Abstract

We propose an efficient and robust method to generate the kaleidoscope vortex beam by employing an astigmatic laser cavity with an extra-cavity cylindrical lens. The kaleidoscope vortex beam is arising from the superposition of Laguerre-Gaussian modes with the longitudinal-transverse coupling effect in the laser cavity. The superposed Laguerre-Gaussian mode leads to the formation of complex phase singularities and implies the participation of different optical orbital angular momentum involved in a single kaleidoscope vortex beam. We experimentally demonstrate that a series of kaleidoscope vortex beams with different symmetry are systematically achieved by using a simple setup. The output power of the laser is dependent on the cavity length. This approach is expected to create high-order optical vortex beams and pave the way for optical entanglement.

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

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    [Crossref] [PubMed]
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    [Crossref]

2018 (2)

Y. Zhang, X. Yang, and J. Gao, “Twisting phase and intensity of light with plasmonic metasurfaces,” Sci. Rep. 8(1), 4884 (2018).
[Crossref] [PubMed]

T. D. Huang and T. H. Lu, “Large astigmatic laser cavity modes and astigmatic compensation,” Appl. Phys. B 124(5), 72 (2018).
[Crossref]

2017 (1)

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

2016 (2)

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116(7), 073601 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (3)

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

P. K. Mondal, B. Deb, and S. Majumder, “Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules,” Phys. Rev. A 89(6), 063418 (2014).
[Crossref]

2013 (1)

2012 (1)

J. G. Huang, J. M. Christian, and G. S. McDonald, “Spontaneous spatial fractal pattern formation in absorptive systems,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250018 (2012).
[Crossref]

2009 (1)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

2008 (3)

M. S. Kumar and B. Dutta-Roy, “Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit,” J. Phys. A 41(7), 075306 (2008).
[Crossref]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A 25(7), 1642–1651 (2008).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

2006 (2)

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

2005 (1)

J. G. Huang and G. S. McDonald, “Spontaneous optical fractal pattern formation,” Phys. Rev. Lett. 94(17), 174101 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

2001 (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).
[Crossref] [PubMed]

2000 (1)

1999 (1)

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[Crossref]

1997 (1)

1992 (1)

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]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 1037–1039 (1990).

Ahmed, N.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Alfano, R. R.

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[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]

Ando, T.

Bao, C.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 1037–1039 (1990).

Beijersbergen, M. W.

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]

Cao, Y.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Chen, Y. F.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Christian, J. M.

J. G. Huang, J. M. Christian, and G. S. McDonald, “Spontaneous spatial fractal pattern formation in absorptive systems,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250018 (2012).
[Crossref]

de Dood, M. J. A.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116(7), 073601 (2016).
[Crossref] [PubMed]

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Deb, B.

P. K. Mondal, B. Deb, and S. Majumder, “Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules,” Phys. Rev. A 89(6), 063418 (2014).
[Crossref]

Dholakia, K.

Dutta-Roy, B.

M. S. Kumar and B. Dutta-Roy, “Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit,” J. Phys. A 41(7), 075306 (2008).
[Crossref]

Erhard, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

Fang, Z. Q.

Z. Q. Fang, K. G. Xia, Y. Yao, and J. L. Li, “Radially polarized and passively Q-Switched Nd: YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).

Fickler, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

Fukuchi, N.

Gao, J.

Y. Zhang, X. Yang, and J. Gao, “Twisting phase and intensity of light with plasmonic metasurfaces,” Sci. Rep. 8(1), 4884 (2018).
[Crossref] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Hara, T.

Hiesmayr, B. C.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116(7), 073601 (2016).
[Crossref] [PubMed]

Huang, H.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Huang, J. G.

J. G. Huang, J. M. Christian, and G. S. McDonald, “Spontaneous spatial fractal pattern formation in absorptive systems,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250018 (2012).
[Crossref]

J. G. Huang and G. S. McDonald, “Spontaneous optical fractal pattern formation,” Phys. Rev. Lett. 94(17), 174101 (2005).
[Crossref] [PubMed]

Huang, K. F.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Huang, T. D.

T. D. Huang and T. H. Lu, “Large astigmatic laser cavity modes and astigmatic compensation,” Appl. Phys. B 124(5), 72 (2018).
[Crossref]

Huber, M.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

Inoue, T.

Karimi, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Karman, G. P.

G. S. McDonald, G. P. Karman, G. H. C. New, and J. P. Woerdman, “Kaleidoscope laser,” J. Opt. Soc. Am. B 17(4), 524–529 (2000).
[Crossref]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[Crossref]

Kaufmann, H.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Krenn, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

Kumar, M. S.

