Abstract

The process of saturable-gain four-wave mixing (DFWM) in a diode-pumped Nd:YVO4 amplifier with interacting beams provided by a Nd:YAG oscillator is investigated. Multipass geometries are employed that arrange for the signal beam to experience an increased interaction length relative to that of the pump beams. DFWM reflectivities up to R = 170% and a diffraction efficiency η = 6% of the volume population hologram written in the Nd:YVO4 amplifier are obtained experimentally. A theoretical analysis of multipass DFWM is presented in the transient (pulsed) regime, including the laser amplification and the mutual interaction of all the interacting beams as well as the spectral mismatch between the beam frequency and the gain line-center frequency of the Nd:YVO4 amplifier. It is shown that because of the close spectral matchup of the Nd:YAG oscillator and the Nd:YVO4 amplifier, the amplitude (gain) grating contribution is predominant compared with that of the phase grating.

© 1995 Optical Society of America

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  1. R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).
    [CrossRef] [PubMed]
  2. 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]
  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]
  4. 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]
  5. 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]
  6. P. A. Routledge and T. A. King, "Phase conjugation in the gain saturation of a flashlamp pumped dye laser," Opt. Commun. 62, 357–359 (1987).
    [CrossRef]
  7. P. J. Soan, A. D. Case, M. J. Damzen, and M. H. R. Hutchinson, "High-reflectivity four-wave mixing by saturable gain in rhodamine 6G dye," Opt. Lett. 17, 781–783 (1992).
    [CrossRef] [PubMed]
  8. A. Tomita, "Phase conjugation using gain saturation of a Nd:YAG laser," Appl. Phys. Lett. 34, 463–464 (1979).
    [CrossRef]
  9. 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]
  10. R. A. Fisher and B. J. Feldman, "On-resonant phaseconjugate reflection and amplification at 10.6 μm in inverted CO2," Opt. Lett. 4, 140–142 (1979).
    [CrossRef] [PubMed]
  11. 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]
  12. G. J. Crofts, R. P. M. Green, and M. J. Damzen, "Investigation of multipass geometries for efficient degenerate fourwave mixing in Nd:YAG," Opt. Lett. 17, 920–922 (1992).
    [CrossRef] [PubMed]
  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, J. Raffy, and J.-P. Huignard, "Transient degenerate four-wave mixing in a saturable Nd:YAG amplifier: effect of pump beam propagation," Opt. Lett. 19, 865–867 (1994).
    [CrossRef] [PubMed]
  16. 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).
  17. A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, "Efficient degenerate four-wave mixing in a diode-pumped microchip Nd:YVO4 amplifier," Opt. Lett. 20, 548–550 (1995).
    [CrossRef] [PubMed]
  18. J. E. Bernard and A. J. Alcock, "High-efficiency diodepumped Nd:YVO4 slab laser," Opt. Lett. 18, 968–970 (1993).
    [CrossRef] [PubMed]
  19. G. Feugnet, M. Schwarz, C. Larat, and J.-P. Pocholle, "TEM00 surface-emitting laser-diode longitudinally pumpedNd:YVO4 laser," Opt. Lett. 18, 2114–2116 (1993).
    [CrossRef] [PubMed]
  20. J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (1994).
    [CrossRef]
  21. R. Scheps, J. F. Myers, and G. Mizell, "High-efficiency1.06-μm output in a monolithic Nd:YVO4 laser," Appl. Opt. 33, 5546–5549 (1994).
    [CrossRef] [PubMed]
  22. 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]
  23. M. J. Damzen, R. P. M. Green, and G. J. Crofts, "Highreflectivity four-wave mixing by gain saturation of nanosecond and microsecond radiation in Nd:YAG," Opt. Lett. 17, 1331–1333 (1992).
    [CrossRef] [PubMed]
  24. 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]
  25. A. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
    [CrossRef]
  26. 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]
  27. A. Brignon and J.-P. Huignard, "Two-wave mixing in Nd:YAG by gain saturation," Opt. Lett. 18, 1639–1641 (1993).
    [CrossRef] [PubMed]
  28. A. Brignon and J.-P. Huignard, "Transient self-diffraction in a saturable Nd:YAG amplifier," Opt. Lett. 19, 451–453 (1994).
    [CrossRef] [PubMed]

