Abstract

It is shown experimentally that a weak optical signal in a Nd:YAG amplifier can have an extraordinarily large gain that is due to transient coherent nonlinear interaction with a strong laser beam. The effect is explained by the diffraction of the strong beam on the dynamic refractive-index grating induced in the interference field of the interacting optical waves and caused by the difference of polarizability of the excited and the unexcited Nd3+ ions. The numerical calculation confirmed the energy transfer from the strong beam to the weak one owing to the predominance of diffraction efficiency of the refractive-index grating over the gain grating in an inverted laser crystal. The investigations give the estimation of the ratio of the real and the imaginary parts of the resonant susceptibility of Nd:YAG at 1064 nm in the range 2–3.

© 1998 Optical Society of America

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References

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  1. H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986), Chap. 6, pp. 159–192.
  2. W. Koechner, Solid State Engineering (Springer-Verlag, New York, 1988).
  3. Ya. I. Khanin, Principles of Laser Dynamics (Elsevier, Amsterdam, 1995), p. 410.
  4. A. Brignon and J.-P. Huignard, “Two-wave mixing in Nd:YAG by gain saturation,” Opt. Lett. 18, 1639–1642 (1993).
    [CrossRef] [PubMed]
  5. R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
    [CrossRef]
  6. E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2726 (1967); G. D. Baldwin and E. P. Riedel, “Measurements of dynamic optical distortion in Nd-doped glass laser rods,” J. Appl. Phys. 38, 2727–2738 (1967).
    [CrossRef]
  7. I. S. Gorban and G. L. Kononchuk, “Refractive index changing of ruby by pumping,” Sov. J. Appl. Spectrosc. 8, 864–867 (1968).
  8. V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Interactions of Light with Matter (Nauka, Moscow, 1977), Chap. 2.
  9. M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
    [CrossRef]
  10. T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63, 185–190 (1987); V. Pilla, P. R. Impinnisi, and T. Catunda, “Measurement of saturation intensities in ion doped solids by transient nonlinear refraction,” Appl. Phys. Lett. 70, 817–819 (1997).
    [CrossRef]
  11. R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser material,” Opt. Lett. 14, 1204–1207 (1989); “Four-wave mixing of Nd3+-doped crystals and glasses,” Phys. Rev. B 41, 8593–8602 (1990).
    [CrossRef] [PubMed]
  12. I. McMichael, R. Saxena, T. Chang, Q. Shu, S. Rand, J. Chen, and H. Tuller, “High gain nondegenerate two-wave mixing in Cr:YaLO3,” Opt. Lett. 19, 1511–1514 (1994).
    [CrossRef] [PubMed]
  13. A. A. Kaminskii and B. M. Antipenko, Multi-Level Operating Schemes of Crystalline Lasers (Nauka, Moscow, 1989), p. 38.
  14. A. P. Bogatov and P. G. Eliseev, “Nonlinear refraction in semiconductor lasers,” Sov. J. Quantum Electron. 12, 465–494 (1985).
  15. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor laser and amplifiers,” J. Opt. Soc. Am. B 5, 147–157 (1988).
    [CrossRef]
  16. Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).
  17. G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
    [CrossRef]
  18. T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).
  19. S. G. Odulov, M. S. Soskin, and A. I. Khyzhniak, Lasers on Dynamic Gratings (Nauka, Moscow, 1990), p. 42.
  20. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 316–323.
  21. O. L. Antipov, A. S. Kuzhelev, and D. V. Chausov, “Nondegenerate four-wave mixing measurement of resonantly induced refractive index grating in Nd:YAG amplifier,” Opt. Lett. 23, 448–450 (1998).
    [CrossRef]
  22. O. L. Antipov, A. S. Kuzhelev, and D. V. Chausov, “Resonant refractive index and gain gratings measurements by four-wave mixings in Nd:YAG amplifiers,” in Advanced Solid State Lasers, W. Bosenberg and M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C. 1998), pp. 555–560.
  23. O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonance scattering of the light beam in the laser crystal with population inversion,” JETP Lett. 63, 13–16 (1996); “Transient stimulated resonant backscattering of light beam in inverted laser crystal,” in Quantum Electronics and Laser Science Conference, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1997), paper QThG 30.
    [CrossRef]
  24. O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Anomalous amplification of optical signal in inverted Nd:YAG due to nonlinear interaction with strong beam,” in Conference on Laser and Electro-Optics, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 118.

