Abstract

The generalized geometric mode with several high-order Hermite-Gaussian (HG) beams localized on ray periodic orbits in the degenerate resonator is generated by an off-axis pumped Nd:YVO4 laser, by performing beam transformation via an astigmatic mode converter, the generalized geometric modes are found that can be converted into the multi-axis vortex beams with the bundled-rings structures. Experimental results reveal that the generated multi-axis vortex beams can preserve quite stable beam structures even under high-power operation. Moreover, the radius of the bundled rings for the multi-axis vortex beams can be flexibly adjusted by the off-axis pumping to lead to vortex structures with easily controlled orbital angular momentum distribution. The good agreement between the experimental and theoretical results of propagation evolution for the astigmatic transformation of generalized geometric modes further verify the feasibility of using the proposed system to realize various high-powered, multi-center vortex beams with good reliability and predictability.

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

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    [Crossref]
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    [Crossref]
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2018 (3)

Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
[Crossref]

P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Realizing High-Pulse-Energy Large-Angular-Momentum Beams by Astigmatic Transformation of Geometric Modes in an Nd: YAG/Cr4+: YAG Laser,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1600809 (2018).

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
[Crossref]

2017 (4)

D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

2016 (3)

J. A. Rodrigo and T. Alieva, “Polymorphic beams and Nature inspired circuits for optical current,” Sci. Rep. 6(1), 35341 (2016).
[Crossref] [PubMed]

J. Wang, “Advances in communications using optical vortices,” Photon. Rev. 4(5), B14–B28 (2016).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

2015 (3)

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
[Crossref]

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

2013 (3)

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
[Crossref] [PubMed]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

2011 (3)

Y. F. Chen, “Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations,” Phys. Rev. A 83(3), 032124 (2011).
[Crossref]

H. A. Nam, M. G. Cohen, and J. W. Noé, “A simple method for creating a robust optical vortex beam with a single cylinder lens,” J. Opt. 13(6), 064026 (2011).
[Crossref]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

2009 (1)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref] [PubMed]

2008 (1)

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]

2005 (1)

J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005).
[Crossref]

2004 (3)

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A, Pure Appl. Opt. 6(5), S157–S161 (2004).
[Crossref]

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

A. Sennaroglu, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Compact femtosecond lasers based on novel multi-pass cavities,” IEEE J. Quantum Electron. 40(5), 519–528 (2004).
[Crossref]

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]

1997 (2)

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
[Crossref]

1996 (1)

1994 (1)

R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
[Crossref]

1991 (1)

E. G. Abramochkin and V. G. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[Crossref]

1965 (1)

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A, Pure Appl. Opt. 6(5), S157–S161 (2004).
[Crossref]

E. G. Abramochkin and V. G. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[Crossref]

Agarwal, A.

D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
[Crossref]

Agarwal, G. S.

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
[Crossref]

Alieva, T.

J. A. Rodrigo and T. Alieva, “Polymorphic beams and Nature inspired circuits for optical current,” Sci. Rep. 6(1), 35341 (2016).
[Crossref] [PubMed]

Bhaduri, R. K.

R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
[Crossref]

Bisson, J.-F.

J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005).
[Crossref]

Boyd, R. W.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
[Crossref] [PubMed]

Chang, C. C.

Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
[Crossref]

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

Chen, W. D.

Chen, Y. F.

Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
[Crossref]

P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Realizing High-Pulse-Energy Large-Angular-Momentum Beams by Astigmatic Transformation of Geometric Modes in an Nd: YAG/Cr4+: YAG Laser,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1600809 (2018).

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Y. F. Chen, “Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations,” Phys. Rev. A 83(3), 032124 (2011).
[Crossref]

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, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
[Crossref]

Chen, Z.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

Chiang, P. Y.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Cho, C. Y.

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

Chremmos, I. D.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

Christodoulides, D. N.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

Cižmár, T.

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
[Crossref]

Cohen, M. G.

H. A. Nam, M. G. Cohen, and J. W. Noé, “A simple method for creating a robust optical vortex beam with a single cylinder lens,” J. Opt. 13(6), 064026 (2011).
[Crossref]

Cuschieri, A.

