Abstract

A new optical resonator based on the combination of a generalized self-filtering unstable resonator (GSFUR) and a positive-branch unstable resonator (PBUR) in a three-mirror scheme is reported. It is shown both theoretically and experimentally that a nearly diffraction-limited Gaussian-output laser beam with a large mode volume can be obtained with this cavity design. The laser cavity is particularly interesting for use in high-threshold pumped gain media and eliminates some disadvantages of the SFUR and GSFUR designs. This resonator, with an effective magnification of -6.16, was applied to a pulsed Nd:YAG laser in free-running and in Q-switched modes of operation. The output energy was ∼70 mJ, 5.5 times greater than when a single GSFUR design was used. The output beam had a pulse duration of ∼30 ns in the Q-switched mode of operation and a beam divergence of 0.26 mrad. The required relations for the GSFUR–PBUR optical design and the output energy were derived and verified experimentally.

© 1999 Optical Society of America

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References

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  1. P. G. Gobbi, G. C. Reali, “A novel unstable resonator configuration with a self-filtering aperture,” Opt. Commun. 52, 195–198 (1984).
    [CrossRef]
  2. P. G. Gobbi, S. Morosi, G. C. Reali, A. S. Zarkasi, “Novel unstable resonator with a self-filtering aperture: experimental characterization of the Nd:YAG loaded cavity,” Appl. Opt. 24, 26–33 (1985).
    [CrossRef] [PubMed]
  3. R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
    [CrossRef]
  4. A. Luches, V. Nassisi, M. R. Perrone, “Experimental characterization of a self-filtering unstable resonator applied to a short pulse XeCl laser,” Appl. Opt. 28, 2047–2051 (1989).
    [CrossRef] [PubMed]
  5. R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
    [CrossRef]
  6. V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
    [CrossRef]
  7. J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
    [CrossRef]
  8. L. H. Min, K. Vogler, “Confocal positive branch-filtering unstable resonator for Nd:YAG Laser,” Opt. Commun. 74, 79–83 (1989).
    [CrossRef]
  9. M. R. Perrone, A. A. Filippo, “Experimental characterization of high magnification self-filtering unstable resonators for XeCl lasers,” Opt. Commun. 88, 115–121 (1992).
    [CrossRef]
  10. P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
    [CrossRef]
  11. P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
    [CrossRef]
  12. A. H. Farahbod, A. Hariri, “Application of generalized self-filtering unstable resonators to a N2-laser pumped dye laser,” Opt. Commun. 108, 84–90 (1994).
    [CrossRef]
  13. A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
    [CrossRef]
  14. M. Mahmodi, A. H. Farahbod, A. Hariri, “Experimental study of generalized self-filtering unstable resonators in an ablative-wall flash-lamp-pumped dye laser,” Appl. Opt. 37, 1053–1059 (1998).
    [CrossRef]
  15. W. Koechner, “Solid-State Laser Engineering,” 4th ed., (Springer-Verlag, Berlin, 1996).
  16. A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
    [CrossRef]
  17. P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
    [CrossRef]

1998

1994

A. H. Farahbod, A. Hariri, “Application of generalized self-filtering unstable resonators to a N2-laser pumped dye laser,” Opt. Commun. 108, 84–90 (1994).
[CrossRef]

1992

M. R. Perrone, A. A. Filippo, “Experimental characterization of high magnification self-filtering unstable resonators for XeCl lasers,” Opt. Commun. 88, 115–121 (1992).
[CrossRef]

1990

A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
[CrossRef]

1989

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

L. H. Min, K. Vogler, “Confocal positive branch-filtering unstable resonator for Nd:YAG Laser,” Opt. Commun. 74, 79–83 (1989).
[CrossRef]

A. Luches, V. Nassisi, M. R. Perrone, “Experimental characterization of a self-filtering unstable resonator applied to a short pulse XeCl laser,” Appl. Opt. 28, 2047–2051 (1989).
[CrossRef] [PubMed]

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

1988

P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
[CrossRef]

P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
[CrossRef]

1987

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

1986

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

1985

1984

P. G. Gobbi, G. C. Reali, “A novel unstable resonator configuration with a self-filtering aperture,” Opt. Commun. 52, 195–198 (1984).
[CrossRef]

Barbini, R.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Bhatnagar, R.

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

Boffa, V.

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Chen, J. W.

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

Dixit, S. K.

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

Farahbod, A. H.

M. Mahmodi, A. H. Farahbod, A. Hariri, “Experimental study of generalized self-filtering unstable resonators in an ablative-wall flash-lamp-pumped dye laser,” Appl. Opt. 37, 1053–1059 (1998).
[CrossRef]

A. H. Farahbod, A. Hariri, “Application of generalized self-filtering unstable resonators to a N2-laser pumped dye laser,” Opt. Commun. 108, 84–90 (1994).
[CrossRef]

Filippo, A. A.

