Abstract

We demonstrate 80 times phase conjugation by four-wave mixing of pico-second pulses in a diode-pumped Nd:YVO4 amplifier. Slight pulse broadening as a result of four wave mixing processes was observed.

© 2005 Optical Society of America

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References

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  1. T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
    [CrossRef]
  2. T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
    [CrossRef]
  3. A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
    [CrossRef]
  4. N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
    [CrossRef]
  5. R. S. Cudney and M. Kaczmarek, “Light-induced removal of 180° ferroelectric domains in Rh:BaTiO3,” Opt. Express 7323–328 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-9-323.
    [CrossRef] [PubMed]
  6. J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
    [CrossRef]
  7. K. Abe, M. Amano, and T. Omatsu, “Efficient phase conjugation by pico-second four-wave-mixing in solid-dye amplifier,” Opt. Express 121243–1248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1243.
    [CrossRef] [PubMed]
  8. A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
    [CrossRef]
  9. R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
    [CrossRef]
  10. D. Shen, A. Liu, J. Song, and K. Ueda, “Efficient Operation of an Intracavity-Doubled Nd:YVO4 KTP Laser End Pumped by a High-Brightness Laser Diode,” Appl. Opt. 377785–7788 (1998).
    [CrossRef]
  11. J. E. Bernard and A J. Alcock, “High-efficiency diode-pumped Nd:YVO4 slab laser,” Opt. Lett. 18968–970 (1993).
    [CrossRef] [PubMed]
  12. J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
    [CrossRef]
  13. S. Mailis, J. Hendrics, D. P. Shepherd, A. C. Tropper, N. Moore, R. W. Eason, G. J. Crofts, M. Trew, and M. J. Damzen, “High-phase-conjugate ref lectivity (800%) obtained by degenerate four-wave mixing in a continuous-wave diode-side-pumped Nd:YVO4 amplifier,” Opt. Lett. 24972–974 (1999).
    [CrossRef]
  14. T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
    [CrossRef]
  15. 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. 20548–550 (1995).
    [CrossRef] [PubMed]
  16. A. Brignon, G. Feugnet, J. -P. Huignard, and J. -P. Pocholle, “Multipass degenerate four-wave mixing in a diode-pumped Nd:YVO4 saturable amplifier,” J. Opt. Soc. Am. B 121316–1325 (1995).
    [CrossRef]
  17. A. E. Siegman, Lasers (University Sicience Books, Mill Vally, 1986), Chap. 9.
  18. M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
    [CrossRef]

2004 (2)

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

K. Abe, M. Amano, and T. Omatsu, “Efficient phase conjugation by pico-second four-wave-mixing in solid-dye amplifier,” Opt. Express 121243–1248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1243.
[CrossRef] [PubMed]

2003 (1)

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

2002 (1)

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

1997 (2)

A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
[CrossRef]

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

1996 (1)

M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
[CrossRef]

1995 (2)

1994 (1)

J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
[CrossRef]

1993 (1)

1987 (1)

R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
[CrossRef]

1984 (1)

J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
[CrossRef]

1977 (1)

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

Abe, K.

Alcock, A J.

J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
[CrossRef]

J. E. Bernard and A J. Alcock, “High-efficiency diode-pumped Nd:YVO4 slab laser,” Opt. Lett. 18968–970 (1993).
[CrossRef] [PubMed]

Amano, M.

K. Abe, M. Amano, and T. Omatsu, “Efficient phase conjugation by pico-second four-wave-mixing in solid-dye amplifier,” Opt. Express 121243–1248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1243.
[CrossRef] [PubMed]

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

Bernard, J. E.

J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
[CrossRef]

J. E. Bernard and A J. Alcock, “High-efficiency diode-pumped Nd:YVO4 slab laser,” Opt. Lett. 18968–970 (1993).
[CrossRef] [PubMed]

Birnbaum, M.

R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
[CrossRef]

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

Brignon, A.

Crofts, G. J.

Cudney, R. S.

Damzen, M. J.

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

S. Mailis, J. Hendrics, D. P. Shepherd, A. C. Tropper, N. Moore, R. W. Eason, G. J. Crofts, M. Trew, and M. J. Damzen, “High-phase-conjugate ref lectivity (800%) obtained by degenerate four-wave mixing in a continuous-wave diode-side-pumped Nd:YVO4 amplifier,” Opt. Lett. 24972–974 (1999).
[CrossRef]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
[CrossRef]

Diel, J. C.

J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
[CrossRef]

Eason, R. W.

Erler, J. W.

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

Feugnet, G.

Fields, R. A.

R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
[CrossRef]

Fincher, C. L.

R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
[CrossRef]

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

Garrett, M. H.

A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
[CrossRef]

Geffroy, D.

A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
[CrossRef]

Goto, M.

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

Green, R. P. M.

M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
[CrossRef]

Hendrics, J.

Hout, N.

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

Huignard, J. -P.

Imaizumi, T.

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

Jonathan, J. M. C.

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

Kaczmarek, M.

Liu, A.

Mailis, S.

Matsumoto, Y.

M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
[CrossRef]

McCullough, E.

J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
[CrossRef]

McMicheal, I. C.

J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
[CrossRef]

Minassian, A.

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

Mnushkina, I.

A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
[CrossRef]

Moore, N.

Ojima, Y.

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

Omatsu, T.

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

K. Abe, M. Amano, and T. Omatsu, “Efficient phase conjugation by pico-second four-wave-mixing in solid-dye amplifier,” Opt. Express 121243–1248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1243.
[CrossRef] [PubMed]

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

Pocholle, J. -P.

Roosen, G.