1995 (2)

1994 (7)

R. Scheps, J. F. Myers, and G. Mizell, "High-efficiency1.06-μm output in a monolithic Nd:YVO4 laser," Appl. Opt. 33, 5546–5549 (1994).
[CrossRef] [PubMed]

A. Brignon and J.-P. Huignard, "Transient self-diffraction in a saturable Nd:YAG amplifier," Opt. Lett. 19, 451–453 (1994).
[CrossRef] [PubMed]

A. Brignon, J. Raffy, and J.-P. Huignard, "Transient degenerate four-wave mixing in a saturable Nd:YAG amplifier: effect of pump beam propagation," Opt. Lett. 19, 865–867 (1994).
[CrossRef] [PubMed]

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]

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).

J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (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 (4)

1992 (3)

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)

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]

1987 (1)

P. A. Routledge and T. A. King, "Phase conjugation in the gain saturation of a flashlamp pumped dye laser," Opt. Commun. 62, 357–359 (1987).
[CrossRef]

1986 (2)

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]

A. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
[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 (1)

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)

1978 (1)

Abrams, R. L.

Alcock, A. J.

J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (1994).
[CrossRef]

J. E. Bernard and A. J. Alcock, "High-efficiency diodepumped Nd:YVO4 slab laser," Opt. Lett. 18, 968–970 (1993).
[CrossRef] [PubMed]

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).

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]

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]

Bernard, J. E.

J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (1994).
[CrossRef]

J. E. Bernard and A. J. Alcock, "High-efficiency diodepumped Nd:YVO4 slab laser," Opt. Lett. 18, 968–970 (1993).
[CrossRef] [PubMed]

Boyd, R. W.

A. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
[CrossRef]

Brignon, A.

Bussac, C.

Case, A. D.

Crofts, G. J.

Damzen, M. J.

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.

Gaeta, A. L.

A. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
[CrossRef]

Green, R. P. M.

Gruneisen, M. T.

A. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
[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.

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]

Hutchinson, M. H. R.

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]

King, T. A.

P. A. Routledge and T. A. King, "Phase conjugation in the gain saturation of a flashlamp pumped dye laser," Opt. Commun. 62, 357–359 (1987).
[CrossRef]

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]

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]

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).

Larat, C.

Lind, R. 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]

McCullough, E.

J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (1994).
[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]

Mizell, G.

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]

Myers, J. F.

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]

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]

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]

Pocholle, J.-P.

Raffy, J.

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]

Routledge, P. A.

P. A. Routledge and T. A. King, "Phase conjugation in the gain saturation of a flashlamp pumped dye laser," Opt. Commun. 62, 357–359 (1987).
[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]

Scheps, R.

Schwarz, M.

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]

Soan, P. J.

Tomita, A.

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

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]

Wonterghem, B. Van

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]

Appl. Opt. (1)

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. (6)

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]

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]

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]

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]

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. L. Gaeta, M. T. Gruneisen, and R. W. Boyd, "Theory of degenerate four-wave mixing in saturable absorbing media with the inclusion of pump propagation effects," IEEE J. Quantum Electron. QE-22, 1095–1101 (1986).
[CrossRef]

J. Phys. (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]

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)

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]

P. A. Routledge and T. A. King, "Phase conjugation in the gain saturation of a flashlamp pumped dye laser," Opt. Commun. 62, 357–359 (1987).
[CrossRef]

J. E. Bernard, E. McCullough, and A. J. Alcock, "High gain, diode-pumped Nd:YVO4 slab amplifier," Opt. Commun. 109, 109–114 (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]

Opt. Lett. (12)

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]

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

A. Brignon and J.-P. Huignard, "Transient self-diffraction in a saturable Nd:YAG amplifier," Opt. Lett. 19, 451–453 (1994).
[CrossRef] [PubMed]