M. R. Perrone, A. A. Filippo, “Experimental characterization of high magnification self-filtering unstable resonators for XeCl lasers,” Opt. Commun. 88, 115–121 (1992).
[CrossRef]

Gallerano, G. P.

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Ghigo, A.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Giordano, G.

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Giorgi, M.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Gobbi, P. G.

Hariri, A.

M. Mahmodi, A. H. Farahbod, A. Hariri, “Experimental study of generalized self-filtering unstable resonators in an ablative-wall flash-lamp-pumped dye laser,” Appl. Opt. 37, 1053–1059 (1998).
[CrossRef]

A. H. Farahbod, A. Hariri, “Application of generalized self-filtering unstable resonators to a N2-laser pumped dye laser,” Opt. Commun. 108, 84–90 (1994).
[CrossRef]

A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
[CrossRef]

Hermsen, T.

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

Hermsen, T. W. P. M.

P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
[CrossRef]

Hermson, T.

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Koechner, W.

W. Koechner, “Solid-State Laser Engineering,” 4th ed., (Springer-Verlag, Berlin, 1996).

Lazzaro, P. D.

P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
[CrossRef]

P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
[CrossRef]

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

Letardi, T.

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Luches, A.

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

A. Luches, V. Nassisi, M. R. Perrone, “Experimental characterization of a self-filtering unstable resonator applied to a short pulse XeCl laser,” Appl. Opt. 28, 2047–2051 (1989).
[CrossRef] [PubMed]

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

Lyer, K. N.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Mahmodi, M.

Min, L. H.

L. H. Min, K. Vogler, “Confocal positive branch-filtering unstable resonator for Nd:YAG Laser,” Opt. Commun. 74, 79–83 (1989).
[CrossRef]

Morosi, S.

Nakhe, S. V.

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

Nassisi, V.

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

A. Luches, V. Nassisi, M. R. Perrone, “Experimental characterization of a self-filtering unstable resonator applied to a short pulse XeCl laser,” Appl. Opt. 28, 2047–2051 (1989).
[CrossRef] [PubMed]

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
[CrossRef]

Nayeri, M.

A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
[CrossRef]

Palucci, A.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Perrone, M. R.

M. R. Perrone, A. A. Filippo, “Experimental characterization of high magnification self-filtering unstable resonators for XeCl lasers,” Opt. Commun. 88, 115–121 (1992).
[CrossRef]

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

A. Luches, V. Nassisi, M. R. Perrone, “Experimental characterization of a self-filtering unstable resonator applied to a short pulse XeCl laser,” Appl. Opt. 28, 2047–2051 (1989).
[CrossRef] [PubMed]

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
[CrossRef]

Radiotis, E.

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

Reali, G. C.

Ribezzio, S.

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

Singh, B.

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

Soltanmoradi, F.

A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
[CrossRef]

Vogler, K.

L. H. Min, K. Vogler, “Confocal positive branch-filtering unstable resonator for Nd:YAG Laser,” Opt. Commun. 74, 79–83 (1989).
[CrossRef]

Zarkasi, A. S.

Zheng, C.

P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
[CrossRef]

Zheng, C. E.

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

P. D. Lazzaro, T. W. P. M. Hermsen, C. Zheng, “A generalization of the self-filtering unstable resonator,” IEEE J. Quantum Electron. QE-24, 1543–1547 (1988).
[CrossRef]

P. D. Lazzaro, V. Nassisi, M. R. Perrone, “Experimental study of a generalized self-filtering unstable resonator applied to a XeCl laser,” IEEE J. Quantum Electron. QE-24, 2284–2287 (1988).
[CrossRef]

V. Boffa, P. D. Lazzaro, G. P. Gallerano, G. Giordano, T. Hermson, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator operation of XeCl excimer laser,” IEEE J. Quantum Electron. QE-23, 1241–1244 (1987).
[CrossRef]

Opt. Commun.

