Abstract

Unusual transverse patterns were observed in a cw-lamp-pumped Nd:YAG laser near the boundaries of the stability zones of the laser resonator. An interpretation of these patterns is given in terms of off-axis modes, which can be excited owing to spherical aberrations and astigmatism of the thermal lens and thermally induced birefringence. Additional evidence of the off-axis character of the observed modes was obtained by analysis of the temporal behavior of the observed patterns.

© 2004 Optical Society of America

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References

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  1. F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
    [CrossRef]
  4. K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. Chabanol, V. Zehlne, “Synchronization and self-organization in arrays of coupled solid-state lasers,” Phys. Rev. A 63, 053809 (2001).
    [CrossRef]
  9. J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).
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    [CrossRef]
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    [CrossRef]
  18. Y. Inoue, Sh. Fujikawa, “Diode-pumped Nd:YAG laser producing 122-W cw power at 1319 μm,” IEEE J. Quantum Electron. 36, 751–756 (2000).
    [CrossRef]
  19. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
    [CrossRef]

2003 (1)

2001 (2)

S. J. Bentley, R. W. Boyd, W. E. Butler, A. C. Melissionos, “Spatial patterns induced in a laser beam by thermal nonlinearities,” Opt. Lett. 26, 1084–1086 (2001).
[CrossRef]

M. Chabanol, V. Zehlne, “Synchronization and self-organization in arrays of coupled solid-state lasers,” Phys. Rev. A 63, 053809 (2001).
[CrossRef]

2000 (2)

Y. Inoue, Sh. Fujikawa, “Diode-pumped Nd:YAG laser producing 122-W cw power at 1319 μm,” IEEE J. Quantum Electron. 36, 751–756 (2000).
[CrossRef]

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

1999 (2)

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
[CrossRef]

1998 (1)

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

1996 (1)

1995 (2)

J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
[CrossRef]

P. V. Korolenko, N. N. Fedotov, V. F. Sharkov, “Main properties and potential practical applications of M-mode lasers,” Quantum Electron. 25, 536–539 (1995).
[CrossRef]

1994 (1)

J. Lega, J. V. Moloney, A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994).
[CrossRef] [PubMed]

1993 (2)

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef] [PubMed]

N. Hodgson, H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. 29, 2497–2507 (1993).
[CrossRef]

1991 (2)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

D. Dick, F. Hanson, “M modes in a diode side-pumped Nd:glass slab laser,” Opt. Lett. 16, 476–477 (1991).
[CrossRef] [PubMed]

1989 (1)

Ackeman, T.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
[CrossRef]

Ashwin, P.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Bentley, S. J.

Boccaletti, S.

F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
[CrossRef]

Boyd, R. W.

Butler, W. E.

Chabanol, M.

M. Chabanol, V. Zehlne, “Synchronization and self-organization in arrays of coupled solid-state lasers,” Phys. Rev. A 63, 053809 (2001).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Dagan, E.

DeShazer, D. J.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Dick, D.

Dunlop, A. M.

Fedotov, N. N.

P. V. Korolenko, N. N. Fedotov, V. F. Sharkov, “Main properties and potential practical applications of M-mode lasers,” Quantum Electron. 25, 536–539 (1995).
[CrossRef]

Firth, W. J.

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Fujikawa, Sh.

Y. Inoue, Sh. Fujikawa, “Diode-pumped Nd:YAG laser producing 122-W cw power at 1319 μm,” IEEE J. Quantum Electron. 36, 751–756 (2000).
[CrossRef]

Fukushima, T.

Gabay, A.

Hanson, F.

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Healtey, D. R.

Hodgson, N.

N. Hodgson, H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. 29, 2497–2507 (1993).
[CrossRef]

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

Hoffer, L. M.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Inoue, Y.

Y. Inoue, Sh. Fujikawa, “Diode-pumped Nd:YAG laser producing 122-W cw power at 1319 μm,” IEEE J. Quantum Electron. 36, 751–756 (2000).
[CrossRef]

Kannari, F.

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

Korolenko, P. V.

P. V. Korolenko, N. N. Fedotov, V. F. Sharkov, “Main properties and potential practical applications of M-mode lasers,” Quantum Electron. 25, 536–539 (1995).
[CrossRef]

Lega, J.

J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
[CrossRef]

J. Lega, J. V. Moloney, A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994).
[CrossRef] [PubMed]

Lippi, G. L.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Melissionos, A. C.

Moloney, J. V.

J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
[CrossRef]

J. Lega, J. V. Moloney, A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994).
[CrossRef] [PubMed]

Nalik, J.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Newell, A. C.

