Abstract

We theoretically analyzed the relationship between quantum Green’s functions of two-dimensional harmonic oscillators and radial-order Laguerre–Gaussian laser modes of spherical resonators. By using a nearly hemispherical resonator and a tight focusing in the end-pumped solid-state laser, we successfully generated various laser transverse modes analogous to quantum Green’s functions. We further experimentally and numerically verified that the transverse order associated with quantum Green’s functions is noticeably raised with increasing the pump power induced by the thermal effect. More importantly, the high lasing efficiency and the salient structure enable the present laser source to be used in exploring the light–matter interaction.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  48. J. Dong, Y. He, X. Zhou, and S. Bai, “Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping,” Quantum Electron. 46, 218–222 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (1)

Y. F. Chen, J. C. Tung, P. H. Tuan, Y. T. Yu, H. C. Liang, and K. F. Huang, “Characterizing classical periodic orbits from quantum Green’s functions in two-dimensional integrable systems: harmonic oscillators and quantum billiards,” Phys. Rev. E 95, 012217 (2017).
[Crossref]

2016 (5)

J. C. Tung, P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Fractal frequency spectrum in laser resonators and three-dimensional geometric topology of optical coherent waves,” Phys. Rev. A 94, 023811 (2016).
[Crossref]

J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, and A. A. Kaminskii, “A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes,” J. Opt. 18, 055205 (2016).
[Crossref]

J. Dong, Y. He, S. C. Bai, K. I. Ueda, and A. A. Kaminskii, “A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes,” Laser Phys. 26, 095004 (2016).
[Crossref]

J. Dong, Y. He, X. Zhou, and S. Bai, “Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping,” Quantum Electron. 46, 218–222 (2016).
[Crossref]

H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
[Crossref]

2014 (2)

2013 (4)

S. Ngcobo, K. Aït-Ameur, N. Passilly, A. Hasnaoui, and A. Forbes, “Exciting higher-order radial Laguerre–Gaussian modes in a diode-pumped solid-state laser resonator,” Appl. Opt. 52, 2093–2101 (2013).
[Crossref]

J. Courtois, A. Mohamed, and D. Romanini, “Degenerate astigmatic cavities,” Phys. Rev. A 88, 043844 (2013).
[Crossref]

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photon. Rev. 7, 839–854 (2013).
[Crossref]

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

2011 (2)

Y. T. Yu, P. H. Tuan, P. Y. Chiang, H. C. Liang, K. F. Huang, and Y. F. Chen, “Wave pattern and weak localization of chaotic versus scarred modes in stadium-shaped surface-emitting lasers,” Phys. Rev. E 84, 056201 (2011).
[Crossref]

A. Hasnaoui, A. Bencheikh, and K. Aït-Ameur, “Tailored TEMp0 beams for large size 3-D laser prototyping,” Opt. Lasers Eng. 49, 248–251 (2011).
[Crossref]

2010 (1)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
[Crossref]

2009 (2)

A. Yu Okulov, “Twisted speckle entities inside wavefront reversal mirrors,” Phys. Rev. A 80, 013837 (2009).
[Crossref]

A. Yu Okulov, “Vortex–antivortex wavefunction of a degenerate quantum gas,” Laser Phys. 19, 1796–1803 (2009).
[Crossref]

2007 (2)

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

T. Ohtomo, K. Kamikariya, K. Otsuka, and S. Chu, “Single-frequency Ince–Gaussian mode operations of laser-diode-pumped microchip solid-state lasers,” Opt. Express 15, 10705–10717 (2007).
[Crossref]

2006 (3)

G. S. Agarwal and J. Banerji, “Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states,” J. Phys. A 39, 11503–11519 (2006).
[Crossref]

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).
[Crossref]

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, 213902 (2006).
[Crossref]

2004 (2)

2003 (1)

Y. F. Chen, Y. P. Lan, and K. F. Huang, “Observation of quantum-classical correspondence from high-order transverse patterns,” Phys. Rev. A 68, 043803 (2003).
[Crossref]

2002 (1)

K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, “Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,” Phys. Rev. Lett. 89, 224102 (2002).
[Crossref]

2001 (2)

Y. F. Chen and Y. P. Lan, “Transverse pattern formation of optical vortices in a microchip laser with a large Fresnel number,” Phys. Rev. A 65, 013802 (2001).
[Crossref]

