Abstract

We investigate both theoretically and experimentally a self-pumped phase-conjugate resonator with two-pass four-wave mixing in a diode-pumped Nd:YAG amplifier. A transient model is presented to fit the energy and temporal results of the experiment. The influence of the input energy in the injected configuration and the influence of the output coupler reflectivity and diode pump energy in the self-starting configuration are analyzed. In the injected case a maximum phase-conjugate reflectivity of 32 is obtained. In the self-starting case a TEM00 mode of 5.5 mJ in a 20-ns single-longitudinal-mode pulse is produced with a 10% reflectivity output coupler.

© 1998 Optical Society of America

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  1. I. M. Bel’dyugin, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
    [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. M. Ouhayoun and Y. Guern, “Laser mirror by degenerate four-wave mixing in a saturable amplifier,” IEEE J. Quantum Electron. QE-22, 2150–2153 (1986).
    [CrossRef]
  4. 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).
  5. 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]
  6. A. Tomita, “Phase conjugation using gain saturation of a Nd:YAG laser,” Appl. Phys. Lett. 34, 463–464 (1979).
    [CrossRef]
  7. R. A. Fisher and B. J. Feldman, “On-resonant phase-conjugate reflection and amplification at 10.6 μm in inverted CO2,” Opt. Lett. 4, 140–142 (1979).
    [CrossRef] [PubMed]
  8. Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
    [CrossRef]
  9. 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]
  10. F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
    [CrossRef]
  11. J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (1983).
    [CrossRef]
  12. J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
    [CrossRef]
  13. R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
    [CrossRef]
  14. 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]
  15. 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]
  16. M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
    [CrossRef]
  17. P. Sillard, A. Brignon, and J.-P. Huignard, “Loop resonators with self-pumped phase-conjugate mirrors in solid-state saturable amplifiers,” J. Opt. Soc. Am. B 14, 2049–2058 (1997).
    [CrossRef]
  18. A. V. Kirsanov and V. V. Yarovoĭ, “Phase conjugation of a speckle-inhomogeneous beam by an Nd glass oscillator based on four-wave mixing with feedback,” Quantum Electron. 27, 239–244 (1997).
    [CrossRef]
  19. 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] [PubMed]
  20. P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
    [CrossRef]
  21. A. Minassian, G. J. Crofts, and M. J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator,” Opt. Lett. 22, 697–699 (1997).
    [CrossRef] [PubMed]
  22. P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
    [CrossRef]
  23. A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Large-field-of-view, high-gain, compact diode-pumped Nd:YAG amplifier,” Opt. Lett. 22, 1421–1423 (1997).
    [CrossRef]
  24. G. Feugnet and J.-P. Pocholle, “8-mJ TEM00 diode-end-pumped frequency-quadrupled Nd:YAG laser,” Opt. Lett. 23, 55–57 (1998).
    [CrossRef]
  25. A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Compact Nd:YAG and Nd:YVO4 amplifiers end-pumped by a high-brightness stacked array,” IEEE J. Quantum Electron. 34, 577–585 (1998).
    [CrossRef]
  26. P. Sillard, A. Brignon, J.-P. Huignard, and J. P. Pocholle, “Self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator,” Opt. Lett. 23, 1093–1095 (1998).
    [CrossRef]
  27. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
  28. S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
    [CrossRef]
  29. G. Feugnet, C. Bussac, C. Larat, M. Schwarz, and J.-P. Pocholle, “High-efficiency TEM00 Nd:YVO4 laser longitudinally pumped by a high-power array,” Opt. Lett. 20, 157–159 (1995).
    [CrossRef] [PubMed]
  30. M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
    [CrossRef]
  31. K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient analysis of four-grating co-polarized four-wave mixing in saturable gain media with finite probe,” J. Opt. Soc. Am. B 13, 1892–1904 (1996).
    [CrossRef]
  32. P. Sillard, C. Grange, A. Brignon, and J.-P. Huignard, “In-line Nd:YAG resonator using self-pumped phase conjugation in Cr4+:YAG,” Opt. Lett. 23, 37–39 (1998).
    [CrossRef]
  33. K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
    [CrossRef]

1998 (6)

P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Compact Nd:YAG and Nd:YVO4 amplifiers end-pumped by a high-brightness stacked array,” IEEE J. Quantum Electron. 34, 577–585 (1998).
[CrossRef]