M. S. Kumar and B. Dutta-Roy, “Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit,” J. Phys. A 41(7), 075306 (2008).
[Crossref]

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

Lavery, M. P.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Lavery, M. P. J.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

Leach, J.

Li, J. L.

Z. Q. Fang, K. G. Xia, Y. Yao, and J. L. Li, “Radially polarized and passively Q-Switched Nd: YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).

Li, L.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Lin, Y. C.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Löffler, W.

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116(7), 073601 (2016).
[Crossref] [PubMed]

Lu, T. H.

T. D. Huang and T. H. Lu, “Large astigmatic laser cavity modes and astigmatic compensation,” Appl. Phys. B 124(5), 72 (2018).
[Crossref]

T. H. Lu and Y. C. Wu, “Observation and analysis of single and multiple high-order Laguerre-Gaussian beams generated from a hemi-cylindrical cavity with general astigmatism,” Opt. Express 21(23), 28496–28506 (2013).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Mair, 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]

Majumder, S.

P. K. Mondal, B. Deb, and S. Majumder, “Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules,” Phys. Rev. A 89(6), 063418 (2014).
[Crossref]

Malik, M.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Marrucci, L.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Matsumoto, N.

McDonald, G. S.

J. G. Huang, J. M. Christian, and G. S. McDonald, “Spontaneous spatial fractal pattern formation in absorptive systems,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250018 (2012).
[Crossref]

J. G. Huang and G. S. McDonald, “Spontaneous optical fractal pattern formation,” Phys. Rev. Lett. 94(17), 174101 (2005).
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G. S. McDonald, G. P. Karman, G. H. C. New, and J. P. Woerdman, “Kaleidoscope laser,” J. Opt. Soc. Am. B 17(4), 524–529 (2000).
[Crossref]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[Crossref]

Milione, G.

Miyaji, G.

Miyanaga, N.

Molisch, A. F.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Mondal, P. K.

P. K. Mondal, B. Deb, and S. Majumder, “Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules,” Phys. Rev. A 89(6), 063418 (2014).
[Crossref]

Nagali, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Nakatsuka, M.

New, G. H. C.

G. S. McDonald, G. P. Karman, G. H. C. New, and J. P. Woerdman, “Kaleidoscope laser,” J. Opt. Soc. Am. B 17(4), 524–529 (2000).
[Crossref]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[Crossref]

Nguyen, T. A.

Nolan, D. A.

Ohtake, Y.

Padgett, M. J.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
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N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
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Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Piccirillo, B.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Poschinger, U. G.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Ren, Y.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Ruster, T.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Santamato, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Schmidt-Kaler, F.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Schmiegelow, C. T.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Schulz, J.

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

Simpson, N. B.

Soskin, M. S.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 1037–1039 (1990).

Spreeuw, R. J. C.

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]

Su, K. W.

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

Sueda, K.

Tur, M.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Vasnetsov, M. V.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 1037–1039 (1990).

Vaziri, 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]

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]

Willner, A. E.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Woerdman, J. P.

G. S. McDonald, G. P. Karman, G. H. C. New, and J. P. Woerdman, “Kaleidoscope laser,” J. Opt. Soc. Am. B 17(4), 524–529 (2000).
[Crossref]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[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, Y. C.

Xia, K. G.

Z. Q. Fang, K. G. Xia, Y. Yao, and J. L. Li, “Radially polarized and passively Q-Switched Nd: YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).

Xie, G.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Yan, Y.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Yang, X.

Y. Zhang, X. Yang, and J. Gao, “Twisting phase and intensity of light with plasmonic metasurfaces,” Sci. Rep. 8(1), 4884 (2018).
[Crossref] [PubMed]

Yao, Y.

Z. Q. Fang, K. G. Xia, Y. Yao, and J. L. Li, “Radially polarized and passively Q-Switched Nd: YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).

Zeilinger, A.

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[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]

Zhang, Y.

Y. Zhang, X. Yang, and J. Gao, “Twisting phase and intensity of light with plasmonic metasurfaces,” Sci. Rep. 8(1), 4884 (2018).
[Crossref] [PubMed]

Zhao, Z.

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

Appl. Phys. B (1)

T. D. Huang and T. H. Lu, “Large astigmatic laser cavity modes and astigmatic compensation,” Appl. Phys. B 124(5), 72 (2018).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

Z. Q. Fang, K. G. Xia, Y. Yao, and J. L. Li, “Radially polarized and passively Q-Switched Nd: YAG laser under annular-shaped pumping,” IEEE J. Sel. Top. Quantum Electron. 21, 1 (2015).