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,l* mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[Crossref]

1998 (1)

V. B. Taranenko, K. Staliunas, and C. O. Weiss, “Pattern formation and localized structures in degenerate optical parametric mixing,” Phys. Rev. Lett. 81, 2236–2239 (1998).
[Crossref]

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, 1025–1031 (1997).
[Crossref]

K. Staliunas, G. Slekys, and C. O. Weiss, “Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns,” Phys. Rev. Lett. 79, 2658–2661 (1997).
[Crossref]

1996 (2)

E. Louvergneaux, D. Hennequin, D. Dangoisse, and P. Glorieux, “Transverse mode competition in a CO2 laser,” Phys. Rev. A 53, 4435–4438 (1996).
[Crossref]

H. Laabs and B. Ozygus, “Excitation of Hermite Gaussian modes in end-pumped solid-state lasers via off-axis pumping,” Opt. Laser Technol. 28, 213–214 (1996).
[Crossref]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

1992 (2)

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992).
[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, 8185–8189 (1992).
[Crossref]

1991 (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[Crossref]

1990 (1)

1989 (1)

1987 (1)

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

1986 (1)

1973 (1)

J. M. Kosterlitz and D. J. Thouless, “Ordering, metastability and phase transitions in two-dimensional systems,” J. Phys. C 6, 1181–1203 (1973).
[Crossref]

1972 (1)

V. L. Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems,” Sov. Phys. J. Exp. Theor. Phys. 34, 610–616 (1972).

Agarwal, G. S.

G. S. Agarwal and J. Banerji, “Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states,” J. Phys. A 39, 11503–11519 (2006).
[Crossref]

Aït-Ameur, K.

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[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, 8185–8189 (1992).
[Crossref]

Alpmann, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photon. Rev. 7, 839–854 (2013).
[Crossref]

Bai, S.

J. Dong, Y. He, X. Zhou, and S. Bai, “Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping,” Quantum Electron. 46, 218–222 (2016).
[Crossref]

Bai, S. C.

J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, and A. A. Kaminskii, “A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes,” J. Opt. 18, 055205 (2016).
[Crossref]

J. Dong, Y. He, S. C. Bai, K. I. Ueda, and A. A. Kaminskii, “A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes,” Laser Phys. 26, 095004 (2016).
[Crossref]

Bandres, M. A.

Banerji, J.

G. S. Agarwal and J. Banerji, “Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states,” J. Phys. A 39, 11503–11519 (2006).
[Crossref]

Barré, N.

Battelier, B.

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).
[Crossref]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[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, 8185–8189 (1992).
[Crossref]

Bencheikh, A.

A. Hasnaoui, A. Bencheikh, and K. Aït-Ameur, “Tailored TEMp0 beams for large size 3-D laser prototyping,” Opt. Lasers Eng. 49, 248–251 (2011).
[Crossref]

Berezinskii, V. L.

V. L. Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems,” Sov. Phys. J. Exp. Theor. Phys. 34, 610–616 (1972).

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
[Crossref]

Broky, J.

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

Brunel, M.

Bužek, V.

Chen, P.

Chen, Y. F.

Y. F. Chen, J. C. Tung, P. H. Tuan, Y. T. Yu, H. C. Liang, and K. F. Huang, “Characterizing classical periodic orbits from quantum Green’s functions in two-dimensional integrable systems: harmonic oscillators and quantum billiards,” Phys. Rev. E 95, 012217 (2017).
[Crossref]

J. C. Tung, P. H. Tuan, H. C. Liang, K. F. Huang, and Y. F. Chen, “Fractal frequency spectrum in laser resonators and three-dimensional geometric topology of optical coherent waves,” Phys. Rev. A 94, 023811 (2016).
[Crossref]

Y. T. Yu, P. H. Tuan, P. Y. Chiang, H. C. Liang, K. F. Huang, and Y. F. Chen, “Wave pattern and weak localization of chaotic versus scarred modes in stadium-shaped surface-emitting lasers,” Phys. Rev. E 84, 056201 (2011).
[Crossref]

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, 213902 (2006).
[Crossref]

Y. F. Chen, Y. P. Lan, and K. F. Huang, “Observation of quantum-classical correspondence from high-order transverse patterns,” Phys. Rev. A 68, 043803 (2003).
[Crossref]

K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, “Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,” Phys. Rev. Lett. 89, 224102 (2002).
[Crossref]

Y. F. Chen and Y. P. Lan, “Transverse pattern formation of optical vortices in a microchip laser with a large Fresnel number,” Phys. Rev. A 65, 013802 (2001).
[Crossref]

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM0,l* mode in a solid-state laser,” Phys. Rev. A 63, 063807 (2001).
[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, 1025–1031 (1997).
[Crossref]

Cheneau, M.

Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, “Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas,” Nature 441, 1118–1121 (2006).
[Crossref]

Chiang, P. Y.

Y. T. Yu, P. H. Tuan, P. Y. Chiang, H. C. Liang, K. F. Huang, and Y. F. Chen, “Wave pattern and weak localization of chaotic versus scarred modes in stadium-shaped surface-emitting lasers,” Phys. Rev. E 84, 056201 (2011).
[Crossref]

Christodoulides, D. N.

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

Chu, S.

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V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
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J. Dong, Y. He, S. C. Bai, K. I. Ueda, and A. A. Kaminskii, “A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes,” Laser Phys. 26, 095004 (2016).
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J. Dong, Y. He, X. Zhou, and S. Bai, “Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping,” Quantum Electron. 46, 218–222 (2016).
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H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
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H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
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J. Dong, Y. He, X. Zhou, and S. Bai, “Highly efficient, versatile, self-Q-switched, high-repetition-rate microchip laser generating Ince–Gaussian modes for optical trapping,” Quantum Electron. 46, 218–222 (2016).
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J. Dong, Y. He, S. C. Bai, K. I. Ueda, and A. A. Kaminskii, “A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes,” Laser Phys. 26, 095004 (2016).
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Kaminskii, A. A.

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J. Dong, Y. He, S. C. Bai, K. I. Ueda, and A. A. Kaminskii, “A Cr4+:YAG passively Q-switched Nd:YVO4 microchip laser for controllable high-order Hermite–Gaussian modes,” Laser Phys. 26, 095004 (2016).
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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, 1025–1031 (1997).
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V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
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V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
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K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, “Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,” Phys. Rev. Lett. 89, 224102 (2002).
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Y. F. Chen, Y. P. Lan, and K. F. Huang, “Observation of quantum-classical correspondence from high-order transverse patterns,” Phys. Rev. A 68, 043803 (2003).
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K. F. Huang, Y. F. Chen, H. C. Lai, and Y. P. Lan, “Observation of the wave function of a quantum billiard from the transverse patterns of vertical cavity surface emitting lasers,” Phys. Rev. Lett. 89, 224102 (2002).
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Y. T. Yu, P. H. Tuan, P. Y. Chiang, H. C. Liang, K. F. Huang, and Y. F. Chen, “Wave pattern and weak localization of chaotic versus scarred modes in stadium-shaped surface-emitting lasers,” Phys. Rev. E 84, 056201 (2011).
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J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, and A. A. Kaminskii, “A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes,” J. Opt. 18, 055205 (2016).
[Crossref]

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E. Louvergneaux, D. Hennequin, D. Dangoisse, and P. Glorieux, “Transverse mode competition in a CO2 laser,” Phys. Rev. A 53, 4435–4438 (1996).
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D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, “Two-dimensional optical lattices in a CO2 laser,” Phys. Rev. A 46, 5955–5958 (1992).
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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, 213902 (2006).
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J. Courtois, A. Mohamed, and D. Romanini, “Degenerate astigmatic cavities,” Phys. Rev. A 88, 043844 (2013).
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W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
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M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
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V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
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V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105, 118103 (2010).
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M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
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J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, and A. A. Kaminskii, “A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes,” J. Opt. 18, 055205 (2016).
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H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
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H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
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Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

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, 1025–1031 (1997).
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J. Opt. (2)

J. Dong, S. C. Bai, S. H. Liu, K. I. Ueda, and A. A. Kaminskii, “A high repetition rate passively Q-switched microchip laser for controllable transverse laser modes,” J. Opt. 18, 055205 (2016).
[Crossref]

H. S. He, M. M. Zhang, J. Dong, and K. I. Ueda, “Linearly polarized pumped passively Q-switched Nd:YVO4 microchip laser for Ince–Gaussian laser modes with controllable orientations,” J. Opt. 18, 055205 (2016).
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J. Opt. Soc. Am. A (1)

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

J. Phys. A (1)

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Opt. Commun. (1)

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Opt. Express (1)

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Phys. Rev. A (11)

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Phys. Rev. E (2)

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N. N. Lebedev, Special Functions & Their Applications (Dover, 1972).

