Abstract

We experimentally demonstrate multiple generations of high-order orbital angular momentum (OAM) modes through third-harmonic generation in a 2D nonlinear photonic crystal. Such third-harmonic generation process is achieved by cascading second-harmonic generation and sum-frequency generation using the non-collinear quasi-phase-matching technique. This technique allows multiple OAM modes with different colors to be simultaneously generated. Moreover, the OAM conservation law guarantees that the topological charge is tripled in the cascaded third-harmonic generation process. Our method is effective for obtaining multiple high-order OAM modes for optical imaging, manipulation, and communications.

© 2017 Optical Society of America

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References

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2016 (5)

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization Shaping for Control of Nonlinear Propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

X. Fang, G. Yang, D. Wei, D. Wei, R. Ni, W. Ji, Y. Zhang, X. Hu, W. Hu, Y. Q. Lu, S. N. Zhu, and M. Xiao, “Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal,” Opt. Lett. 41(6), 1169–1172 (2016).
[Crossref] [PubMed]

R. Ni, Y. Niu, L. Du, X. P. Hu, Y. Zhang, and S. N. Zhu, “Topological charge transfer in frequency doubling of fractional orbital angular momentum state,” Appl. Phys. Lett. 109(15), 151103 (2016).
[Crossref]

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

2015 (2)

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y. Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

2014 (1)

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

2013 (3)

G. H. Shao, Z. J. Wu, J. H. Chen, F. Xu, and Y. Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching,” Phys. Rev. A 88(6), 063827 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(9), 2432 (2013).
[PubMed]

2012 (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (2)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[Crossref]

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

2010 (1)

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (3)

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

R. K. Tyson, M. Scipioni, and J. Viegas, “Generation of an optical vortex with a segmented deformable mirror,” Appl. Opt. 47(33), 6300–6306 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

Y. Zhang, Z. Qi, W. Wang, and S. N. Zhu, “Quasi-phase-matched Cerenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide,” Appl. Phys. Lett. 89(17), 171113 (2006).
[Crossref]

L. Marrucci, L. C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 6(16), 163905 (2006).

H. I. Sztul and R. R. Alfano, “Double-slit interference with Laguerre-Gaussian beams,” Opt. Lett. 31(7), 999–1001 (2006).
[Crossref] [PubMed]

2004 (2)

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

2003 (2)

2001 (2)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
[Crossref]

1998 (2)

A. Beržanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[Crossref]

1996 (2)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

W. P. Schleich, “Quantum optics: optical coherence and quantum optics,” Science 272(5270), 1897–1898 (1996).
[Crossref]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref] [PubMed]

1990 (1)

G. C. Hegerfeldt, “Photons and atoms–introduction to quantum electrodynamics,” Science 247(4943), 732–733 (1990).
[Crossref] [PubMed]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Alfano, R. R.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
[Crossref]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[Crossref]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(9), 2432 (2013).
[PubMed]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
[Crossref]

Ashihara, S.

Barnett, S.

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Berger, V.

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81(19), 4136–4139 (1998).
[Crossref]

Beržanskis, A.

A. Beržanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
[Crossref]

Bouchard, F.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization Shaping for Control of Nonlinear Propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Boyd, R. W.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization Shaping for Control of Nonlinear Propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[Crossref]

Chen, J. H.

G. H. Shao, Z. J. Wu, J. H. Chen, F. Xu, and Y. Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching,” Phys. Rev. A 88(6), 063827 (2013).
[Crossref]

Chen, P.

M. J. Tang, P. Chen, W. L. Zhang, A. M. Tam, V. G. Chigrinov, W. Hu, and Y. Q. Lu, “Integrated and reconfigurable optical paths based on stacking optical functional films,” Opt. Express 24(22), 25510–25514 (2016).
[Crossref] [PubMed]

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y. Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Chen, Z. H.

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Chigrinov, V.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y. Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Chigrinov, V. G.

Cizmar, T.

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P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, Q. J.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

Wang, W.

Wang, Y. M.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

Wei, B. Y.

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y. Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

Wei, D.

Wei, D. Z.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Wen, J.

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

White, A. G.

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wu, Z. J.

G. H. Shao, Z. J. Wu, J. H. Chen, F. Xu, and Y. Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching,” Phys. Rev. A 88(6), 063827 (2013).
[Crossref]

Xiao, M.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

X. Fang, G. Yang, D. Wei, D. Wei, R. Ni, W. Ji, Y. Zhang, X. Hu, W. Hu, Y. Q. Lu, S. N. Zhu, and M. Xiao, “Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal,” Opt. Lett. 41(6), 1169–1172 (2016).
[Crossref] [PubMed]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Xu, F.

G. H. Shao, Z. J. Wu, J. H. Chen, F. Xu, and Y. Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching,” Phys. Rev. A 88(6), 063827 (2013).
[Crossref]

Xu, P.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, G.

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yao, A. M.

F. Bouchard, H. Larocque, A. M. Yao, C. Travis, I. De Leon, A. Rubano, E. Karimi, G. L. Oppo, and R. W. Boyd, “Polarization Shaping for Control of Nonlinear Propagation,” Phys. Rev. Lett. 117(23), 233903 (2016).
[Crossref] [PubMed]

Yu, X. Q.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Zhang, W. L.

Zhang, Y.

