Abstract

We demonstrate that the spatially diffractive properties of cylindrical vector beams could be controlled via linear interactions with anisotropic crystals. It is the first time to show experimentally that the diffraction of the vector beams can be either suppressed or enhanced significantly during propagation, depending on the sign of anisotropy. Importantly, it is also possible to create a linear non-spreading and shape-preserving vector beam, by vanishing its diffraction during propagation via strong anisotropy in a crystal. The manageable diffractive effect enables manipulating propagation dynamics of the circular Airy vector beams, i.e., their propagation trajectories can be dynamically controlled by weakening or enhancing self-acceleration of the Airy beam. We further demonstrate that the cylindrical vector beams with initially zero orbital angular momentum can be rotated either clockwise or anticlockwise, relying on the sign of the anisotropy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2017 (8)

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

Y. Zhou, J. Lin, X. Zhang, L. Xu, C. Gu, B. Sun, A. Wang, and Q. Zhan, “Self-starting passively mode-locked all fiber laser beased on carbon nanotubes with radially polarized emission,” Photon. Res. 4, 327 (2017).

M Lian, B. Gu, Y. Zhang, G. Rui, J. He, Q. Zhan, and Y. Cui, “Polarization rotation of hybridly polarized beams in a uniaxial crystal orthogonal to the optical axis: theory and experiment,” J. Opt. Soc. Am. A 34, 1 (2017).

C. Hernández-García, A. Turpin, J. S. Román, A. Picón, R. Drevinskas, A. Cerkauskaite, P. G. Kazansky, C. G. Durfee, and Í. J. Sola, “Extreme ultraviolet vector beams driven by infrared lasers,” Optica 4, 520 (2017).

C. Chang, Y. Gao, J. Xia, S. Nie, and J. Ding, “Shaping of optical vector beams in three dimensions,” Opt. Lett. 42, 3884 (2017).

2016 (5)

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Y. Zhou, A. Wang, C. Gu, B. Sun, L. Xu, F. Li, D. Chung, and Q. Zhan, “Actively mode-locked all fiber laser with cylindrical vector beam output,” Opt. Lett. 41, 548 (2016).

K. Yan, J. Lin, Y. Zhou, C. Gu, L. Xu, A. Wang, P. Yao, and Q. Zhan, “Bi2Te3 based passively Q-switched fiber laser with cylindrical vector beam emission,” Appl. Opt. 55, 3026 (2016).

V. Salakhutdinov, M. Sondermann, L. Carbone, E. Giacobino, A. Bramati, and G. Leuchs, “Optical trapping of nanoparticles by full solid-angle focusing,” Optica 3, 1181 (2016).

2015 (1)

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

2014 (4)

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2044012 (2014).

2013 (3)

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416 (2013).

2012 (2)

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q–plates with different topological charges,” Appl. Opt. 51, C1 (2012).

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

2011 (4)

2010 (1)

2009 (1)

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

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

2007 (2)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

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 (2007).

2005 (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

2003 (2)

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun. 220, 33 (2003).

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).

2002 (1)

A. Ciattoni, G. Cincotti, D. Provenziani, and C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002).

1999 (1)

1994 (1)

Ambrosio, A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

Antoniou, N.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Arie, A.

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

Bouchard, F.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Boyd, R. W.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Bramati, A.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Cai, Y.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

Camacho-Morales, R.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Campos, J.

Capasso, F.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

Carbone, L.

Cardano, F.

Carletti, L.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Cerkauskaite, A.

Chang, C.

Chen, Y.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Chen, Z.

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675 (2011).

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

Chremmos, I.

Christodoulides, D. N.

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675 (2011).

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842 (2011).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Chung, D.

Ciattoni, A.

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun. 220, 33 (2003).

A. Ciattoni, G. Cincotti, D. Provenziani, and C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002).

Cincotti, G.

G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun. 220, 33 (2003).

A. Ciattoni, G. Cincotti, D. Provenziani, and C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002).

Cottrell, D. M.

Cui, Y.

D’Ambrosio, V.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Davis, J. A.

De Angelis, C.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

De Leon, I.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

de Lisio, C.

Devlin, R. C.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

Ding, J.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Dong, Y.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).

Drevinskas, R.

Durfee, C. G.

Efremidis, N. K.

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675 (2011).

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842 (2011).

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Fu, S.

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

Gao, Y.

Genevet, P.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

Giacobino, E.

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

Grbic, A.

C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2044012 (2014).

Groever, B.

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

Gu, B.

Gu, C.

Guo, C.

Hall, D. G.

He, J.

Hernández-García, C.

Hu, Y.

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Jagadish, C.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Jia, X.

Jordan, R. H.

Karimi, E.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q–plates with different topological charges,” Appl. Opt. 51, C1 (2012).

Karouta, F.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Kats, M. A.

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

Kazansky, P. G.

Kivshar, Y. S.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Kozawa, Y.

Kruk, S.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Larocque, H.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

Leuchs, G.