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

P. Sillard, C. Grange, A. Brignon, and J.-P. Huignard, “In-line Nd:YAG resonator using self-pumped phase conjugation in Cr4+:YAG,” Opt. Lett. 23, 37–39 (1998).
[CrossRef]

G. Feugnet and J.-P. Pocholle, “8-mJ TEM00 diode-end-pumped frequency-quadrupled Nd:YAG laser,” Opt. Lett. 23, 55–57 (1998).
[CrossRef]

P. Sillard, A. Brignon, J.-P. Huignard, and J. P. Pocholle, “Self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator,” Opt. Lett. 23, 1093–1095 (1998).
[CrossRef]

1997 (5)

P. Sillard, A. Brignon, and J.-P. Huignard, “Loop resonators with self-pumped phase-conjugate mirrors in solid-state saturable amplifiers,” J. Opt. Soc. Am. B 14, 2049–2058 (1997).
[CrossRef]

A. Minassian, G. J. Crofts, and M. J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator,” Opt. Lett. 22, 697–699 (1997).
[CrossRef] [PubMed]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Large-field-of-view, high-gain, compact diode-pumped Nd:YAG amplifier,” Opt. Lett. 22, 1421–1423 (1997).
[CrossRef]

A. V. Kirsanov and V. V. Yarovoĭ, “Phase conjugation of a speckle-inhomogeneous beam by an Nd glass oscillator based on four-wave mixing with feedback,” Quantum Electron. 27, 239–244 (1997).
[CrossRef]

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[CrossRef]

1996 (1)

1995 (3)

1994 (2)

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (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]

1993 (1)

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

1990 (1)

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

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 (2)

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).

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

1986 (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]

M. Ouhayoun and Y. Guern, “Laser mirror by degenerate four-wave mixing in a saturable amplifier,” IEEE J. Quantum Electron. QE-22, 2150–2153 (1986).
[CrossRef]

1985 (1)

I. M. Bel’dyugin, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[CrossRef]

1984 (1)

J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

1983 (1)

J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (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]

1981 (2)

F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
[CrossRef]

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

1979 (2)

Barashkov, M. S.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

Bel’dyugin, B. Y.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

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, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[CrossRef]

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).

Brignon, A.

P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Compact Nd:YAG and Nd:YVO4 amplifiers end-pumped by a high-brightness stacked array,” IEEE J. Quantum Electron. 34, 577–585 (1998).
[CrossRef]

P. Sillard, C. Grange, A. Brignon, and J.-P. Huignard, “In-line Nd:YAG resonator using self-pumped phase conjugation in Cr4+:YAG,” Opt. Lett. 23, 37–39 (1998).
[CrossRef]

P. Sillard, A. Brignon, J.-P. Huignard, and J. P. Pocholle, “Self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator,” Opt. Lett. 23, 1093–1095 (1998).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Large-field-of-view, high-gain, compact diode-pumped Nd:YAG amplifier,” Opt. Lett. 22, 1421–1423 (1997).
[CrossRef]

P. Sillard, A. Brignon, and J.-P. Huignard, “Loop resonators with self-pumped phase-conjugate mirrors in solid-state saturable amplifiers,” J. Opt. Soc. Am. B 14, 2049–2058 (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, “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]

Bunkin, F. V.

F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
[CrossRef]

Bussac, C.

Crofts, G. J.

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

A. Minassian, G. J. Crofts, and M. J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator,” Opt. Lett. 22, 697–699 (1997).
[CrossRef] [PubMed]

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient analysis of four-grating co-polarized four-wave mixing in saturable gain media with finite probe,” J. Opt. Soc. Am. B 13, 1892–1904 (1996).
[CrossRef]

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Damzen, M. J.

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

A. Minassian, G. J. Crofts, and M. J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator,” Opt. Lett. 22, 697–699 (1997).
[CrossRef] [PubMed]

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient analysis of four-grating co-polarized four-wave mixing in saturable gain media with finite probe,” J. Opt. Soc. Am. B 13, 1892–1904 (1996).
[CrossRef]

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] [PubMed]

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Diels, J. C.

J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

Djeu, N.

J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (1983).
[CrossRef]

Dutton, T. E.

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

Feldman, B. J.

Feugnet, G.

Fisher, R. A.

Grange, C.

Green, R. P. M.

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] [PubMed]

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

Guern, Y.

M. Ouhayoun and Y. Guern, “Laser mirror by degenerate four-wave mixing in a saturable amplifier,” IEEE J. Quantum Electron. QE-22, 2150–2153 (1986).
[CrossRef]

Huignard, J.-P.