J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
[CrossRef]

J. Lega, J. V. Moloney, A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994).
[CrossRef] [PubMed]

Ogava, T.

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

Ramzza, P. L.

F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
[CrossRef]

Roy, R.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Scholz, T.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Sharkov, V. F.

P. V. Korolenko, N. N. Fedotov, V. F. Sharkov, “Main properties and potential practical applications of M-mode lasers,” Quantum Electron. 25, 536–539 (1995).
[CrossRef]

Shinozuka, M.

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Staliunas, K.

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef] [PubMed]

Sterman, B.

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Terry, J. R.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Thornburg, K. S.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Uchida, A.

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

Van Wiggeren, G. D.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Vorgerd, Ch.

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Weber, H.

N. Hodgson, H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. 29, 2497–2507 (1993).
[CrossRef]

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

Wright, E. M.

Yatsiv, Sh.

Zehlne, V.

M. Chabanol, V. Zehlne, “Synchronization and self-organization in arrays of coupled solid-state lasers,” Phys. Rev. A 63, 053809 (2001).
[CrossRef]

Zhu, Sh.

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

N. Hodgson, H. Weber, “Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers,” IEEE J. Quantum Electron. 29, 2497–2507 (1993).
[CrossRef]

Y. Inoue, Sh. Fujikawa, “Diode-pumped Nd:YAG laser producing 122-W cw power at 1319 μm,” IEEE J. Quantum Electron. 36, 751–756 (2000).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical cavity surface emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Opt. Commun. (1)

T. Ackeman, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, G. L. Lippi, “Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping,” Opt. Commun. 147, 411–428 (1998).
[CrossRef]

Opt. Lett. (5)

Phys. Rep. (1)

F. T. Arecchi, S. Boccaletti, P. L. Ramzza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).
[CrossRef]

Phys. Rev. A (2)

M. Chabanol, V. Zehlne, “Synchronization and self-organization in arrays of coupled solid-state lasers,” Phys. Rev. A 63, 053809 (2001).
[CrossRef]

K. Staliunas, “Laser Ginzburg-Landau equation and laser hydrodynamics,” Phys. Rev. A 48, 1573–1581 (1993).
[CrossRef] [PubMed]

Phys. Rev. E (2)

J. R. Terry, K. S. Thornburg, D. J. DeShazer, G. D. Van Wiggeren, Sh. Zhu, P. Ashwin, R. Roy, “Synchronization of chaos in an array of three lasers,” Phys. Rev. E 59, 4036–4043 (1999).
[CrossRef]

A. Uchida, T. Ogava, M. Shinozuka, F. Kannari, “Accuracy of chaos synchronization in ND:YVO4 microchip lasers,” Phys. Rev. E 62, 1960–1971 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

J. Lega, J. V. Moloney, A. C. Newell, “Swift-Hohenberg equation for lasers,” Phys. Rev. Lett. 73, 2978–2981 (1994).
[CrossRef] [PubMed]

Physica D (1)

J. Lega, J. V. Moloney, A. C. Newell, “Universal description of laser dynamics near threshold,” Physica D 83, 478–498 (1995).
[CrossRef]

Quantum Electron. (1)

P. V. Korolenko, N. N. Fedotov, V. F. Sharkov, “Main properties and potential practical applications of M-mode lasers,” Quantum Electron. 25, 536–539 (1995).
[CrossRef]

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

N. Hodgson, H. Weber, Optical Resonators: Fundamentals, Advanced Concepts and Applications (Springer-Verlag, London, 1997).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for observing off-axis modes.

Fig. 2
Fig. 2

Stability diagram for an equivalent resonator. Because of thermal lensing the equivalent resonator moves along the straight line when the pump power varies.

Fig. 3
Fig. 3

Images of laser spots on the visualizer.

Fig. 4
Fig. 4

Linear fits to measured refractive powers of the thermal lens. Squares and triangles, to horizontal and vertical directions, respectively. Filled and open symbols, radial and azimuthal polarizations, respectively. Horizontal line, refractive power for which resonator lies on the boundary of the stable zone. Vertical lines confine the range of pumping power when transverse pattern changes take place.

Fig. 5
Fig. 5

Calculated Gaussian beam radius on mirror M2 (solid curve) and on the right end face of the rod (dashed curve).

Fig. 6
Fig. 6

Possible types of off-axis mode a, c, folded modes; b, linear modes; d, ring modes.

Fig. 7
Fig. 7

Time traces of the outermost two laser spots of the off-axis mode.

Tables (1)

Tables Icon

Table 1 Pump Powers for the Appearance and Disappearance of Patterns in Fig. 3

Equations (2)

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

nr,θr=n01- Dr,θ2n0l r2,
Dr=D01-γrb2,

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