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
[Crossref]

Dudley, A.

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Efremidis, N. K.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

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D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
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Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
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A. Sennaroglu, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Compact femtosecond lasers based on novel multi-pass cavities,” IEEE J. Quantum Electron. 40(5), 519–528 (2004).
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Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
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I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
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Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
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Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
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D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
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A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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A. Sennaroglu, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Compact femtosecond lasers based on novel multi-pass cavities,” IEEE J. Quantum Electron. 40(5), 519–528 (2004).
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Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
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Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
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C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
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I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
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R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
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Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
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P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Realizing High-Pulse-Energy Large-Angular-Momentum Beams by Astigmatic Transformation of Geometric Modes in an Nd: YAG/Cr4+: YAG Laser,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1600809 (2018).

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Lin, H.

D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
[Crossref]

Lin, Y. C.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

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]

Lipson, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Lu, T. H.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

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]

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D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
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D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
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Miyamoto, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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Morita, R.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
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H. A. Nam, M. G. Cohen, and J. W. Noé, “A simple method for creating a robust optical vortex beam with a single cylinder lens,” J. Opt. 13(6), 064026 (2011).
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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
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B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
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D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
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J. A. Rodrigo and T. Alieva, “Polymorphic beams and Nature inspired circuits for optical current,” Sci. Rep. 6(1), 35341 (2016).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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Roux, F. S.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Russell, P. St. J.

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
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B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
[Crossref]

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A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
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A. Sennaroglu, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Compact femtosecond lasers based on novel multi-pass cavities,” IEEE J. Quantum Electron. 40(5), 519–528 (2004).
[Crossref]

Shi, Z.

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
[Crossref] [PubMed]

Šiler, M.

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
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J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
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B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
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[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
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Takahashi, F.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
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P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Realizing High-Pulse-Energy Large-Angular-Momentum Beams by Astigmatic Transformation of Geometric Modes in an Nd: YAG/Cr4+: YAG Laser,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1600809 (2018).

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

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Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
[Crossref]

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, C. L. Sung, J. C. Tung, K. W. Su, H. C. Liang, W. D. Chen, and G. Zhang, “High-peak-power large-angular-momentum beams generated from passively Q-switched geometric modes with astigmatic transformation,” Photon. Res. 5(6), 561–566 (2017).
[Crossref]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Turtaev, S.

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
[Crossref]

Ueda, K.-I.

J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005).
[Crossref]

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]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A, Pure Appl. Opt. 6(5), S157–S161 (2004).
[Crossref]

E. G. Abramochkin and V. G. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[Crossref]

Waddington, J. C.

R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
[Crossref]

Wang, C. L.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
[Crossref]

Wang, J.

J. Wang, “Advances in communications using optical vortices,” Photon. Rev. 4(5), B14–B28 (2016).
[Crossref]

Wang, S. C.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
[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]

Yang, A. H. J.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref] [PubMed]

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, G.

Zhang, Y.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Zhao, J.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

IEEE J. Quantum Electron. (3)

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33(8), 1424–1429 (1997).
[Crossref]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, “Generation of Hermite Gaussian modes in fiber-coupled laser-diode end-pumped lasers,” IEEE J. Quantum Electron. 33(6), 1025–1031 (1997).
[Crossref]

A. Sennaroglu, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, “Compact femtosecond lasers based on novel multi-pass cavities,” IEEE J. Quantum Electron. 40(5), 519–528 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

D. Kita, H. Lin, A. Agarwal, K. Richardson, I. Luzinov, T. Gu, and J. Hu, “On-chip infrared spectroscopic sensing: redefining the benefits of scaling,” IEEE J. Sel. Top. Quantum Electron. 23(2), 5900110 (2017).
[Crossref]

P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Realizing High-Pulse-Energy Large-Angular-Momentum Beams by Astigmatic Transformation of Geometric Modes in an Nd: YAG/Cr4+: YAG Laser,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1600809 (2018).