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Compact Nd:YAG and Nd:YVO4 amplifiers end-pumped by a high-brightness stacked array,” IEEE J. Quantum Electron. 34, 577–585 (1998).
[CrossRef]

P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

P. Sillard, A. Brignon, J.-P. Huignard, and J. P. Pocholle, “Self-pumped phase-conjugate diode-pumped Nd:YAG loop resonator,” Opt. Lett. 23, 1093–1095 (1998).
[CrossRef]

P. Sillard, C. Grange, A. Brignon, and J.-P. Huignard, “In-line Nd:YAG resonator using self-pumped phase conjugation in Cr4+:YAG,” Opt. Lett. 23, 37–39 (1998).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Large-field-of-view, high-gain, compact diode-pumped Nd:YAG amplifier,” Opt. Lett. 22, 1421–1423 (1997).
[CrossRef]

P. Sillard, A. Brignon, and J.-P. Huignard, “Loop resonators with self-pumped phase-conjugate mirrors in solid-state saturable amplifiers,” J. Opt. Soc. Am. B 14, 2049–2058 (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, “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]

Hutchinson, J. A.

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

Kharchenko, M. A.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

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).

Kir’yanov, Y. F.

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

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]

Kirsanov, A. V.

A. V. Kirsanov and V. V. Yarovoĭ, “Phase conjugation of a speckle-inhomogeneous beam by an Nd glass oscillator based on four-wave mixing with feedback,” Quantum Electron. 27, 239–244 (1997).
[CrossRef]

Kochemasov, G. G.

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

Kriminskii?, M. I.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

Larat, C.

Martynova, S. M.

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

McMichael, I.

J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[CrossRef]

Minassian, A.

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).

Nikolaev, V. D.

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

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]

Oshkin, S. P.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

Ouhayoun, M.

M. Ouhayoun and Y. Guern, “Laser mirror by degenerate four-wave mixing in a saturable amplifier,” IEEE J. Quantum Electron. QE-22, 2150–2153 (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]

Pashinin, P. P.

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[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.

Pocholle, J.-P.

Reintjes, J.

J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (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]

Rentzepis, P. M.

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

Saltiel, S. M.

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

Savranskii?, V. V.

F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
[CrossRef]

Schwarz, M.

Shafeev, G. A.

F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
[CrossRef]

Shkolvskii?, E. I.

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[CrossRef]

Shkunov, V. V.

I. M. Bel’dyugin, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[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).

Sidorin, V. S.

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[CrossRef]

Sillard, P.

Syed, K. S.

Tomita, A.

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

Tumorin, V. V.

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[CrossRef]

Ummov, A. F.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

Van Wonterghem, B.

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

Vanherzeele, H.

J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[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. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (1983).
[CrossRef]

Wexler, B. L.

J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (1983).
[CrossRef]

Yarovoi?, V. V.

A. V. Kirsanov and V. V. Yarovoĭ, “Phase conjugation of a speckle-inhomogeneous beam by an Nd glass oscillator based on four-wave mixing with feedback,” Quantum Electron. 27, 239–244 (1997).
[CrossRef]

Zel’dovich, B. Y.

I. M. Bel’dyugin, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[CrossRef]

Zolotarev, M. V.

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[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, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[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. (7)

M. Ouhayoun and Y. Guern, “Laser mirror by degenerate four-wave mixing in a saturable amplifier,” IEEE J. Quantum Electron. QE-22, 2150–2153 (1986).
[CrossRef]

P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quantum Electron. 34, 465–472 (1998).
[CrossRef]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, “Compact Nd:YAG and Nd:YVO4 amplifiers end-pumped by a high-brightness stacked array,” IEEE J. Quantum Electron. 34, 577–585 (1998).
[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]

J. C. Diels, I. McMichael, and H. Vanherzeele, “Degenerate four-wave mixing of picosecond pulses in the saturable amplification of a dye laser,” IEEE J. Quantum Electron. QE-20, 630–636 (1984).
[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]

S. M. Saltiel, B. Van Wonterghem, T. E. Dutton, J. A. Hutchinson, and P. M. Rentzepis, “Investigation of retroreflection scheme for optical phase conjugation by degenerate four-wave mixing,” IEEE J. Quantum Electron. 24, 2302–2307 (1988).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. (Paris) (1)