A. Brignon, J. Raffy, and J.-P. Huignard, "Transient degenerate four-wave mixing in a saturable Nd:YAG amplifier: effect of pump beam propagation," Opt. Lett. 19, 865–867 (1994).
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M. J. Damzen, R. P. M. Green, and G. J. Crofts, "Highreflectivity four-wave mixing by gain saturation of nanosecond and microsecond radiation in Nd:YAG," Opt. Lett. 17, 1331–1333 (1992).
[CrossRef] [PubMed]

P. J. Soan, A. D. Case, M. J. Damzen, and M. H. R. Hutchinson, "High-reflectivity four-wave mixing by saturable gain in rhodamine 6G dye," Opt. Lett. 17, 781–783 (1992).
[CrossRef] [PubMed]

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).
[CrossRef] [PubMed]

R. A. Fisher and B. J. Feldman, "On-resonant phaseconjugate reflection and amplification at 10.6 μm in inverted CO2," Opt. Lett. 4, 140–142 (1979).
[CrossRef] [PubMed]

G. J. Crofts, R. P. M. Green, and M. J. Damzen, "Investigation of multipass geometries for efficient degenerate fourwave mixing in Nd:YAG," Opt. Lett. 17, 920–922 (1992).
[CrossRef] [PubMed]

A. Brignon, G. Feugnet, J.-P. Huignard, and J.-P. Pocholle, "Efficient degenerate four-wave mixing in a diode-pumped microchip Nd:YVO4 amplifier," Opt. Lett. 20, 548–550 (1995).
[CrossRef] [PubMed]

J. E. Bernard and A. J. Alcock, "High-efficiency diodepumped Nd:YVO4 slab laser," Opt. Lett. 18, 968–970 (1993).
[CrossRef] [PubMed]

G. Feugnet, M. Schwarz, C. Larat, and J.-P. Pocholle, "TEM00 surface-emitting laser-diode longitudinally pumpedNd:YVO4 laser," Opt. Lett. 18, 2114–2116 (1993).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (2)

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[CrossRef]

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[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic of the (a) single-pass, (b) two-pass, and (c) four-pass DFWM geometries in a saturable amplifier. In (b) and (c) the z = L face of the medium is high-reflection coated.

Fig. 2
Fig. 2

DFWM reflectivity R versus the forward pump beam fluence U f(0) normalized to the saturation fluence U sat for 1, single-pass; 2, two-pass; and 4, four-pass DFWM geometries and for different values of the small-intensity gain-length product: (a) α0L = 0.5, (b) α0L = 1.5.

Fig. 3
Fig. 3

DFWM reflectivity R versus the forward pump beam fluence U f(0) normalized to the saturation fluence U sat for a single-pass DFWM scheme for various values of the detuning parameter from the line-center frequency δ: (a) constant values of the line-center small-intensity gain–length product α 0 0 L = 3 and saturation fluence U sat 0, (b) constant values of the frequency-dependent small-intensity gain–length product α0L = 3 and saturation fluence U sat.

Fig. 4
Fig. 4

Nd:YVO4 crystal with inverted beam focused through a lens duct.

Fig. 5
Fig. 5

Schematic of the two-pass diode-pumped Nd:YVO4 amplifier. The λ = 1064 nm radiation is provided by a Q-switched Nd:YAG oscillator.

Fig. 6
Fig. 6

Gain G of the two-pass diode-pumped Nd:YVO4 amplifier versus the input fluence U f(0). The points are the measured values, and the solid curve is the theoretical fit plotted with α0L = 1.2 and U sat = 120 mJ/cm2.

Fig. 7
Fig. 7

Experimental points and theoretical curves of the DFWM reflectivity R versus the normalized forward pump beam fluence for the two-pass geometry (open diamonds and dashed curve) and the four-pass geometry (closed diamonds and solid curve).