1998 (1)

1996 (1)

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

1994 (2)

I. McMichael, R. Saxena, T. Chang, Q. Shu, S. Rand, J. Chen, and H. Tuller, “High gain nondegenerate two-wave mixing in Cr:YaLO3,” Opt. Lett. 19, 1511–1514 (1994).
[CrossRef] [PubMed]

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

1993 (1)

1988 (1)

1985 (2)

A. P. Bogatov and P. G. Eliseev, “Nonlinear refraction in semiconductor lasers,” Sov. J. Quantum Electron. 12, 465–494 (1985).

G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
[CrossRef]

1978 (1)

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

1970 (1)

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

1968 (1)

I. S. Gorban and G. L. Kononchuk, “Refractive index changing of ruby by pumping,” Sov. J. Appl. Spectrosc. 8, 864–867 (1968).

Agrawal, G. P.

Antipov, O. L.

Basiev, T. T.

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

Bogatov, A. P.

A. P. Bogatov and P. G. Eliseev, “Nonlinear refraction in semiconductor lasers,” Sov. J. Quantum Electron. 12, 465–494 (1985).

Brignon, A.

Bubnov, M. M.

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

Chang, T.

Chausov, D. V.

Chen, J.

Crofts, G. J.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Damzen, M. J.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Denker, B. I.

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

Dergachev, A. Yu.

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

Dianov, E. M.

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

Eliseev, P. G.

A. P. Bogatov and P. G. Eliseev, “Nonlinear refraction in semiconductor lasers,” Sov. J. Quantum Electron. 12, 465–494 (1985).

Gorban, I. S.

I. S. Gorban and G. L. Kononchuk, “Refractive index changing of ruby by pumping,” Sov. J. Appl. Spectrosc. 8, 864–867 (1968).

Green, R. P. M.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Grudinin, A. B.

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

Hubbard, W.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Huignard, J.-P.

Kim, D. H.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Kononchuk, G. L.

I. S. Gorban and G. L. Kononchuk, “Refractive index changing of ruby by pumping,” Sov. J. Appl. Spectrosc. 8, 864–867 (1968).

Kuzhelev, A. S.

McMichael, I.

Orlovskii, Yu. V.

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

Osiko, V. V.

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

Powell, R. C.

G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
[CrossRef]

Prokhorov, A. M.

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

Quarles, G. J.

G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
[CrossRef]

Rand, S.

Saxena, R.

Shu, Q.

Timoshechkin, M. I.

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

Tuller, H.

Udaiyan, D.

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

Venikouas, G. E.

G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
[CrossRef]

Voron’ko, Yu. K.

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

IEEE J. Quantum Electron. (1)

R. P. M. Green, G. J. Crofts, W. Hubbard, D. Udaiyan, D. H. Kim, and M. J. Damzen, “Dynamic laser control using feedback from a gain grating,” IEEE J. Quantum Electron. 32, 371–377 (1996).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. B (1)

G. J. Quarles, G. E. Venikouas, and R. C. Powell, “Sequential two-photon excitation processes of Nd3+ ions in solids,” Phys. Rev. B 31, 6935–6940 (1985).
[CrossRef]

Proc. IOFAN (1)

T. T. Basiev, A. Yu. Dergachev, Yu. V. Orlovskii, V. V. Osiko, and A. M. Prokhorov, “Multi-phonon nano- and subnanosecond relaxation from high-lying levels of Nd3+ ions in laser fluorides and oxides,” Proc. IOFAN 46, 3–63 (1994).

Sov. J. Appl. Spectrosc. (1)

I. S. Gorban and G. L. Kononchuk, “Refractive index changing of ruby by pumping,” Sov. J. Appl. Spectrosc. 8, 864–867 (1968).

Sov. J. Quantum Electron. (2)

M. M. Bubnov, A. B. Grudinin, E. M. Dianov, and A. M. Prokhorov, “Deformation of resonator of Nd-glass laser caused by polarizability changing of excited Nd ions,” Sov. J. Quantum Electron. 8, 275–279 (1978).
[CrossRef]

A. P. Bogatov and P. G. Eliseev, “Nonlinear refraction in semiconductor lasers,” Sov. J. Quantum Electron. 12, 465–494 (1985).

Sov. Phys. Dokl. (1)

Yu. K. Voron’ko, B. I. Denker, V. V. Osiko, A. M. Prokhorov, and M. I. Timoshechkin, “X-ray fluorescence of rare-earth ions in Y3Al5O12 crystals,” Sov. Phys. Dokl. 14, 998–1000 (1970).