J. Reintjes, B. L. Wexler, N. Djeu, and J. L. Walsh, “Degenerate frequency mixing in saturable amplifiers,” J. Phys. (Paris) 44, C2–27–C2–37 (1983).
[CrossRef]

Opt. Commun. (3)

R. P. M. Green, G. J. Crofts, and M. J. Damzen, “Phase conjugate reflectivity and diffraction efficiency of gain gratings in Nd:YAG,” Opt. Commun. 102, 288–292 (1993).
[CrossRef]

M. J. Damzen, R. P. M. Green, and G. J. Crofts, “Spatial characteristics of a laser oscillator formed by optically-written holographic gain-grating,” Opt. Commun. 110, 152–156 (1994).
[CrossRef]

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient modelling of a self-starting holographic laser oscillator,” Opt. Commun. 146, 181–185 (1998).
[CrossRef]

Opt. Lett. (8)

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).

Quantum Electron. (2)

A. V. Kirsanov and V. V. Yarovoĭ, “Phase conjugation of a speckle-inhomogeneous beam by an Nd glass oscillator based on four-wave mixing with feedback,” Quantum Electron. 27, 239–244 (1997).
[CrossRef]

P. P. Pashinin, V. S. Sidorin, V. V. Tumorin, and E. I. Shkolvskiĭ, “Laser with stimulated-Brillouin-scattering and self-pumping phase-conjugating mirrors,” Quantum Electron. 27, 52–53 (1997).
[CrossRef]

Sov. J. Quantum Electron. (6)

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, B. Y. Zel’dovich, M. V. Zolotarev, and V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1600 (1985).
[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]

Y. F. Kir’yanov, G. G. Kochemasov, S. M. Martynova, and V. D. Nikolaev, “Four-wave mixing in resonantly amplifying media in the inversion saturation regime,” Sov. J. Quantum Electron. 11, 1047–1051 (1981).
[CrossRef]

F. V. Bunkin, V. V. Savranskiĭ, and G. A. Shafeev, “Resonant wavefront reversal in an active medium containing copper vapor,” Sov. J. Quantum Electron. 11, 810–810 (1981).
[CrossRef]

M. S. Barashkov, B. Y. Bel’dyugin, M. V. Zolotarev, M. I. Kriminskiĭ, S. P. Oshkin, A. F. Ummov, and M. A. Kharchenko, “Stimulated emission in a solid-state ring laser with a stimulated Brillouin scattering mirror,” Sov. J. Quantum Electron. 20, 631–633 (1990).
[CrossRef]

Other (1)

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

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Figures (12)

Fig. 1
Fig. 1

Schematic of the experiment of the SPPC resonator with two-pass FWM in a diode-pumped Nd:YAG amplifier. Ga, Gb, and Gc: diode-end-pumped Nd:YAG amplifiers; P: Glan polarizer; FR: Faraday rotator; λ/2: half-wave plate; Tc: transmission factor in the clockwise direction; Ta: transmission factor in the anticlockwise direction; f: long focal lens.

Fig. 2
Fig. 2

Schematic of (a) the two-pass FWM geometry in amplifier Ga and of (b), (c) the two-pass amplification geometries in amplifiers Gb and Gc, respectively.

Fig. 3
Fig. 3

Phase-conjugate reflectivity R=Uout/Uin as a function of the input fluence Uin, normalized to Usat, for the injected configuration in a two-pass FWM geometry with αaLa=1.5 with uniform gains (solid curve) and distributed gains (dashed curve). Phase-conjugate reflectivities obtained with single-pass FWM geometries (αaLa=1.5 and αaLa=3) are shown as the dotted curves for comparison. αbLb=αcLc=1.3.

Fig. 4
Fig. 4

Output fluence Uout, normalized to Usat, as a function of the output coupler reflectivity Roc, for the self-starting configuration in a two-pass FWM geometry with αaLa=1.5 (solid curve). Output fluences obtained with single-pass FWM geometries (αaLa=1.5 and αaLa=3) are shown as the dotted curves for comparison. αbLb=αcLc=1.3.

Fig. 5
Fig. 5

(a) Input spatial profile. (b) High-quality output spatial profile from the injected configuration. (c) Distorted spatial profile of a TEM00 beam after the beam passes through the phase plate aberrator. (d) Output spatial profile corrected for those aberrations.

Fig. 6
Fig. 6

(a) Experimental plots of the output fluence Uout/Usat, and the phase-conjugate reflectivity R versus Uin/Usat for the injected configuration. (b) Theoretical curves plotted with the experimental parameters.  

