Abstract

We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamics of mode formation. Simulations of an axially symmetrical empty resonator rely on an analytical description of radiation diffraction from a narrow ring. Reflection of an incident wave with a specified amplitude-phase distribution from the mirror is calculated by the Green function method. The process of mode formation is characterized by relaxation oscillations of various frequencies depending on the resonator parameters. The evolution of the relaxation oscillation amplitude can be aperiodic in nature, or it can occur as beats of a different frequency. It has been shown that there is a consistency between the known conditions of paraxial resonance obtained in the approximation of geometric optics and the aperiodic processes of evolution of relaxation oscillation amplitude in mode forming. An investigation has been performed on the factors affecting the time of mode formation. The possibility has been shown for multipass mode suppression and TEM10 mode generation by the use of an absorber mask on the resonator mirror.

© 2010 Optical Society of America

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2010

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12, 015708 (2010).
[CrossRef]

2008

2007

2005

A. A. Ishaaya, N. Davidson, and A. A. Friesem, “Very high-order pure Laguerre–Gaussian mode selection in a passive Q-switched Nd:YAG laser,” Opt. Express 13, 4952–4962(2005).
[CrossRef]

A. V. Nesterov and V. G. Niziev, “Vector solution of the diffraction task using the Hertz vector,” Phys. Rev. E 71, 046608(2005).
[CrossRef]

2003

2001

N. K. Anatol, G. E. Katranji, and A. R. Anatol, “Axicon-based Bessel resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
[CrossRef]

J. Dingjan, M. P. Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser,” Opt. Commun. 188, 345–351 (2001).
[CrossRef]

H. H. Wu and W. F. Hsieh, “Observations of multipass transverse modes in an axially pumped solid-state laser with different fractionally degenerate resonator configurations,” J.  Opt. Soc. Am. B 18, 7–12 (2001).
[CrossRef]

1996

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

1992

1970

1966

1961

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–458 (1961).

Anan’ev, Y. A.

Y. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Institute of Physics Publishing, 1992).

Anatol, A. R.

Anatol, N. K.

Cao, H.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Capjack, C. E.

Chen, C. H.

Chen, Y.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Chiu, C. F.

Crosignani, B.

S. Solimeno, B. Crosignani, and P. Guiding DiPorto, Diffraction and Confinement of Optical Radiation (Academic, 1986).

Davidson, N.

Degnan, J. J.

Deng, S.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Dingjan, J.

J. Dingjan, M. P. Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser,” Opt. Commun. 188, 345–351 (2001).
[CrossRef]

DiPorto, P. Guiding

S. Solimeno, B. Crosignani, and P. Guiding DiPorto, Diffraction and Confinement of Optical Radiation (Academic, 1986).

Endo, M.

Exter, M. P.

J. Dingjan, M. P. Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser,” Opt. Commun. 188, 345–351 (2001).
[CrossRef]

Fox, A. G.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–458 (1961).

Friesem, A. A.

Gao, Y.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Haus, H. A.

H. A. HausWaves and Fields in Optoelectronics (Prentice-Hall, 1984).

He, Y.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Hodgson, N.

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

Hsieh, W. F.

C. H. Chen, P. T. Tai, M. D. Wei, and W. F. Hsieh, “Multibeam-waist modes in an end-pumped Nd-YVO4 laser,” J. Opt. Soc. Am. B 20, 1220–1226 (2003).
[CrossRef]

H. H. Wu and W. F. Hsieh, “Observations of multipass transverse modes in an axially pumped solid-state laser with different fractionally degenerate resonator configurations,” J.  Opt. Soc. Am. B 18, 7–12 (2001).
[CrossRef]

Huang, P. Y.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12, 015708 (2010).
[CrossRef]

Ishaaya, A. A.

Katranji, G. E.

Kogelnik, H.

Kuo, C. W.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12, 015708 (2010).
[CrossRef]

Li, T.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef]

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–458 (1961).

Li, X.

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Nesterov, A. V.

A. V. Nesterov and V. G. Niziev, “Vector solution of the diffraction task using the Hertz vector,” Phys. Rev. E 71, 046608(2005).
[CrossRef]

Nikumb, S. K.

Niziev, V. G.

A. V. Nesterov and V. G. Niziev, “Vector solution of the diffraction task using the Hertz vector,” Phys. Rev. E 71, 046608(2005).
[CrossRef]

Ramsay, I. A.

Reshef, H.

Seguin, H. J. J.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Solimeno, S.

S. Solimeno, B. Crosignani, and P. Guiding DiPorto, Diffraction and Confinement of Optical Radiation (Academic, 1986).

Tai, P. T.

Weber, H.

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

Wei, M. D.

Woerdman, J. P.

J. Dingjan, M. P. Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser,” Opt. Commun. 188, 345–351 (2001).
[CrossRef]

Wu, H. H.

H. H. Wu and W. F. Hsieh, “Observations of multipass transverse modes in an axially pumped solid-state laser with different fractionally degenerate resonator configurations,” J.  Opt. Soc. Am. B 18, 7–12 (2001).
[CrossRef]

Yelden, E. F.

Appl. Opt.

Bell Syst. Tech. J.

A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–458 (1961).

J. Opt.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12, 015708 (2010).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J.? Opt. Soc. Am. B

H. H. Wu and W. F. Hsieh, “Observations of multipass transverse modes in an axially pumped solid-state laser with different fractionally degenerate resonator configurations,” J.  Opt. Soc. Am. B 18, 7–12 (2001).
[CrossRef]

Opt. Commun.

J. Dingjan, M. P. Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd:YVO4 laser,” Opt. Commun. 188, 345–351 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

A. V. Nesterov and V. G. Niziev, “Vector solution of the diffraction task using the Hertz vector,” Phys. Rev. E 71, 046608(2005).
[CrossRef]

Proc. SPIE

X. Li, Y. Chen, T. Li, Y. He, Y. Gao, H. Cao, andS. Deng, “Development of red internal mirror He–Ne lasers with near-critical concave–convex stable resonator,” Proc. SPIE 2889, 358–366 (1996).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, 1986).

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

Y. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Institute of Physics Publishing, 1992).

H. A. HausWaves and Fields in Optoelectronics (Prentice-Hall, 1984).

S. Solimeno, B. Crosignani, and P. Guiding DiPorto, Diffraction and Confinement of Optical Radiation (Academic, 1986).

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