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Figures (8)

Fig. 1.
Fig. 1. Calculated results to display the correspondence between quantum Green’s functions and classical periodic-orbit bundles for two cases: (a) (x˜s,y˜s)=(0,0) and (b) (x˜s,y˜s)=(0,2.6).
Fig. 2.
Fig. 2. Numerical calculations for the relationship between the pump-to-mode size ratio and the coefficient |bn,m|2 in the y direction for the location of the excitation source at (a) y˜s=0, (b) y˜s=1, and (c) y˜s=2.6.
Fig. 3.
Fig. 3. Experimental setup for a solid-state laser selectively end-pumped by a laser diode in a nearly hemispherical cavity.
Fig. 4.
Fig. 4. Experimental results for the output power and the lasing modes obtained by varying the pump power Pin for the source at (x˜s,y˜s)=(0,0). Bottom: theoretical patterns |GN(x˜,y˜;0)| for comparison.
Fig. 5.
Fig. 5. Calculation result for the coefficient cn,m as a function of the transverse order m of eigenmodes with various pump positions y˜s in the y direction.
Fig. 6.
Fig. 6. Transformed patterns for the lasing modes in Figs. 4(c) and 4(d). Right side: numerically reconstructed patterns.
Fig. 7.
Fig. 7. Experimental results for the output power and the lasing modes obtained by varying the pump power Pin for the source at (x˜s,y˜s)=(0,1). Bottom: theoretical patterns |GN(x˜,y˜;1)| for comparison.
Fig. 8.
Fig. 8. Experimental results for the output power and the lasing modes obtained by varying the pump power Pin for the source at (x˜s,y˜s)=(0,2.6). Bottom: theoretical patterns |GN(x˜,y˜;2.6)| for comparison.

Equations (16)

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ψn,m(x˜,y˜)=(2n+mn!m!π)1/2e(x˜2+y˜2)/2Hn(x˜)Hm(y˜),
[12(d2dx˜2+d2dy˜2x˜2y˜2)+vn,m]ψn,m(x˜,y˜)=0.
[12(d2dx˜2+d2dy˜2x˜2y˜2)+v]Gv(r;rs)=δ(rrs),
Gv(r;rs)=m=0n=0ψn,m(x˜s,y˜s)ψn,m(x˜,y˜)vvn,m.
GN(r;rs)=n=0Nψn,Nn(x˜s,y˜s)ψn,Nn(x˜,y˜).
Hn(x)=k=0[n/2](1)kn!k!(n2k)!(2x)n2k,
GN(x˜,y˜;ds)=1π12Nn=0[N/2]AN,n(ds)H2n(x˜)HN2n(y˜)e(x˜2+y˜2)/2,
AN,n(ds)=k=0[N/2]n(1)n+k(2ds)N2n2keds2/2n!k!(N2n2k)!.
G2p(x˜,y˜;0)=1π(1)p22pn=0pH2n(x˜)H2p2n(y˜)n!(pn)!e(x˜2+y˜2)/2.
Lp(x2+y2)=(1)p22pn=0pH2n(x)H2p2n(y)n!(pn)!,
G2p(x˜,y˜;0)=1πer˜2/2Lp(r˜2)p1πJ0(2p+1/2r˜),
[12(d2dx˜2+d2dy˜2x˜2y˜2)+v]Ψv(r;rs)=F(r;rs).
Ψv(r;rs)=m=0n=0bn,mψn,m(x˜,y˜)vvn,m,
bn,m=y˜say˜s+ax˜sax˜s+aψn,m(x˜,y˜)F(r;rs)dx˜dy˜,
F(r;rs)=(12a)2exp[(x˜x˜s)2+(y˜y˜s)2a2].
cn,m=y˜say˜s+ax˜sax˜s+a|ψn,m(x˜,y˜)|2e(x˜x˜s)2+(y˜y˜s)2a2dx˜dy˜.

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