon. (3)

L. Kang, Q. Ren, and D. H. Werner, “Leveraging superchiral light for manipulation of optical chirality in the near-field of plasmonic metamaterials,” ACS Photon. 4, 1298–1305 (2017).
[Crossref]

P. Chen, S. Ge, W. Duan, B. Wei, G. Cui, W. Hu, and Y. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
[Crossref]

E. Plum, K. F. Macdonald, X. Fang, D. Faccio, and N. I. Zheludev, “Controlling the optical response of 2D matter in standing waves,” ACS Photon. 4, 3000–3011 (2017).
[Crossref]

Adv. Opt. Mater. (1)

L. Zhang, S. Mei, K. Huang, and C. Qiu, “Advances in full control of electromagnetic waves with metasurfaces,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Appl. Phys. Lett. (2)

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[Crossref]

Nano Today (1)

N. Yang, Y. Tang, and A. E. Cohen, “Spectroscopy in sculpted field,” Nano Today 4, 269–279 (2009).
[Crossref]

Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

Nat. Phys. (1)

J. L. Everett, G. T. Campbell, Y.-W. Cho, P. Vernaz-Gris, D. B. Higginbottom, O. Pinel, N. P. Robins, P. K. Lam, and B. C. Buchler, “Dynamical observations of self-stabilizing stationary light,” Nat. Phys. 13, 68–73 (2016).
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Nature (1)

L. D. Barron, “Parity and optical activity,” Nature 238, 17–19 (1972).
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Opt. Express (5)

Opt. Lett. (9)

P. Li, Y. Zhang, S. Liu, L. Han, H. Cheng, and J. Zhao, “Quasi-Bessel beams with longitudinally varying polarization state generated by employing spectrum engineering,” Opt. Lett. 41, 4811–4814 (2016).
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X. Wang, J. Ding, W. Ni, C. Guo, and H. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007).
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P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41, 2205–2208 (2016).
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S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
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T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37, 2034–2036 (2012).
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T. A. Vieira, M. R. R. Gesualdi, M. Zamboni-Rached, and E. Recami, “Production of dynamic frozen waves: controlling shape, location (and speed) of diffraction-resistant beams,” Opt. Lett. 40, 5834–5837 (2015).
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Optica (1)

Photon. Res. (2)

Phys. Rep. (2)

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovshi, “Metasurface: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

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

Phys. Rev. A (1)

P. W. Smorenburg, J. H. M. Kanters, A. Lassise, G. J. H. Brussaard, L. P. J. Kamp, and O. J. Luiten, “Polarization-dependent ponderomotive gradient force in a standing wave,” Phys. Rev. A 83, 063810 (2011).
[Crossref]

Phys. Rev. Lett. (5)

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric effects in local light-matter interactions,” Phys. Rev. Lett. 113, 033601 (2014).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, Stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107, 053601 (2011).
[Crossref]

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

X. Wang, J. Chen, Y. Li, J. Ding, C. Guo, and H. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Sci. Rep. (3)

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[Crossref]

S. Fu, S. Zhang, and C. Gao, “Bessel beams with spatial oscillating polarization,” Sci. Rep. 6, 30765 (2016).
[Crossref]

X. Fang, K. F. MacDonald, E. Plum, and N. I. Zheludev, “Coherent control of light-matter interactions in polarization standing waves,” Sci. Rep. 6, 31141 (2016).
[Crossref]

Science (1)

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Illustration of constructing polarization oscillating beams. (a) Zeroth- and first-order frozen waves that have rectangular and sinusoidal intensity profiles, respectively. The dashed lines denote where the intensity lines come from. (b) Evolution of transverse SoP of a polarization oscillating beam constructed from two sinusoidal frozen waves with opposite spin states and initial phase difference φ0=π/2. The red and blue lines schematically depict the real parts of two electric fields. (c) Hybrid Poincaré sphere and the SoP conversion trajectory corresponding to the evolution in (b).
Fig. 2.
Fig. 2. Experiment setup for constructing polarization oscillating beams. SLM, spatial light modulator; BS, beam splitter; BT, beam terminal; L, lens; F, filter; QWP, quarter-wave plate; G, grating; CCD, charge-coupled device. Insets: (a) computer-generated hologram encoded on SLM; (b) intensity pattern of a first-order frozen wave at a certain location.
Fig. 3.
Fig. 3. Intensities of constituent zeroth-order frozen waves and transverse SoP distributions of the resultant field at different propagation distances, respectively. The red and cyan ellipses in the bottom diagrams denote the local polarization ellipticity calculated from the measured Stokes parameters [11].
Fig. 4.
Fig. 4. (a) Longitudinal intensity distributions of two first-order frozen waves (denoted as red dots and black squares) with sinusoidal profiles. Dots, experiment result; curves, analyzed results. (b) Lateral intensity patterns of the synthesized field in equally spaced planes.
Fig. 5.
Fig. 5. (a), (b) SoP distributions of the |D1,1 and |A1,1 states. (c)–(f) Experimentally measured SoP distributions at two adjacent nodes and antinodes. Left, polarization orientation (background) and polarization ellipticity distributions; right, S3 distributions. Black line and ellipse depict the linear and ellipse polarizations, respectively.
Fig. 6.
Fig. 6. (a) Intensity pattern of the second-order field at the z=0 plane. (b)–(e) Polarization orientation (upper) and intensity (bottom) distributions in four adjacent nodal planes. Arrows, the orientation of linear polarizer; dashed square, bound of selected areas corresponding to (b)–(e).
Fig. 7.
Fig. 7. (a) Intensity distribution of fifth-order field at the z=0 plane; (b)–(d) zoom-in vertical component distributions at three adjacent nodal planes.

Equations (2)

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F(ρ,ϕ,z,l)=eiωtj=NNAjJl(kρjρ)eikzjzeilϕ,
Aj=1L0LF(z,l)e2πjz/Ldz.

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