C. Y. Lee, C. C. Chang, C. Y. Cho, P. H. Tuan, and Y. F. Chen, “Generation of Higher Order Vortex Beams From a YVO4/Nd:YVO4 Self-Raman Laser via Off-Axis Pumping With Mode Converter,” IEEE J. Sel. Top. Quantum Electron. 21(1), 318–322 (2015).
[Crossref]

J. Opt. (1)

H. A. Nam, M. G. Cohen, and J. W. Noé, “A simple method for creating a robust optical vortex beam with a single cylinder lens,” J. Opt. 13(6), 064026 (2011).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A, Pure Appl. Opt. 6(5), S157–S161 (2004).
[Crossref]

J. Phys. Math. Gen. (1)

R. K. Bhaduri, S. Li, K. Tanaka, and J. C. Waddington, “Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator,” J. Phys. Math. Gen. 27(15), L553–L558 (1994).
[Crossref]

Laser Phys. (2)

C. C. Chang, Y. H. Hsieh, C. Y. Lee, C. L. Sung, P. H. Tuan, J. C. Tung, H. C. Liang, and Y. F. Chen, “Generating high-peak-power structured lights in selectively pumped passively Q-switched lasers with astigmatic mode transformations,” Laser Phys. 27(12), 125805 (2017).
[Crossref]

Y. F. Chen, C. C. Chang, C. Y. Lee, J. C. Tung, H. C. Liang, and K. F. Huang, “Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams,” Laser Phys. 28(1), 015002 (2018).
[Crossref]

Laser Phys. Lett. (1)

J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005).
[Crossref]

Nat. Commun. (1)

M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, “Efficient separation of the orbital angular momentum eigenstates of light,” Nat. Commun. 4(1), 2781 (2013).
[Crossref] [PubMed]

Nat. Photonics (2)

D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincaré sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. St. J. Russell, and T. Čižmár, “Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre,” Nat. Photonics 12(1), 33–39 (2018).
[Crossref]

Nat. Phys. (1)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Nature (2)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[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]

New J. Phys. (1)

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, L. L. Sánchez-Soto, and G. S. Agarwal, “Experimental violation of a Bell-like inequality with optical vortex beams,” New J. Phys. 17(11), 113046 (2015).
[Crossref]

Opt. Commun. (1)

E. G. Abramochkin and V. G. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[Crossref]

Opt. Lett. (1)

Photon. Res. (1)

Photon. Rev. (1)

J. Wang, “Advances in communications using optical vortices,” Photon. Rev. 4(5), B14–B28 (2016).
[Crossref]

Phys. Rev. A (3)

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Y. F. Chen, “Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations,” Phys. Rev. A 83(3), 032124 (2011).
[Crossref]

Phys. Rev. Lett. (2)

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]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Sci. Rep. (2)

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5(1), 12086 (2015).
[Crossref] [PubMed]

J. A. Rodrigo and T. Alieva, “Polymorphic beams and Nature inspired circuits for optical current,” Sci. Rep. 6(1), 35341 (2016).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 The intracavity ray traces and the corresponding far-field transverse patterns for the planar geometric modes with P/Q to be (a) 1/4, (b) 2/7, (c) 1/3, and (d) 2/5, respectively.
Fig. 2
Fig. 2 The calculated far-field patterns of | Ψ n o , m o M (x,y,z; ϕ o ) | at z = 2L with M = 10, mo = 36, and increasing no from 0 to 35 for degenerate conditions of P/Q = (a)1/4, (b) 2/7, (c) 1/3, and (d) 2/5, respectively. (aʹ)-(dʹ) show the corresponding multi-axis LG beams via astigmatic mode conversion. The final columns of (aʹ)-(dʹ) are the corresponding phase structures for the cases with no = 35.
Fig. 3
Fig. 3 The experimental setup for generating the multi-axis vortex beams.
Fig. 4
Fig. 4 Average output power versus input pump power for generalized geometric modes at different degenerate conditions P/Q of (a) 1/4, (b) 2/7, (c) 1/3, and (d) 2/5 with central mode orders (no, mo) = (0, 36), (15, 36), and (35,36), respectively.
Fig. 5
Fig. 5 (a)-(d) Experimental far-field patterns of generalized geometric modes corresponding to the output power performance shown in Figs. 4(a)-4(d).
Fig. 6
Fig. 6 (a)-(d) The transformed beams corresponding to the generalized geometric modes in Figs. 5(a)-5(d) via astigmatic mode conversion.
Fig. 7
Fig. 7 Experimental results (upper rows) and theoretical reconstructions (lower rows) of the propagation evolution of transverse patterns for generalized geometric modes with operation parameters (no, mo, P/Q, α) to be (a) (36, 35, 2/7, π/4), (b) (36, 35, 1/3, π/4), and (c) (36, 15, 2/5, π/7), respectively.