X. Fang, G. Yang, D. Wei, D. Wei, R. Ni, W. Ji, Y. Zhang, X. Hu, W. Hu, Y. Q. Lu, S. N. Zhu, and M. Xiao, “Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal,” Opt. Lett. 41(6), 1169–1172 (2016).
[Crossref] [PubMed]

R. Ni, Y. Niu, L. Du, X. P. Hu, Y. Zhang, and S. N. Zhu, “Topological charge transfer in frequency doubling of fractional orbital angular momentum state,” Appl. Phys. Lett. 109(15), 151103 (2016).
[Crossref]

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Y. Zhang, Z. Qi, W. Wang, and S. N. Zhu, “Quasi-phase-matched Cerenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide,” Appl. Phys. Lett. 89(17), 171113 (2006).
[Crossref]

Zhong, W. H.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Zhu, S. N.

X. Fang, G. Yang, D. Wei, D. Wei, R. Ni, W. Ji, Y. Zhang, X. Hu, W. Hu, Y. Q. Lu, S. N. Zhu, and M. Xiao, “Coupled orbital angular momentum conversions in a quasi-periodically poled LiTaO3 crystal,” Opt. Lett. 41(6), 1169–1172 (2016).
[Crossref] [PubMed]

R. Ni, Y. Niu, L. Du, X. P. Hu, Y. Zhang, and S. N. Zhu, “Topological charge transfer in frequency doubling of fractional orbital angular momentum state,” Appl. Phys. Lett. 109(15), 151103 (2016).
[Crossref]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104(18), 183901 (2010).
[Crossref] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
[Crossref] [PubMed]

Y. Zhang, Z. Qi, W. Wang, and S. N. Zhu, “Quasi-phase-matched Cerenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide,” Appl. Phys. Lett. 89(17), 171113 (2006).
[Crossref]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

Zhu, Y. Y.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, “Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal,” Phys. Rev. Lett. 93(13), 133904 (2004).
[Crossref] [PubMed]

Zhu, Y. Z.

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

P. Chen, W. Ji, B. Y. Wei, W. Hu, V. Chigrinov, and Y. Q. Lu, “Generation of arbitrary vector beams with liquid crystal polarization converters and vector-photoaligned q-plates,” Appl. Phys. Lett. 107(24), 241102 (2015).
[Crossref]

X. Y. Fang, D. Z. Wei, D. M. Liu, W. H. Zhong, R. Ni, Z. H. Chen, X. P. Hu, Y. Zhang, S. N. Zhu, and M. Xiao, “Multiple copies of orbital angular momentum states through second-harmonic generation in a two-dimensional periodically poled LiTO3,” Appl. Phys. Lett. 107(16), 161102 (2015).
[Crossref]

R. Ni, Y. Niu, L. Du, X. P. Hu, Y. Zhang, and S. N. Zhu, “Topological charge transfer in frequency doubling of fractional orbital angular momentum state,” Appl. Phys. Lett. 109(15), 151103 (2016).
[Crossref]

Y. M. Wang, D. Z. Wei, Y. Z. Zhu, X. Y. Huang, X. Y. Fang, W. H. Zhong, Q. J. Wang, Y. Zhang, and M. Xiao, “Conversion of the optical orbital angular momentum in a plasmon-assisted second-harmonic generation,” Appl. Phys. Lett. 109(8), 081105 (2016).
[Crossref]

Y. Zhang, Z. Qi, W. Wang, and S. N. Zhu, “Quasi-phase-matched Cerenkov second-harmonic generation in a hexagonally poled LiTaO3 waveguide,” Appl. Phys. Lett. 89(17), 171113 (2006).
[Crossref]

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

Nat. Commun. (1)

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4(9), 2432 (2013).
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K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
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J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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A. Beržanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150(1–6), 372–380 (1998).
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M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
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Opt. Lett. (4)

Phys. Rev. A (4)

G. H. Shao, Z. J. Wu, J. H. Chen, F. Xu, and Y. Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching,” Phys. Rev. A 88(6), 063827 (2013).
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[Crossref] [PubMed]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Cerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100(16), 163904 (2008).
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[Crossref] [PubMed]

Science (4)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of the reciprocal lattice for the 2D hexagonally poled LiTaO3 crystal. In the experiments, the propagation of the fundamental beam was in the y direction. Note that the direction of y is same as e 1 . (b) QPM SHG with G 0,1 and G 0,1 . (c) QPM THG was achieved by cascading the SHG andSFG processes with G 1,1 and G 1,1 .
Fig. 2
Fig. 2 (a) Schematic diagram of the experimental setup. (b) Distribution of the second and third harmonics on the screen. QWP: quarter wave plate; opo: optical parametric oscillator; CL: cylindrical lens.
Fig. 3
Fig. 3 (a) Image of the second-harmonic-carrying OAM. After using the cylinder lens, converted patterns are obtained for l2 = 2, 4, 6, and 8 in panels (b–e), respectively.
Fig. 4
Fig. 4 (a) Image of the OAM-carrying third-harmonic beam. After using the cylinder lens, converted patterns are obtained for l3 = 3, 6, 9, and 12 in panels (b–e), respectively.
Fig. 5
Fig. 5 The conversion efficiencies of SH and TH OAM generations with different input topological charges.

Equations (7)

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

G m,n = 4π m 2 + n 2 +mn d 3 ,
ω 2 =2 ω 1 ,
ω 3 = ω 1 + ω 2 =3 ω 1 .
Δ k 1 = k 2ω 2 k ω G m,n =0,
Δ k 2 = k 3ω k 2ω k ω G m',n' =0,
l 2 =2 l 1 ,
l 3 = l 1 + l 2 =3 l 1 .

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