Abstract

Loop resonators with self-pumped phase conjugate mirrors (SPPCM’s) based on a four-wave mixing (FWM) interaction in solid-state saturable amplifiers are investigated in the short-pulse regime. A model using a transient treatment of FWM with the appropriate boundary conditions imposed by the loop geometry allows us to analyze the threshold condition for oscillation, the temporal dynamics, including self-Q switching, and the energy characteristics of such loop resonators. The influence of the gains of the saturable amplifiers and the influence of the transmission factors around the loop are also analyzed. A loop resonator with a SPPCM in a Nd:YAG amplifier is experimentally investigated at λ=1.064 µm in the nanosecond regime. A maximum reflectivity of 42 and a maximum extraction of 47 mJ, corresponding to a 20% extraction efficiency, are measured. Experimental and theoretical results are in good agreement.

© 1997 Optical Society of America

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References

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  1. I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
    [CrossRef]
  2. I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
    [CrossRef]
  3. A. A. Betin and O. V. Mitropol’skiı̆, “Generation of radiation by four-wave interaction in a feedback system in the λ =10 µ range,” Sov. J. Quantum Electron. 17, 636–640 (1987).
    [CrossRef]
  4. A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979).
    [CrossRef]
  5. J. Reintjes and L. J. Palumbo, “Phase conjugation in saturable amplifiers by degenerate frequency mixing,” IEEE J. Quantum Electron. QE-18, 1934–1940 (1982).
    [CrossRef]
  6. J. L. Walsh and J. Reintjes, “Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers,” Opt. Commun. 48, 221–224 (1983).
    [CrossRef]
  7. M. J. Damzen, R. P. M. Green, and G. J. Crofts, “High-reflectivity four-wave mixing by gain saturation of nanosecond and microsecond radiation in Nd:YAG,” Opt. Lett. 17, 1331–1333 (1992).
    [CrossRef] [PubMed]
  8. A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally-polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
    [CrossRef]
  9. A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Multipass degenerate four-wave mixing in a diode-pumped Nd:YVO4 amplifier,” J. Opt. Soc. Am. B 12, 1316–1325 (1995).
    [CrossRef]
  10. G. J. Crofts, X. Banti, and M. J. Damzen, “Tunable phase conjugation in a Ti:sapphire amplifier,” Opt. Lett. 20, 1634–1636 (1995).
    [CrossRef] [PubMed]
  11. A. Brignon and J.-P. Huignard, “Energy efficiency of phase conjugation by saturable-gain degenerate four-wave mixing in Nd:YAG amplifiers,” Opt. Commun. 119, 171–177 (1995).
    [CrossRef]
  12. I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
    [CrossRef]
  13. R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Holographic laser resonators in Nd:YAG,” Opt. Lett. 19, 393–395 (1994).
    [PubMed]
  14. O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).
  15. M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
    [CrossRef] [PubMed]
  16. K. S. Syed, R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
    [CrossRef]
  17. V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).
  18. M. J. Damzen, R. P. M. Green, and K. S. Syed, “Self-adaptive solid-state laser oscillator formed by dynamic gain-grating holograms,” Opt. Lett. 20, 1704–1706 (1995).
    [CrossRef]
  19. A. Brignon and J.-P. Huignard, “Two-wave mixing in Nd:YAG by gain saturation,” Opt. Lett. 18, 1639–1641 (1993).
    [CrossRef] [PubMed]
  20. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  21. P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
    [CrossRef]
  22. A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing in saturable absorbers: application to Cr4+:GSGG at 1.06 µm,” Opt. Commun. 110, 717–726 (1994).
    [CrossRef]

1997 (1)

P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
[CrossRef]

1995 (4)

1994 (6)

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Holographic laser resonators in Nd:YAG,” Opt. Lett. 19, 393–395 (1994).
[PubMed]

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Reflectivity and oscillation conditions of a gain medium in a self-conjugating loop geometry,” Opt. Lett. 19, 34–36 (1994).
[CrossRef] [PubMed]

K. S. Syed, R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally-polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing in saturable absorbers: application to Cr4+:GSGG at 1.06 µm,” Opt. Commun. 110, 717–726 (1994).
[CrossRef]

1993 (1)

1992 (1)

1989 (1)