V. Salakhutdinov, M. Sondermann, L. Carbone, E. Giacobino, A. Bramati, and G. Leuchs, “Optical trapping of nanoparticles by full solid-angle focusing,” Optica 3, 1181 (2016).

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).

Li, F.

Li, J.

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).

Li, P.

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).

Li, Y.

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

Lian, M

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

Lin, J.

Liu, S.

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416 (2013).

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

Malomed, B. A.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

Marrucci, L.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q–plates with different topological charges,” Appl. Opt. 51, C1 (2012).

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

Miroshnichenko, A.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Moreno, I.

Mueller, J. P. B.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

Nagali, E.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Naureen, S.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Neshev, D. N.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Ni, W.

Nie, S.

Oppo, G.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

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A. Ciattoni, G. Cincotti, D. Provenziani, and C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002).

Papazoglou, D. G.

Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Controlling vector Bessel beams with metasurfaces,” Phys. Rev. Appl. 2044012 (2014).

Picón, A.

Prakash, J.

Provenziani, D.

A. Ciattoni, G. Cincotti, D. Provenziani, and C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002).

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).

Rahmani, M.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Román, J. S.

Rubano, A.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Rubin, N. A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin to orbital angular momentum conversion of light,” Science 358, 896 (2017).

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).

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Salakhutdinov, V.

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G. Cincotti, A. Ciattoni, and C. Sapia, “Radially and azimuthally polarized vortices in uniaxial crystals,” Opt. Commun. 220, 33 (2003).

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Sciarrino, F.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Shemer, L.

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Slussarenko, S.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q–plates with different topological charges,” Appl. Opt. 51, C1 (2012).

Smirnova, D. A.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Sola, Í. J.

Solntsev, A. S.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Sondermann, M.

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

Sun, B.

Tan, H. H.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

Travis, C.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Tsur, Y.

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

Turpin, A.

Tzortzakis, S.

Vallone, G.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

Villoresi, P.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space Quantum Key Distribution by Rotation-Invariant Twisted Photons,” Phys. Rev. Lett. 113, 060503 (2014).

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie, “Generation of electron Airy beams,” Nature 494, 331 (2013).

Vora, K.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Walborn, S. P.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Wang, A.

Wang, F.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

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 (2007).

Wang, L.

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Wang, M.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).

Wang, X.

Wang, Y.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

Xia, J.

Xiao, S.

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

Xie, X.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Xu, L.

Yan, K.

Yang, K.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Yao, A. M.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. Oppo, and R. W. Boyd, “Polarization shaping for control of nonlinear propagation,” Phys. Rev. Lett. 117233903 (2016).

Yao, L.

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

Yao, P.

Yu, J.

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

Yzuel, M. J.

Zhan, Q.

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).

Zhang, P.

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416 (2013).

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675 (2011).

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-Accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), 1–46.

Zhang, X.

Zhang, Y.

Zhao, C.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

Zhao, J.

Zhou, J.

S. Fu, J. Zhou, Y. Li, L. Shemer, and A. Arie, “Dispersion Management of Propagating Waveguide Modes on the Water Surface,” Phys. Rev. Lett. 118, 144501 (2017).

S. Fu, Y. Tsur, J. Zhou, L. Shemer, and A. Arie, “Propagation dynamics of Airy water-wave pulses,” Phys. Rev. Lett. 115, 034501 (2015).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Zhou, Y.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107, 126804 (2011).

Adv. Opt. Photonics (1)

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

App. Phys. B (1)

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” App. Phys. B 117, 905 (2014).

Appl. Opt. (3)

J. Mod. Opt. (1)

J. Yu, S. Xiao, L. Yao, S. Liu, and J. Li, “Propagation of the finite energy Airy-Hermite-Gaussian beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 64, 616 (2017).

J. Opt. B (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53 (2005).

J. Opt. Soc. Am. A (1)

Nano Lett. (2)

J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269 (2013).

R. Camacho-Morales, M. Rahmani, S. Kruk, L. Wang, L. Xu, D. A. Smirnova, A. S. Solntsev, A. Miroshnichenko, H. H. Tan, F. Karouta, S. Naureen, K. Vora, L. Carletti, C. De Angelis, C. Jagadish, Y. S. Kivshar, and D. N. Neshev, “Nonlinear generation of vector beams from AlGaAs nanoantennas,” Nano Lett. 16, 7191 (2016).

Nat. Commun. (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501 (2008).