Fig. 7
Fig. 7

(a) Temporal trace of the input and output beams from the injected configuration for Uin=0.04 Usat. (b) Theoretical curves of the input intensity Iin(t), the round-trip gain γ(t), and the output intensity Iout(t), plotted with the experimental parameters.

Fig. 8
Fig. 8

(a) High-quality diffraction-limited TEM00 profile of the output beam from the self-starting configuration. (b) Distorted spatial profile of a TEM00 beam after the beam passes through the phase plate aberrator. (c) Output spatial profile corrected for those aberrations.

Fig. 9
Fig. 9

(a) Experimental plots of the output fluence Uout/Usat versus the output coupler reflectivity Roc, for the self-starting configuration. (b) Theoretical curve plotted with the experimental parameters.

Fig. 10
Fig. 10

(a) Temporal output trace from the self-starting configuration with Roc=10%. (b) Theoretical curves of the round-trip gain γ(t) and the output intensity Iout(t), plotted with the experimental parameters. The origin of time is chosen arbitrarily.

Fig. 11
Fig. 11

Q-switched output pulses from the self-starting version for Roc=10% and Roc=40% with the corresponding pump pulse.

Fig. 12
Fig. 12

(a) Experimental plots of the output fluence Uout/Usat as a function of the pump energy incident upon the crystals Ep, for the self-starting version for Roc=10% and for Roc=40%. (b) Theoretical curves plotted with the experimental parameters.

Tables (1)

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Table 1 Conditions for Nonlinear Coefficients γa,jh

Equations (69)