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

1988 (1)

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

1987 (1)

A. A. Betin and O. V. Mitropol’skiı̆, “Generation of radiation by four-wave interaction in a feedback system in the λ =10 µ range,” Sov. J. Quantum Electron. 17, 636–640 (1987).
[CrossRef]

1986 (1)

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

1984 (1)

I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
[CrossRef]

1983 (1)

J. L. Walsh and J. Reintjes, “Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers,” Opt. Commun. 48, 221–224 (1983).
[CrossRef]

1982 (1)

J. Reintjes and L. J. Palumbo, “Phase conjugation in saturable amplifiers by degenerate frequency mixing,” IEEE J. Quantum Electron. QE-18, 1934–1940 (1982).
[CrossRef]

1979 (1)

A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979).
[CrossRef]

Antipov, O. L.

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).

Banti, X.

Bel’dyugin, I. M.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
[CrossRef]

Belyaev, S. I.

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).

Berenberg, V. A.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Betin, A. A.

A. A. Betin and O. V. Mitropol’skiı̆, “Generation of radiation by four-wave interaction in a feedback system in the λ =10 µ range,” Sov. J. Quantum Electron. 17, 636–640 (1987).
[CrossRef]

Brignon, A.

P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Multipass degenerate four-wave mixing in a diode-pumped Nd:YVO4 amplifier,” J. Opt. Soc. Am. B 12, 1316–1325 (1995).
[CrossRef]

A. Brignon and J.-P. Huignard, “Energy efficiency of phase conjugation by saturable-gain degenerate four-wave mixing in Nd:YAG amplifiers,” Opt. Commun. 119, 171–177 (1995).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally-polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing in saturable absorbers: application to Cr4+:GSGG at 1.06 µm,” Opt. Commun. 110, 717–726 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Two-wave mixing in Nd:YAG by gain saturation,” Opt. Lett. 18, 1639–1641 (1993).
[CrossRef] [PubMed]

Crofts, G. J.

Damzen, M. J.

Feugnet, G.

Galushkin, M. G.

I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
[CrossRef]

Green, R. P. M.

Huignard, J.-P.

P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Multipass degenerate four-wave mixing in a diode-pumped Nd:YVO4 amplifier,” J. Opt. Soc. Am. B 12, 1316–1325 (1995).
[CrossRef]

A. Brignon and J.-P. Huignard, “Energy efficiency of phase conjugation by saturable-gain degenerate four-wave mixing in Nd:YAG amplifiers,” Opt. Commun. 119, 171–177 (1995).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally-polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing in saturable absorbers: application to Cr4+:GSGG at 1.06 µm,” Opt. Commun. 110, 717–726 (1994).
[CrossRef]

A. Brignon and J.-P. Huignard, “Two-wave mixing in Nd:YAG by gain saturation,” Opt. Lett. 18, 1639–1641 (1993).
[CrossRef] [PubMed]

Kharchenko, M. A.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Kireev, S. E.

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

Kuzhelev, A. S.

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).

Mitropol’skii?, O. V.

A. A. Betin and O. V. Mitropol’skiı̆, “Generation of radiation by four-wave interaction in a feedback system in the λ =10 µ range,” Sov. J. Quantum Electron. 17, 636–640 (1987).
[CrossRef]

Mochalov, I. V.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Odintsov, A. I.

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

Palumbo, L. J.

J. Reintjes and L. J. Palumbo, “Phase conjugation in saturable amplifiers by degenerate frequency mixing,” IEEE J. Quantum Electron. QE-18, 1934–1940 (1982).
[CrossRef]

Petnikova, V. M.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

Petrovskii, G. T.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Pocholle, J.-P.

Reintjes, J.

J. L. Walsh and J. Reintjes, “Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers,” Opt. Commun. 48, 221–224 (1983).
[CrossRef]

J. Reintjes and L. J. Palumbo, “Phase conjugation in saturable amplifiers by degenerate frequency mixing,” IEEE J. Quantum Electron. QE-18, 1934–1940 (1982).
[CrossRef]

Shuvalov, V. V.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Siegman, A. E.

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

Sillard, P.

P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
[CrossRef]

Syed, K. S.