J. W. Chen, A. Luches, V. Nassisi, M. R. Perrone, “High brightness single transverse mode operation of XeCl laser,” Opt. Commun. 72, 225–229 (1989).
[CrossRef]

L. H. Min, K. Vogler, “Confocal positive branch-filtering unstable resonator for Nd:YAG Laser,” Opt. Commun. 74, 79–83 (1989).
[CrossRef]

M. R. Perrone, A. A. Filippo, “Experimental characterization of high magnification self-filtering unstable resonators for XeCl lasers,” Opt. Commun. 88, 115–121 (1992).
[CrossRef]

R. Bhatnagar, S. K. Dixit, B. Singh, S. V. Nakhe, “Performance of a copper vapor laser with self-filtered unstable resonator,” Opt. Commun. 74, 93–96 (1989).
[CrossRef]

R. Barbini, A. Ghigo, M. Giorgi, K. N. Lyer, A. Palucci, S. Ribezzio, “Injection-locked single-mode high-power low-divergence TEA CO2 laser using SFUR configuration,” Opt. Commun. 60, 239–243 (1986).
[CrossRef]

A. H. Farahbod, A. Hariri, “Application of generalized self-filtering unstable resonators to a N2-laser pumped dye laser,” Opt. Commun. 108, 84–90 (1994).
[CrossRef]

A. Luches, V. Nassisi, M. R. Perrone, E. Radiotis, “High mode volume self-filtering unstable resonator applied to a short pulse XeCl laser,” Opt. Commun. 71, 97–102 (1989).
[CrossRef]

P. G. Gobbi, G. C. Reali, “A novel unstable resonator configuration with a self-filtering aperture,” Opt. Commun. 52, 195–198 (1984).
[CrossRef]

P. D. Lazzaro, T. Hermsen, T. Letardi, C. E. Zheng, “Self-filtering unstable resonator: an approximate analytical model with comparison to computed and XeCl laser experimental results,” Opt. Commun. 61, 393–396 (1987).
[CrossRef]

Rev. Sci. Instrum.

A. Hariri, F. Soltanmoradi, M. Nayeri, “Generation of single longitudinal mode in a pulsed passively Q-switchedNd:YAG laser,” Rev. Sci. Instrum. 61, 2247–2248 (1990).
[CrossRef]

Other

W. Koechner, “Solid-State Laser Engineering,” 4th ed., (Springer-Verlag, Berlin, 1996).

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic diagram of the coupled GSFUR and PBUR (GSFUR–PBUR) setup: M1, M2, and M3 are totally reflecting mirrors with focal lengths of f 1 = 50 cm, f 2 = 25 cm, and f 3 = -15 cm, respectively. AM, amplifying medium; other abbreviations defined in text. (b) Equivalent sequence of the lenses and field-limiting aperture of the coupled GSFUR–PBUR design. The optical lengths that correspond to the distances GT–OC and GT–FLA have been neglected in the calculation (OC ∼ GT).

Fig. 2
Fig. 2

(a) Plot of the calculated GSFUR–PBUR mode intensity versus radial distance, (b) The phase is almost constant across the beam cross section calculated for one and two round-trip time(s).

Fig. 3
Fig. 3

Plot of the calculated GSFUR–PBUR mode intensity distribution based on the numerical method of Huygens’ integral (solid curve) and Gaussian-beam (dotted curve) approximations.

Fig. 4
Fig. 4

Calculated output energy of the GSFUR and the GSFUR–PBUR systems (E G and E GP ), E GP /E G , and M eff versus GSFUR magnification |M G | (filled circles), experimental values for |M G | = 1.85 and 2a OC = 3.3 mm (filled triangles), and theoretical value for |M G | = 1.85 and 2a OC = 2.98 mm (filled diamonds).

Fig. 5
Fig. 5

Output energy as a function of the charging input energy for the GSFUR–PBUR and GSFUR designs. The scale on the abscissa must be multiplied by ∼0.56 for the lamp’s input energy. The theoretical points show the calculated output energies E GP and E G .

Fig. 6
Fig. 6

Measured value of the reflectivity for the GT–QWP combination (R GT–QWP) as a function of the charging input energy. The scale on the abscissa must be multiplied by ∼0.56 for the lamp’s input energy.

Fig. 7
Fig. 7

Ratio of the GSFUR–PBUR output energy to that of the GSFUR design as a function of the charging input energy, obtained from the data in Fig. 5.

Fig. 8
Fig. 8

Typical Q-switched laser pulses for the GSFUR–PBUR and the GSFUR designs. Time scale, 20 ns/division for both cases.

Fig. 9
Fig. 9

Typical near-field spatial distribution of the GSFUR–PBUR laser beam versus beam radius, measured at a distance of 45 cm from the OC. Solid curve, Gaussian profile of E(r) = E(0)exp(-2r 2/w 2), where E is the energy density.

Fig. 10
Fig. 10

Typical far-field output energy transmitted through calibrated pinholes versus the diameter of the pinholes placed at the focal plane of a focusing lens (f = 100 cm).