Nature (1)

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Opt. Commun. (1)

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Figures (11)

Fig. 1
Fig. 1 Illustrations of cylindrical vector beams with typical polarization modes: (a) geometry sketch for illustration of polarization angle θ, (b) radial polarization (θ = 0), (c) azimuthal polarization (θ = π/2) and (c) spiral polarization (θ = π/4).
Fig. 2
Fig. 2 Propagation dynamics of CV beams in anisotropic medium under different cases of polarizations: (a) radial polarization (θ = 0), (b) spiral polarization (θ = π/4), and (c) azimuthal polarization (θ = π/2). In simulations, the parameters were set as: γ =0.94, σ0 =20 µm.
Fig. 3
Fig. 3 (a) Experimental setup for generating the LG vector beams with θ = 0. ND: neutral density, PC: polarization converter, PH: pinhole (50 µm) located at z = 0, and CCD: charge coupled device. (b)–(c) The generated radially polarized LG beams: (b) the intensity distribution, (c) the horizontal, and (d) the perpendicular polarization components. (e)(f) Intensity distributions at z = 30 mm for the cases of (e) free space and (f) crystal. (g) The corresponding profiles at z = 30 mm. The red curves represent the measurements, while the blue curves are simulations.
Fig. 4
Fig. 4 Generation of the circular Airy beams with radial polarization. (a) Intensity distribution of the Airy ring pattern without polarizer; (b) The horizontal polarization component; and (c) the perpendicular polarization component.
Fig. 5
Fig. 5 Illustrations of dynamic control of the circular Airy beams with radial polarization (θ = 0). (a) Top: intensity distributions at two propagating positions; bottom: propagation dynamics only in free space; (b) Top: intensity distributions at two propagating positions; bottom: propagation dynamics in crystal (10 mm, marked in white curve) and free space; (c) Top: intensity distributions at two propagating positions; bottom: propagation dynamics in crystal (30 mm, marked in white curved) and free space. In simulations, the related parameters were set as: r0 =0.37 mm, ω =40 µm, and α =0.1.
Fig. 6
Fig. 6 (a) The relation between the autofocusing position zf of the circular Airy vector beams and the crystal length. (b) Linear modulation of the autofocusing position zf via controlling the value of the anisotropy strength γ. In simulations, the parameters were set as: r0=0.37 mm, ω = 40 µm, and α = 0.1.
Fig. 7
Fig. 7 Propagation dynamics of the circular Airy beams with radial polarization (θ = 0). (a) Top: intensity distributions at two propagating positions; bottom: propagation dynamics only in free space; (b) Top: intensity distributions at two propagating positions; bottom: propagation dynamics in 30-mm-length BBO crystal (marked in white curve) and free space. In simulations, the related parameters were set as: r0 =0.39 mm, ω =33 μm, and α =0.1.
Fig. 8
Fig. 8 Simulations for propagation dynamics of the circular Airy beams with radial polarization (θ = 0) in a crystal of nx = ny =2, and (a) γ = −0.38; (b) γ =0; and (c) γ =0.24. Other parameters are the same with that shown in Fig. 7.
Fig. 9
Fig. 9 Experimental setup for generating the LG vector beam with spiral polarization θ = π/4. A linearly polarized He-Ne laser was expanded and collimated. The expanded beam was first split into two linearly polarized beams by a beam splitter, and then they were coaxially combined after passing through two polarization conversion (PC) elements, respectively. The combined beam illuminated a neutral density (ND), and was focused by a lens, generating the spirally polarized LG beam. The rest of the setup is the same as that shown in Fig. 3(a).
Fig. 10
Fig. 10 Observations of polarization rotations of LG beam with θ = π/4 after passing through the YVO4 (a)–(f) and BBO (g)(h) crystals, with different crystal lengths: (a)(d) Lc = 10 mm; (b)(e) Lc = 20 mm; (c)(f) Lc = 30 mm; and (g)(h) Lc = 30 mm (BBO). (d)–(f) and (h) are simulations for (a)–(c) and (g) respectively. (i) Initial intensity distribution of the horizontal component of the generated LG beams. All figures show the horizontal components of the vector fields, and have the same scale as shown in (i).
Fig. 11
Fig. 11 Spatial state of polarization of the spirally polarized LG beam (θ = π/4) after passing through the uniaxial crystals: (a) YVO4 crystal of length Lc =30 mm; (c) BBO crystal of length Lc = 30 mm. (b) and (d) are the magnified areas marked with square in (a) and (c). The incident conditions of the beams are the same as that shown in Fig. 10.

Equations (6)

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ε = [ n x 2 0 0 0 n y 2 0 0 0 n z 2 ]
× [ μ 1 ( × E ) ] = ε 2 E t 2 ,
i β x E x z + n x 2 n z 2 2 E x x 2 + 2 E x y 2 = γ y 2 E y y x exp ( + i 2 Δ β z ) , i β y E y z + n y 2 n z 2 2 E y y 2 + 2 E y x 2 = γ x 2 E x x y exp ( i 2 Δ β z ) ,
E ( r , 0 ) = E 0 ( r ) [ cos ( φ + θ ) x ^ + sin ( φ + θ ) y ^ ] ,
E ( r , 0 ) = A i ( r 0 r ω ) exp ( α r 0 r ω ) [ cos φ x ^ + sin φ y ^ ] ,
E ˜ ( k ) = ω 2 ( r 0 ω + k 2 ω 2 ) exp ( α k 2 ω 2 ) 3 k r 0 + k 3 ω 3 3 k r 0 + 3 k 3 ω 3 J 0 ( k r 0 + k 3 ω 3 3 ) ,

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