M. J. Damzen, R. P. M. Green, and K. S. Syed, “Self-adaptive solid-state laser oscillator formed by dynamic gain-grating holograms,” Opt. Lett. 20, 1704–1706 (1995).
[CrossRef]

K. S. Syed, R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

Tomita, A.

A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979).
[CrossRef]

Vasil’ev, A. E.

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Walsh, J. L.

J. L. Walsh and J. Reintjes, “Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers,” Opt. Commun. 48, 221–224 (1983).
[CrossRef]

Zemskov, E. M.

I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
[CrossRef]

Zolotarev, M. V.

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Reintjes and L. J. Palumbo, “Phase conjugation in saturable amplifiers by degenerate frequency mixing,” IEEE J. Quantum Electron. QE-18, 1934–1940 (1982).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonally-polarized pump beams in a saturable Nd:YAG amplifier,” IEEE J. Quantum Electron. 30, 2203–2210 (1994).
[CrossRef]

P. Sillard, A. Brignon, and J.-P. Huignard, “Nd:YAG loop resonator with a Cr4+:YAG self-pumped phase conjugate mirror,” IEEE J. Quantum Electron. 33, 483–489 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Laser crystal with nonreciprocal feedback as a parametric mirror which performs passive optical phase conjugation,” JETP Lett. 60, 165–170 (1994).

Opt. Commun. (4)

A. Brignon and J.-P. Huignard, “Energy efficiency of phase conjugation by saturable-gain degenerate four-wave mixing in Nd:YAG amplifiers,” Opt. Commun. 119, 171–177 (1995).
[CrossRef]

K. S. Syed, R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Transient modeling of pulsed phase conjugation experiments in a saturable Nd:YAG amplifier,” Opt. Commun. 112, 175–180 (1994).
[CrossRef]

J. L. Walsh and J. Reintjes, “Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers,” Opt. Commun. 48, 221–224 (1983).
[CrossRef]

A. Brignon and J.-P. Huignard, “Transient analysis of degenerate four-wave mixing in saturable absorbers: application to Cr4+:GSGG at 1.06 µm,” Opt. Commun. 110, 717–726 (1994).
[CrossRef]

Opt. Lett. (6)

Opt. Spektrosk. (1)

V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Emission of solid-state lasers with a self-pumped phase-conjugation resonator,” Opt. Spektrosk. 65, 302–312 (1988).

Sov. J. Quantum Electron. (4)

I. M. Bel’dyugin, V. A. Berenberg, A. E. Vasil’ev, I. V. Mochalov, V. M. Petnikova, G. T. Petrovskii, M. A. Kharchenko, and V. V. Shuvalov, “Solid state lasers with self-pumped phase-conjugate mirrors in an active medium,” Sov. J. Quantum Electron. 19, 740–742 (1989).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, and E. M. Zemskov, “Wavefront reversal of optical radiation using feedback in four-wave interaction,” Sov. J. Quantum Electron. 14, 602–605 (1984).
[CrossRef]

I. M. Bel’dyugin, M. V. Zolotarev, S. E. Kireev, and A. I. Odintsov, “Copper vapor laser with a self-pumped wavefront-reversing mirror,” Sov. J. Quantum Electron. 16, 535–537 (1986).
[CrossRef]

A. A. Betin and O. V. Mitropol’skiı̆, “Generation of radiation by four-wave interaction in a feedback system in the λ =10 µ range,” Sov. J. Quantum Electron. 17, 636–640 (1987).
[CrossRef]

Other (1)

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

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the loop geometry of the resonator with a SPPCM.

Fig. 2
Fig. 2

Theoretical curves of the net round-trip gain γ(t) and the output intensity Iout(t) of the loop resonator with a SPPCM as a function of time (a) for a Gaussian input pulse and (b) for a multipeak input pulse Iin(t). The input fluence is fixed at Uin =0.04Usat.

Fig. 3
Fig. 3

Minimum α0L required in amplifier G inside the loop cavity to reach threshold as a function of α0L in amplifier G used for FWM.

Fig. 4
Fig. 4

Round-trip gain γ at the end of the writing period and output fluence Uout versus the input fluence Uin normalized to the saturation fluence Usat.

Fig. 5
Fig. 5

Round-trip gain γ at the end of the writing period and output fluence Uout versus the writing beam fluence ratio β =Uin/U3. The input fluence is fixed at Uin=0.04Usat, which corresponds to the theoretical maximum extraction from the loop resonator.