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

Rytz, D.

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

Shen, D.

Shepherd, D. P.

Siegman, A. E.

A. E. Siegman, Lasers (University Sicience Books, Mill Vally, 1986), Chap. 9.

Song, J.

Thompson, B. A.

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

Trew, M.

Tropper, A. C.

Tucker, A. W.

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

Ueda, K.

Vanherzeele, H. V.

J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
[CrossRef]

Watanabe, K.

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

T. Omatsu, Y. Ojima, B. A. Thompson, A. Minassian, and M. J. Damzen, “150-times phase conjugation by degenerate four-wave mixing in a continuous-wave Nd:YVO4 amplifier,” Appl. Phys. B 75493–495 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

R. A. Fields, M. Birnbaum, and C. L. Fincher, “Highly efficient Nd:YVO4 diode-laser end-pumped laser,” Appl. Phys. Lett. 511885–1886 (1987).
[CrossRef]

IEEE J. Quantuum. Electron. (1)

J. C. Diel, I. C. McMicheal, and H. V. Vanherzeele, “Degenerate Four-Wave Mixing of Picosecond Pulses in a Saturable Amplification of a Dye laser,” IEEE J. Quantuum. Electron. QE-20630–636 (1984).
[CrossRef]

J. Appl. Phys. (1)

A. W. Tucker, M. Birnbaum, C. L. Fincher, and J. W. Erler, “Stimulated-emission cross section at 1064 and 1342 nm in Nd:YVO4,” J. Appl. Phys. 484907–4911 (1977).
[CrossRef]

J. Opt. A (1)

T. Omatsu, T. Imaizumi, M. Amano, Y. Ojima, and K. Watanabe, “Multi-watt diffraction-limited picosecond pulses from a diode-pumped Nd:YVO4 amplifier with a photorefractive phase conjugate mirror,” J. Opt. A 5S467–S470 (2003).
[CrossRef]

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

Japansese J. Appl. Phys. (1)

T. Imaizumi, M. Goto, Y. Ojima, and T. Omatsu, “Characterization of a pico-second phase conjugate Nd:YVO4 laser system,” Japansese J. Appl. Phys. 432515–2518 (2004).
[CrossRef]

Opt. Commun. (4)

A. Brignon, D. Geffroy, J. -P. Huignard, M. H. Garrett, and I. Mnushkina, “Experimental investigations of the photorefractive properties of rhodium-doped BaTiO3 at 1.06 µm,” Opt. Commun. 137311–316 (1997).
[CrossRef]

N. Hout, J. M. C. Jonathan, D. Rytz, and G. Roosen, “Self-pumped phase conjugation in a ring cavity at 1.06 µm in cw and nanosecond regimes using photorefractive BaTiO3:Rh,” Opt. Commun. 140296–298 (1997).
[CrossRef]

J. E. Bernard, E. McCullough, and A J. Alcock, “High gain, diode-pumped Nd:YVO4 slab amplifier,” Opt. Commun. 109109–114 (1994).
[CrossRef]

M. J. Damzen, Y. Matsumoto, G. J. Crofts, and R. P. M. Green, “Bragg-selectivity of a volume gain grating,” Opt. Commun. 123182–188 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Other (1)

A. E. Siegman, Lasers (University Sicience Books, Mill Vally, 1986), Chap. 9.

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of experimental setup for phase conjugation. L1, L2,spherical lenses (focal length 100mm); HM1, HM2, half mirrors; PBS1, PBS2, polarizing beam splitters; FR, faraday rotator; HWP, half wave plate, P, prisms.

Fig. 2.
Fig. 2.

Experimental phase conjugate reflectivity as a function of normalized forward pump beam intensity.

Fig. 3.
Fig. 3.

Experimental far field spatial forms of (a) the probe beam, (b) the probe beam with the phase aberrating plate, (c) the phase conjugation and (d) the phase conjugation with the phase aberrating plate.

Fig. 4.
Fig. 4.

Experimental diffraction efficiency as a function of normalized forward pump beam intensity.

Fig. 5.
Fig. 5.

Intensity autocorrelation traces of the signal pulse (dashed line) and the phase conjugation (solid line).

Fig. 6.
Fig. 6.

Schematic diagram of numerically simulated model. K is wave number vector of the grating. k A 2 and k A 4 are wave number vectors of backward pump beam and phase conjugation at ω=ω0 . k A 2 and k A 4 represent wave number vectors at ω=ω0 +Δω(Δω>0). η(Δω) is the phase mismatching.

Fig. 7.
Fig. 7.

(a) Numerically simulated diffraction efficiency at the forward pump of 0.025 I s as a function of detuning frequency. (b) Numerically simulated wavelength selectivity as a function of normalized forward pump beam intensity

Fig. 8.
Fig. 8.

Experimental frequency spectra of the signal pulse (dashed line) and the phase coinjugation (solid line). Origin is 1064.5nm.

Equations (10)

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

dA 1 dz = γ A 1 κ A 3
dA 2 dz = γ A 2 + κ A 4
dA 3 dz = γ A 3 κ A 1
dA 4 dz = γ A 4 + κ A 2
γ = g ( Δ ω ) ( S 2 C 2 ) 1 2 + j η ( Δ ω )
κ = g ( Δ ω ) C [ 1 S ( S 2 C 2 ) 1 2 ]
g ( Δ ω ) = g 0 exp ( ln 2 ( Δ ω Δ ω 0 ) 2 )
η ( Δ ω ) = π Δ ω n 0 Λ 2 cos θ
S = 1 + j = 1 4 A 1 2 I s
C = 2 ( A 1 A 3 + A 2 A 4 ) I s

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