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Ea(z, t)=j=14Aj(z, t)exp(-ijkzj)+j=14Aj(z, t)exp(ijkzj),
Eb(z, t)=j=12Bj(z, t)exp(-ijkzj)+j=12Bj(z, t)exp(ijkzj),
Ec(z, t)=j=12Cj(z, t)exp(-ijkzj)+j=12Cj(z, t)exp(ijkzj).
χy(z, t)=igy(z)kexp-0t|Ey(z, t)|2dtUsat,
χa(z, t)=2iΓakexp{-Ua,12cos[k(1z1-2z2)]}×exp{-Ua,13cos[k(1z1-3z3)]}×exp{-Ua,14cos[k(1z1-4z4)]}×exp{-Ua,23cos[k(2z2-3z3)]}×exp{-Ua,24cos[k(2z2-4z4)]}×exp{-Ua,34cos[k(3z3-4z4)]},
Γa=ga(z)2exp-12j=14Ua,jj,
Ua,jh(z, t)=20tAjAhdtUsat.
χa(z, t)=2iΓakn23=-n24=-n34=-(-1)NaI|n23|(Ua,23)×I|n24|(Ua,24)I|n34|(Ua,34)exp[-ik(N22z2+N33z3+N44z4)],
dA1dz=Γaγa,00A1,
jdAjdz=Γaγa,00Aj+hjγa,jhAh,
-dA1dz=Γaγa,00A1,
-jdAjdz=Γaγa,00Aj+hjγa,jhAh,
γa,jh=n23=-n24=-n34=-(-1)NaI|n23|(Ua,23)×I|n24|(Ua,24)I|n34|(Ua,34),
N2=N3=N4=0forγa,00,
Nj=1,Nh=-1,Nk=0,
withj=(2, 3), h=(3, 4), kj,hforγa,jh.
χy(z, t)=2iΓykNy(-1)NyI|Ny|(Uy,12)×exp[-ikNy(1z1-2z2)],
Γy=gy(z)2exp-12j=12Uy,jj,
Ub,jh(z, t)=20tBjBhdtUsat,
Uc,jh(z, t)=20tCjChdtUsat,
jdBjdz=Γb(γb,0Bj-γb,1Bj+j),
-jdBjdz=Γb(γb,0Bj-γb,1Bj+j),
jdCjdz=Γc(γc,0Cj-γc,1Cj+j),
-jdCjdz=Γc(γc,0Cj-γc,1Cj+j),
|A1(0, t)|2 =inputpulseintensity,
|A2(La, t)|2 = |A1(La, t)|2,
|B1(0, t)|2 = |A2(0, t-ta)|2Tc,
|B2(Lb, t)|2 = |B1(Lb, t)|2,
|C1(0, t)|2 = |B2(0, t-tb)|2,
|C2(Lc, t)|2 = |C1(Lc, t)|2,
|A3(0, t)|2 = |C2(0, t-tc)|2,
|A4(La, t)|2 = |A3(La, t)|2,
|A2(0, t)|2 =intracavityintensityI(t),
|A1(La, t)|2 = |A2(La, t)|2,
|A4(0, t)|2 =0;
A3(La, t)|2 = |A4(La, t)|2,
|C2(0, t)|2 = |A3(0, t-tc)|2,
|C1(Lc, t)|2 = |C2(Lc, t)|2,
|B2(0, t)|2 = |C1(0, t-tb)|2,
|B1(Lb, t)|2 = |B2(Lb, t)|2,
γ(t)=|A3(0, t)|2|A2(0, t)|2|C1(0, t)|2|C2(0, t)|2|B1(0, t)|2|B2(0, t)|2 Ta.
dIdt=1Tln[γ(t)]I(t).
Ua,jh(z, t)=20T+tpAjAhdtUsat+2T+tptAjAhdtUsat,
Ub,jh(z, t)=2tata+tpBjBhdtUsat+2(T+tp)+(tc+tb)tBjBhdtUsat,
Uc,jh(z, t)=2(ta+tb)(ta+tb)+tpCjChdtUsat+2(T+tp)+tctCjChdtUsat,
χa(z, t)=2iΓakexp{-(Ua,24+Ua,24)×cos[k(2z2-4z4)]}×exp{-(Ua,24+Ua,24)×cos[k(2z2+4z4)]}×exp[-Ua,22cos(2k2z2)-Ua,44cos(2k4z4)],
Γa=ga(z)2exp-12j=14(Ua,jj+Ua,jj),
j=(-1)j+1,
Ua,jh(z, t)=20tAjAhdtUsat,
Ua,jh(z, t)=20tAjAhdtUsat,
χa(z, t)=2iΓakn24=-(-1)n24I|n24|(Ua,24+Ua,24)×exp[-ikn24(2z2-4z4)]×n24=-(-1)n24I|n24|(Ua,24+Ua,24)×exp[-ikn24(2z2+4z4)]×{1-[Ua,22cos(2kz2)+Ua,44cos(2kz4)]+[Ua,22cos(2kz2)+Ua,44cos(2kz4)]2/2},
χa(z, t)=2iΓakn24=-n24=-I|n24|(Ua,24+Ua,24)×I|n24|(Ua,24+Ua,24)n22=-11×n44=-11(-1)NaUa,222|n22|Ua,442|n44|×exp[-ik(N22z2+N44z4)]+n22=-2,0,2(-1)MaUa,22221|n22|!×exp[-ik(M22z2+M44z4)]+n44=-2,0,2(-1)PaUa,44221|n44|!×exp[-ik(P22z2+P44z4)],
dA1dz=Γaγa,00A1,dA1dz=Γaγa,00A1,
-dA3dz=Γaγa,00A3,-dA3dz=Γaγa,00A3,
-dA2dz=Γa(γa,00A2+γa,22A2+γa,24A4+γa,24A4),
dA2dz=Γa(γa,22A2+γa,00A2+γa,24A4+γa,24A4),
-dA4dz=Γa(γa,24A2+γa,24A2+γa,00A4+γa,44A4),
-dA4dz=Γa(γa,24A2+γa,24A2+γa,44A4+γa,00A4),
γa,jh=n24=-n24=-I|n24|(Ua,24+Ua,24)I|n24|×(Ua,24+Ua,24)n22=-11n44=-11(-1)Na×Ua,222|n22|Ua,442|n44|+n22=-2,0,2(-1)MaUa,22221|n22|!+n44=-2,0,2(-1)PaUa,44221|n44|!,
χy(z, t)=2iΓykNy(-1)NyI|Ny|(Uy,12)×exp[-ikNy(1z1-2z2)],
Γy=gy(z)2exp-12j=12(Uy,jj+Uy,jj),
Ub,jh(z, t)=20tBjBhdtUsat,
Ub,jh(z, t)=20tBjBhdtUsat,
Uc,jh(z, t)=20tCjChdtUsat,
Uc,jh(z, t)=20tCjChdtUsat,
jdBjdz=Γb(γb,0Bj-γb,1Bj+j),
-jdBjdz=Γb(γb,0Bj-γb,1Bj+j),
jdCjdz=Γc(γc,0Cj-γc,1Cj+j),
-jdCjdz=Γc(γc,0Cj-γc,1Cj+j),

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