Fig. 6
Fig. 6

Schematic diagram of the experiment of the loop resonator with a Nd:YAG SPPCM at λ=1.064 µm in the nanosecond regime: FI, Faraday isolator; D’s, pyroelectric detectors; BS, beam splitter; G, G, flash-lamp-pumped Nd:YAG amplifiers; P’s, Glan polarizers; FR, Faraday rotator; λ/2, half-wave plate.

Fig. 7
Fig. 7

(a) Distorted spatial profile of beam A3 after it has propagated around the loop cavity and before it interferes with A1. (b) High-quality diffraction-limited TEM00 profile of the output beam extracted from the loop resonator.

Fig. 8
Fig. 8

(a) Multipeak temporal trace of the input beam. (b) Temporal trace of the output beam for maximum extraction. The mode beating corresponds to the round-trip time of the loop cavity, 7 ns.

Fig. 9
Fig. 9

Experimental (symbols) and theoretical (curves) plots of the output fluence Uout normalized to Usat and the reflectivity, R=Uout/Uin, versus Uin/Usat.

Fig. 10
Fig. 10

(Bottom) experimental plots of the output fluence normalized to Usat versus Uin/Usat for a fixed value of α0L=3.6 in amplifier G used for FWM and for different values of α0L in amplifier G inside the loop. (Top) theoretical curves plotted with the experimental parameters.

Fig. 11
Fig. 11

(Bottom) experimental plots of the output fluence normalized to Usat versus Uin/Usat for a fixed value of α0L=3.4 in amplifier G inside the loop and for different values of α0L in amplifier G used for FWM. (Top) theoretical curves plotted with the experimental parameters.

Fig. 12
Fig. 12

(Bottom) experimental plots of the output fluence Uout normalized to Usat versus the writing beam’s fluence ratio β for Uin=0.027Usat and for Uin=0.083Usat. (Top) theoretical curves plotted with the experimental parameters.

Fig. 13
Fig. 13

Energy characteristics of the Nd:YAG loop resonator with a SPPCM in a Cr4+:GSGG saturable absorber. (Bottom) experimental plots of the output fluence normalized to Usatabs and the reflectivity, R=Uout/Uin, versus Uin/Usatabs. (Top) theoretical curves plotted with the experimental parameters.

Equations (21)

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E(r, t)=j=14 Aj(z, t)exp[-i(kjr-ωt)]e,
E(r, t)=A1(z, t)exp[-i(k1r-ωt)]e+A4(z, t)exp[-i(k4r-ωt)]e.
d|A1|dz=γ0|A1|-γ1|A3|,
d|A3|dz=γ0|A3|-γ1|A1|,
d|A2|dz=-γ0|A2|-γ1|A4|,
d|A4|dz=-γ0|A4|-γ1|A2|,
γn(z, t)=α02exp-0t |A1|2dtUsat-0t |A3|2dtUsat×In2 0t |A1||A3|dtUsat,
d|A1|dz=γ0|A1|,
d|A4|dz=-γ0|A4|,
γ0(z, t)=α02exp-0t |A1|2dtUsat,
|A1(z=0, t)|2=inputpulseintensity,
|A1(z=0, t)|2=|A1(z=L, t-t1)|2Tc,
|A3(z=0, t)|2=|A1(z=L, t-t2)|2,
|A2(z=L, t)|2=intracavityintensityI(t),
|A4(z=L, t)|2=0,
|A4(z=L, t)|2=|A4(z=0, t-t2)|2,
γ(t)=|A4(z=0, t)|2|A2(z=L, t)|2|A4(z=0, t)|2|A4(z=L, t)|2Ta.
dIdt=1Tln[γ(t)]I(t).
γ0,1(z, t)=α02exp-0tp |A1|2dtUsat-TT+tp |A3|2dtUsat-T+tpt |A2|2+|A4|2dtUsat×I0,12 Ttp |A1||A3|dtUsat-2 T+tpt |A2||A4|dtUsat,
γ0(z, t)=α02exp-t1t1+tp |A1|2dtUsat-(T+tp)+t2t |A4|2dtUsat.
=UoutUin+(α0L+α0L)Usat.

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