Other (13)

O. L. Antipov, A. S. Kuzhelev, and D. V. Chausov, “Resonant refractive index and gain gratings measurements by four-wave mixings in Nd:YAG amplifiers,” in Advanced Solid State Lasers, W. Bosenberg and M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C. 1998), pp. 555–560.

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Stimulated resonance scattering of the light beam in the laser crystal with population inversion,” JETP Lett. 63, 13–16 (1996); “Transient stimulated resonant backscattering of light beam in inverted laser crystal,” in Quantum Electronics and Laser Science Conference, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1997), paper QThG 30.
[CrossRef]

O. L. Antipov, S. I. Belyaev, and A. S. Kuzhelev, “Anomalous amplification of optical signal in inverted Nd:YAG due to nonlinear interaction with strong beam,” in Conference on Laser and Electro-Optics, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 118.

A. A. Kaminskii and B. M. Antipenko, Multi-Level Operating Schemes of Crystalline Lasers (Nauka, Moscow, 1989), p. 38.

S. G. Odulov, M. S. Soskin, and A. I. Khyzhniak, Lasers on Dynamic Gratings (Nauka, Moscow, 1990), p. 42.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 316–323.

T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63, 185–190 (1987); V. Pilla, P. R. Impinnisi, and T. Catunda, “Measurement of saturation intensities in ion doped solids by transient nonlinear refraction,” Appl. Phys. Lett. 70, 817–819 (1997).
[CrossRef]

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser material,” Opt. Lett. 14, 1204–1207 (1989); “Four-wave mixing of Nd3+-doped crystals and glasses,” Phys. Rev. B 41, 8593–8602 (1990).
[CrossRef] [PubMed]

V. S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Interactions of Light with Matter (Nauka, Moscow, 1977), Chap. 2.

E. P. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2726 (1967); G. D. Baldwin and E. P. Riedel, “Measurements of dynamic optical distortion in Nd-doped glass laser rods,” J. Appl. Phys. 38, 2727–2738 (1967).
[CrossRef]

H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986), Chap. 6, pp. 159–192.

W. Koechner, Solid State Engineering (Springer-Verlag, New York, 1988).

Ya. I. Khanin, Principles of Laser Dynamics (Elsevier, Amsterdam, 1995), p. 410.

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Figures (6)

Fig. 1
Fig. 1

Experimental scheme for two-wave mixing in Nd:YAG: M’s, mirrors; D’s, diaphragms; PhD, photodetector; BS, beam splitter.

Fig. 2
Fig. 2

Oscillograms of the strong-wave pulse (1) with durations (a) 30 ns and (b) 100 ns, the amplified signal for mutual coherence of the waves (2) or their incoherence (4), and the noise in the direction of the signal (3), the latter being absent.

Fig. 3
Fig. 3

Dependence of the maximum of power amplification of the signal in the presence of the strong wave (normalized to the gain of this signal in the absence of the strong wave) on the input intensity of the strong wave (normalized to the saturation intensity).

Fig. 4
Fig. 4

Energy levels of the Nd3+ ion in the Nd:YAG crystal. The dashed arrows indicate the 4f5d transitions from ground and excited states; other arrows indicate the 4f4f transition of a working Nd:YAG amplifier.

Fig. 5
Fig. 5

Numerically calculated dynamics of amplified signal for different frequency shifts ΩT1 equal to 23 (1), 2.1 (2), 0 (3), and 16 (4), and β equal to 2.2 (1,2), 0 (3), and 3 (4). The time was normalized to T1.

Fig. 6
Fig. 6

Numerically calculated intensity of the amplified signal (normalized to its maximum in the absence of the strong wave) versus the time (normalized to T1) for gain 8 and different values of the β parameter: 2.2 (1), 4 (2), and 0 (3).

Equations (8)

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

Δpme24π2m ffdνmg(2νfd-νmg)(νfd2-νwt2)(νfd2-νwt2+νmg2-2νfdνmg),
Δχ=Δχre+iΔχim=2πF12ΔpeNe+i n0λσNm4π,
β=χreχim=2πΔnexαλ=8π2F12ΔpeNen0σλNm,
N0t+N0T1=Up-ItotN0Wsat-NgrEstEwk*+c.c.Wsat,
Ngrt+NgrT1=-ItotNgrWsat-Est*EwkN0Wsat,
2 Ewkz=σ(1+iβ)(EwkN0+EstNgr),
-2 Estz=σ(1+iβ)(EstN0+EwkNgr*),
Isp+z=σIsp+N0,Isp-z=-σIsp-N0,

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