Fig. 8
Fig. 8

DFWM reflectivity R versus the diode-pumping power of (a) the two-pass geometry with U f ( 0 ) = 0.1 U sat and (b) the four-pass scheme with U f ( 0 ) = 0.06 U sat. The experimental results are in the left-hand plots, and the theoretical predictions are in the right-hand plots.

Fig. 9
Fig. 9

(a) Writing and (b) readout processes of a volume population hologram in a two-pass saturable amplifier.

Fig. 10
Fig. 10

Diffraction efficiency η as a function of the input writing-beam fluence in a two-pass saturable amplifier having a small-intensity product of α0L = 1.5 (solid curve). Diffraction efficiencies obtained with classical single-pass amplifiers (α0L = 1.5 and α0L = 3) are shown as the dashed curves for comparison.

Fig. 11
Fig. 11

Diffraction efficiency η as a function of the input writing-beam fluence in the two-pass diode-pumped Nd:YVO4 amplifier. The diamonds are the experimental values and the solid curve is the theoretical plot calculated with α0L = 1.2 and δ = 0.4.

Equations (59)

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E ( r , t ) = E 0 ( r , t ) + Δ E ( r , t ) ,
E 0 ( z , t ) = A f ( z , t ) exp ( - i k z ) + A b ( z , t ) exp ( + i k z ) ,
Δ E ( r , t ) = j = 1 N S j ( z j , t ) exp ( - i k z j ) + j = 1 N C j ( z j , t ) exp ( + i k z j ) ,
χ ( r , t ) = i ( 1 + i δ ) g ( r ) k exp [ - 0 t E ( r , t ) 2 d t U sat ] ,
α 0 = 1 L 0 L g ( z ) d z .
δ = 2 ( ν - ν 0 ) Δ ν ,
α 0 = α 0 0 ( 1 + δ 2 ) - 1 ,
U sat = U sat 0 ( 1 + δ 2 ) .
χ ( z , t ) = 2 i ( 1 + i δ ) k [ 1 - 0 t ( E 0 Δ E * + E 0 * Δ E ) d t U sat ] × F ( z , t ) ,
F ( z , t ) = n = - + ( - 1 ) n γ n exp ( - 2 i k n z ) .
γ n ( z , t ) = g ( z ) 2 exp [ - U S ( z , t ) ] I n [ U M ( z , t ) ] .
U S ( z , t ) = 0 t ( A f + 2 A b 2 ) d t / U sat ,
U M ( z , t ) = 2 0 t A f A b d t / U sat .
d A f d z = α f A f ,
- d A b d z = α b A b ,
( - 1 ) j + 1 d S j d z = α S j - κ C j * ,
( - 1 ) j d C j d z = a C j - κ S j * ,
α f ( z , t ) / ( 1 + i δ ) = γ 0 - γ 1 A b / A f ,
α b ( z , t ) / ( 1 + i δ ) = γ 0 - γ 1 A f / A b ,
α ( z , t ) / ( 1 + i δ ) = ( 1 - U s ) γ 0 + U M γ 1 ,
κ ( z , t ) / ( 1 + i δ ) = [ U M γ 0 - U S γ 1 ] exp ( i ϕ ) ,
A f , b = A f , b exp ( + i ϕ f , b ) ,             ϕ = ϕ f + ϕ b .
A f ( 0 , t ) = pump in ,
A b ( L , t ) = A f ( L , t )             or             A b ( L , t ) = A f ( 0 , t ) ,
S 1 ( 0 , t ) = signal in ,
C 1 ( L , t ) = 0
A f ( 0 , t ) = pump in ,             A b ( L , t ) = A f ( L , t ) ,