Equations (14)

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Φ n,m,s ( HG ) (x,y,z)= 2 L ψ n ( x ˜ ) ψ m ( y ˜ )sin[ k n,m,s z ˜ ( n+m+1 ) θ G (z) ]
ψ n ( x ˜ )= 1 2 n n! π H n ( x ˜ ) e x ˜ 2 /2 ; ψ m ( y ˜ )= 1 2 m m! π H m ( y ˜ ) e y ˜ 2 /2 ,
Ψ n o , m o M (x,y,z; ϕ o )= 1 2 M/2 K=0 M M! K!( MK )! e iK ϕ o Φ n o , m o +QK, s o PK ( HG ) (x,y,z),
Φ n,m ( HG+ ) (x,y,z)=[ ψ n ( x ˜ ) e i( n+1/2 ) θ G,x (z) e i k x 2 / 2 R x (z) ][ ψ m ( y ˜ ) e i( m+1/2 ) θ G,y (z) e i k y 2 / 2 R y (z) ]
ψ n ( x ˜ ) ψ Nn ( y ˜ )= n =0 N B n ,n N (α) ψ n ( x ˜ ) ψ N n ( y ˜ ) ,
B n ,n N (α) = ν=max(0, n n) min( n ,Nn) ( 1 ) ν n ! ( N n )! n! ( Nn )! ( cosα ) Nn+ n 2ν ( sinα ) n n +2ν ( n ν )!ν!( n n +ν )!( Nnν )! .
Φ ˜ n,m ( HG+ ) (x,y,z;α)= e i[ ( N+1/2 ) θ G, y (z)+ θ G, x (z)/2 ] φ ˜ n,m (x,y,z;α) e iΘ(x,y,z;α) ,
θ G, x (z)= π 2 + tan 1 ( z z R z R ), θ G, y (z)= tan 1 ( z+ z R z R );
φ ˜ n,m (x,y,z;α)= n =0 N e i n β(z) B n ,n N (α) ψ n ( x ˜ ) ψ N n ( y ˜ ) ;
Θ(x,y,z)= 1 2 z R [ z( x ˜ 2 + y ˜ 2 ) z R ( x ˜ 2 y ˜ 2 ) ];
Φ ˜ n ˜ , m ˜ ( LG ) (x,y,z)=( μ=0 N e i μπ/2 B μ, n ˜ 2 n ˜ + m ˜ ψ 2 n ˜ + m ˜ μ ( x ˜ ) ψ μ ( y ˜ ) ) × e i[ ( 2 n ˜ + m ˜ +1/2 ) θ G, y (z)+ θ G, x (z)/2 ] e iΘ(x,y,z)
B μ, n ˜ 2 n ˜ + m ˜ = ν=max(0,μ n ˜ ) min(μ, n ˜ + m ˜ ) ( 1 ) ν ( n ˜ + m ˜ )!n!( 2 n ˜ + m ˜ n )!μ! 2 2 n ˜ + m ˜ ( μν )!ν!( nμ+ν )!( n ˜ + m ˜ ν )! .
Ψ ˜ n ˜ o , m ˜ o M (x,y,z; ϕ o )= 1 2 M/2 K=0 M M! K!( MK )! e iK ϕ o Φ n ˜ o , m ˜ o +QK, s o PK ( LG ) (x,y,z),
L f = f m ( 1+ z Ro f c z Ro 2 f m 2 )and L c = z Ro 2 + L f ( L f f m ) z Ro 2 + ( L f f m ) 2 f m ,

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