Tables (4)

Tables Icon

Table 1 Design Parameters Used for the GSFUR and GSFUR–PBUR Systemsa

Tables Icon

Table 2 Comparison of δ Values

Tables Icon

Table 3 Pumping Rate Parametersa

Tables Icon

Table 4 Experimental and Theoretical Comparison of the GSFUR–PBUR Beam Parametersa

Equations (48)

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

L=f1+f2=D2/λ1/5.491-γdg+1-γdg1/2,
MP  |MG|.
2aOC1.52w3,
A3B3C3D3=2g3-12L3g3-1/f32g3-1,
w3=wGA3+B3RG2+λB3πwG221/2,
wGa|MG|,  RG=-2g2L22g2-1,
a=g2L2λ1/2,  MG=-L1g1L2g2=2g1-12g2-1,
g1=1-L12f1,  g2=1-L22f2.
πλ wG2πλ a2|MG|2=πλg2L2λ2g1-12g2-1|MG|=π2 |MG|2g1-1|RG||RG|.
w3wGA31+B3A3RG=wG2g3-11+2L3g32g3-1RG.
D  1.52w3.
MP  2g3-11-L3g3L2g22g2-12g3-1.
ABCDPBUR=1L10110-1/f111L1+L301×10-1/f311L301.
qO=AqG+BCqG+D,  1qG=1RG-2ikwG2,  1qO=1RO-2ikwO2,
AC+1RGAD+BC+BD 1RG2+λπwG22=0,
δ=L1+L3-f1+f3.
A=MC-δ/f31-L1/f1,  MC=-f1/f3,
C=δ/f1f3,
D=δ/f3δ/f1+1-L1/f1+1/MC,
B=AD-1/C.
δf34S4+δf33S3+δf32S2+δf3S1+S0=0,
S0=-f1γC2g1-11/RG2+λ/πwG22+1/RG,
S1=f12g1-121-2γCMC+1/MC1/RG2+λ/πwG22-MC1/f1+2/RGγC2g1-1,
S2=f12g1-12γC+2g1-121/RG2+λ/πwG22+1/f12g1-1+2/RG2g1-12+1,
S3=-f1/MC2g1-12+11/RG2+λ/πwG22,
S4=f1/MC22g1-11/RG2+λ/πwG22
δf12g1-1γC2g1-122+1πMG2+g11-g12MCg11-g121+γC2g1-122g11-g1-1+2g1-121-2γCMC22g1-122+1πMG2.
wO=wGA+BRG2+BλπwG221/2.
wOa|MG|MC1+f1γCMCRG=a|MG|MC1-f12g2-1γC2MCL2g2.
uGx=-aa-aa uixK2x, xK1x, xdxdx.
u3x=-asas uGxKlx, xdx,  l=3,
Klx, x=iλBl1/2 exp-i k2BlAlx2-2xx+Dlx2,
uO=-asas Klx, xu3xdx,  l=1,
A1B1C1D1=2g1-12L1g1-1/f12g1-1.
αxuix=uOx= uixKxiv, x, x, x, xdxivdxdxdx,
Kxiv, x, x, x, x=K1xiv, x×K3x, xK2x, xK1x, x.
f2  2g2L2,  f1  B1e,
A1eB1eC1eD1e=A1B1C1D1A3B3C3D3A1B1C1D1,
γd1-|αx|21-1.39B1e2L2g21-0.286B1e2L2g22,
dN2/dt=-c/nAMσeΦN2-g2g1 N1-N2/τf+WPt,
dΦ/dt=nAMLAM/Lc/nAMσeΦN2-g2g1 N1-Φ/τc+1/4ππA2/LAM2N2/τf,
EG=RGTQWPhν002π0tpc/nAMϕGt ×exp-2r2/wG2rdrdφdt=RGTQWPhνc/nAMπwG2/2 0tp ϕGtdt,
0tp ϕGtdtτcnAMLAM/LG0tp WPtdt-0tpN2/τfdt-1/cτcσeLG/LAM+τc/τfA/2LAM20tp N2dt.
EG=RGTQWPhνπwG2/2cτc/nAM×nAMLAM/LG0tp WPtdt-1/cσeτcLG/LAM-1τfnAMLAM/LG-A/2LAM20tp N2dt.
EG=RGTQWPhνπwG2/2cτcLAM/LG×0tp WPtdt-1/σe1+tp/τf,
EGP=ROChν02π00tpc/nAMϕGPt×exp-2r2/wO2rdrdφdt-02π0aOC0tpc/nAMϕGPt×exp-2r2/wO2rdrdφdt,
EGP=ROChνπaMeff2/2exp-2aOC/aMeff2×2cτcLAM/LGP0tp WPtdt-1/σe×1+tp/τf1-A/2LAM2LGP/2nAMLAM.
WPt=W0a1 exp-t-t1b12+a2 exp-t-t2b22+a3 exp-t-t3b32,

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