S 1 ( 0 , t ) = signal in ,             S 2 ( L , t ) = S 1 ( L , t ) ,
C 2 ( 0 , t ) = 0 ,             C 1 ( L , t ) = C 2 ( L , t )
A f ( 0 , t ) = pump in , A b ( L , t ) = A f ( L , t ) , S 1 ( 0 , t ) = signal in , S 2 ( L , t ) = S 1 ( L , t ) ,
S 3 ( 0 , t ) = S 2 ( 0 , t ) , S 4 ( L , t ) = S 3 ( L , t ) , C 4 ( 0 , t ) = 0 , C 3 ( L , t ) = C 4 ( L , t ) ,
C 2 ( 0 , t ) = C 3 ( 0 , t ) ,             C 1 ( L , t ) = C 2 ( L , t ) .
R = t = 0 t = + C 1 ( 0 , t ) 2 d t t = 0 t = + S 1 ( 0 , t ) 2 d t .
E ( z , t ) = A f ( z , t ) exp ( - i k z ) + A b ( z , t ) exp ( + i k z ) .
d A f d z = γ 0 A f - γ 1 A b ,
- d A b d z = γ 0 A b - γ 1 A f ,
G = U b ( z = 0 ) U f ( z = 0 ) ,
U j ( z ) = t = 0 t = + A j ( z , t ) 2 d t .
E ( r , t ) = j = 1 4 A j ( z j , t ) exp ( - i k z j ) ,
χ ( r , t ) = 2 i k Γ 0 j = 1 4 h = 1 h > j 4 f ( A j , A h ) ,
Γ 0 = g ( z ) ( 1 + i δ ) 2 exp ( - 1 2 j = 1 4 U j j ) ,
f ( A j , A h ) = n j h = - + ( - 1 ) n j h I n j h ( U j h ) exp [ - i n j h k ( z j - z h ) ] ,
U j h ( z , t ) = 2 0 t A j A h d t U sat .
χ ( r , t ) = 2 i k Γ 0 n 12 n 13 n 14 n 23 n 24 n 34 ( - 1 ) a I n 12 ( U 12 ) × I n 13 ( U 13 ) I n 14 ( U 14 ) I n 23 ( U 23 ) I n 24 ( U 24 ) × I n 34 ( U 34 ) exp [ - i k ( b 1 z 1 + b 2 z 2 + b 3 z 3 + b 4 z 4 ) ,
a = n 12 + n 13 + n 14 + n 23 + n 24 + n 34 ,
b 1 = n 12 + n 13 + n 14 , b 2 = - n 12 + n 23 + n 24 , b 3 = - n 13 - n 23 + n 34 , b 4 = - n 14 - n 24 - n 34 .
j d A j d z = Γ 0 ( γ 00 A j + h = 1 h j 4 γ j h A h ) ,
d P 3 d z = Γ 0 ( γ 13 P 1 + γ 23 D 2 + γ 00 P 3 + γ 34 D 4 ) ,
- d P 1 d z = Γ 0 ( γ 00 P 1 + γ 12 D 2 + γ 13 P 3 + γ 14 D 4 ) ,
d D 4 d z = Γ 0 ( γ 14 P 1 + γ 24 D 2 + γ 34 P 3 + γ 00 D 4 ) ,
- d D 2 d z = Γ 0 ( γ 12 P 1 + γ 00 D 2 + γ 23 P 3 + γ 24 D 4 ) ,
γ j h = n 12 n 13 n 14 n 23 n 24 n 34 ( - 1 ) a I n 12 ( U 12 ) I n 13 ( U 13 ) × I n 14 ( U 14 ) I n 23 ( U 23 ) I n 24 ( U 24 ) I n 34 ( U 34 ) ,
b j = 1 ,             b h = - 1 ,             b k = 0             ( k = 1 , 2 , 3 , 4 and k j , h ) .
b 1 = b 2 = b 3 = b 4 = 0.
A 1 ( 0 , t ) = writing 1 in ,             A 2 ( 0 , t ) = writing 2 in ,
A 3 ( L , t ) = A 1 ( L , t ) ,             A 4 ( L , t ) = A 2 ( L , t ) ,
P 3 ( 0 , t ) = probe in ,             P 1 ( L , t ) = P 3 ( L , t ) ,
D 4 ( 0 , t ) = 0 ,             D 2 ( L , t ) = D 4 ( L , t ) .
η = t = 0 t = + D 2 ( z = 0 , t ) 2 d t t = 0 t = + P 3 ( z = 0 , t ) 2 d t .

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