J. Nonlinear Opt. Phys. Mater. (1)

J. G. Huang, J. M. Christian, and G. S. McDonald, “Spontaneous spatial fractal pattern formation in absorptive systems,” J. Nonlinear Opt. Phys. Mater. 21(02), 1250018 (2012).
[Crossref]

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

J. Opt. Soc. Am. B (2)

J. Phys. A (1)

M. S. Kumar and B. Dutta-Roy, “Commensurate anisotropic oscillator, SU(2) coherent states and the classical limit,” J. Phys. A 41(7), 075306 (2008).
[Crossref]

JETP Lett. (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 1037–1039 (1990).

Nat. Commun. (3)

Y. Yan, G. Xie, M. P. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5(1), 4502 (2014).
[Crossref] [PubMed]

C. T. Schmiegelow, J. Schulz, H. Kaufmann, T. Ruster, U. G. Poschinger, and F. Schmidt-Kaler, “Transfer of optical orbital angular momentum to a bound electron,” Nat. Commun. 7, 12998 (2016).
[Crossref] [PubMed]

Nature (3)

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]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, “Fractal modes in unstable resonators,” Nature 402(6758), 138 (1999).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Philos Trans A Math Phys Eng Sci (1)

M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes,” Philos Trans A Math Phys Eng Sci 375(2087), 20150442 (2017).
[Crossref] [PubMed]

Phys. Rev. A (2)

P. K. Mondal, B. Deb, and S. Majumder, “Angular momentum transfer in interaction of Laguerre-Gaussian beams with atoms and molecules,” Phys. Rev. A 89(6), 063418 (2014).
[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]

Phys. Rev. Lett. (6)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[Crossref] [PubMed]

B. C. Hiesmayr, M. J. A. de Dood, and W. Löffler, “Observation of four-photon orbital angular momentum entanglement,” Phys. Rev. Lett. 116(7), 073601 (2016).
[Crossref] [PubMed]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, “Devil’s staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces,” Phys. Rev. Lett. 96(21), 213902 (2006).
[Crossref] [PubMed]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Three-dimensional coherent optical waves localized on trochoidal parametric surfaces,” Phys. Rev. Lett. 101(23), 233901 (2008).
[Crossref] [PubMed]

J. G. Huang and G. S. McDonald, “Spontaneous optical fractal pattern formation,” Phys. Rev. Lett. 94(17), 174101 (2005).
[Crossref] [PubMed]

Sci. Rep. (1)

Y. Zhang, X. Yang, and J. Gao, “Twisting phase and intensity of light with plasmonic metasurfaces,” Sci. Rep. 8(1), 4884 (2018).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Numerical calculation of the formation of kaleidoscope vortex modes from the superposed LG modes represented by SLG( p 0 , l 0 ,u,v,M ). The indices depict the parameters of SLG( p 0 , l 0 ,u,v,M ). The symmetry of the pattern is controlled by the parameter v, the interval of the azimuthal index of the LG modes.
Fig. 2
Fig. 2 Numerical phase distribution corresponding to the numerical kaleidoscope modes shown in Fig. 1.
Fig. 3
Fig. 3 Bottom left: Experimental setup and results of the high-order astigmatic HG mode from the near field to the far field. Top right: Experimental setup with the extra-cavity cylindrical lens and the formation of the kaleidoscope vortex beam.
Fig. 4
Fig. 4 Experimental kaleidoscope vortex modes with different spatial symmetry corresponding to different degenerate cavities and pump offsets. The rational number ( 1/3, 1/4, 1/5, 1/6) of each row represents the ratio of transverse and longitudinal mode spacing of the degenerate cavity.
Fig. 5
Fig. 5 Experimental kaleidoscope vortex modes with different spatial symmetry corresponding to different degenerate cavities and pump offsets. The rational number ( 2/7, 2/9, 3/10, 11/3) of each row represents the ratio of transverse and longitudinal mode spacing of the degenerate cavity.
Fig. 6
Fig. 6 Beam shape of the 808 nm pump beam on focus and different defocus magnitude.
Fig. 7
Fig. 7 The kaleidoscope vortex beam of different defocus magnitude corresponding to the pump beam shape in Fig. 6. The cavity length and pump offset are fixed from (a) to (e).
Fig. 8
Fig. 8 Output power and the dependence cavity length and pump offset. The dashed line indicates the corresponding degenerate cavity defined by Δ f T /Δ f L .

Equations (1)

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

Φ p,l,s (ρ,z)= 2p! π(p+| l |)! 1 w(z) ( 2 ρ w(z) ) | l | L p | l | ( 2 p 2 w (z) 2 )exp[ ρ 2 w (z) 2 ] ×exp{ i k p,l,s z[ 1+ ρ 2 2( z 2 + z R 2 ) ] }exp[ i( 2p+| l |+1 ) θ G (z) ]

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