Abstract

We demonstrate energy exchange by nondegenerate two-wave mixing in ruby. Our results are in agreement with the theory of nondegenerate two-wave mixing when the theory is generalized to take into account a complex nonlinear index. Two-wave mixing gain exceeding the absorption and reflection losses is demonstrated, and we show that these experiments provide a simple and accurate method for determining the complex nonlinear index, response time, and saturation intensity of the medium.

© 1988 Optical Society of America

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References

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  1. D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
    [Crossref]
  2. Y. Anan’ev, Sov. J. Quantum Electron. 4, 929 (1975).
    [Crossref]
  3. V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).
  4. G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
    [Crossref] [PubMed]
  5. M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
    [Crossref] [PubMed]
  6. I. McMichael, P. Yeh, J. Opt. Soc. Am. B 4 (13), P32 (1987).
  7. P. Yeh, J. Opt. Soc. Am. B 3, 747 (1986).
    [Crossref]
  8. T. Catunda, J. Andreeta, J. Castro, Appl. Opt. 25, 2391 (1986).
    [Crossref] [PubMed]

1987 (1)

I. McMichael, P. Yeh, J. Opt. Soc. Am. B 4 (13), P32 (1987).

1986 (4)

P. Yeh, J. Opt. Soc. Am. B 3, 747 (1986).
[Crossref]

T. Catunda, J. Andreeta, J. Castro, Appl. Opt. 25, 2391 (1986).
[Crossref] [PubMed]

G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
[Crossref] [PubMed]

M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
[Crossref] [PubMed]

1977 (1)

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

1975 (1)

Y. Anan’ev, Sov. J. Quantum Electron. 4, 929 (1975).
[Crossref]

1972 (1)

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

Amodei, J.

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

Anan’ev, Y.

Y. Anan’ev, Sov. J. Quantum Electron. 4, 929 (1975).
[Crossref]

Andreeta, J.

Boyd, R.

M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
[Crossref] [PubMed]

Castro, J.

Catunda, T.

Grynberg, G.

G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
[Crossref] [PubMed]

Kramer, M.

M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
[Crossref] [PubMed]

Kukhtarev, N.

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

Le Bihan, E.

G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
[Crossref] [PubMed]

McMichael, I.

I. McMichael, P. Yeh, J. Opt. Soc. Am. B 4 (13), P32 (1987).

Odulov, S.

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

Pinard, M.

G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
[Crossref] [PubMed]

Soskin, M.

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

Staebler, D.

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

Tompkin, W.

M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
[Crossref] [PubMed]

Vinetskii, V.

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

Yeh, P.

I. McMichael, P. Yeh, J. Opt. Soc. Am. B 4 (13), P32 (1987).

P. Yeh, J. Opt. Soc. Am. B 3, 747 (1986).
[Crossref]

Appl. Opt. (1)

J. Appl. Phys. (1)

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

J. Opt. Soc. Am. B (2)

I. McMichael, P. Yeh, J. Opt. Soc. Am. B 4 (13), P32 (1987).

P. Yeh, J. Opt. Soc. Am. B 3, 747 (1986).
[Crossref]

J. Phys. (Paris) (1)

G. Grynberg, E. Le Bihan, M. Pinard, J. Phys. (Paris) 47, 1321 (1986); D. Grandclément, G. Grynberg, M. Pinard, Phys. Rev. Lett. 59, 40 (1987); M. Gruneisen, K. MacDonald, R. Boyd, J. Opt. Soc. Am. B 5, 123 (1988).
[Crossref] [PubMed]

Phys. Rev. A (1)

M. Kramer, W. Tompkin, R. Boyd, Phys. Rev. A 34, 2026 (1986).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

Y. Anan’ev, Sov. J. Quantum Electron. 4, 929 (1975).
[Crossref]

Sov. Phys. Tech. Phys. (1)

V. Vinetskii, N. Kukhtarev, S. Odulov, M. Soskin, Sov. Phys. Tech. Phys. 22, 729 (1977).

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Figures (6)

Fig. 1
Fig. 1

Schematic of two-wave mixing. Two beams interfere in a nonlinear medium and modulate the optical susceptibility to produce a grating. When the frequency shift between the two beams is of the order of the response time of the medium, the modulation of the optical susceptibility is shifted spatially with respect to the interference pattern, and one beam gains energy from the other.

Fig. 2
Fig. 2

Calculations of the nondegenerate two-wave mixing gain as a function of the frequency detuning between the two waves for various ratios r of the imaginary to real parts of the nonlinear index n2.

Fig. 3
Fig. 3

Experimental setup for nondegenerate two-wave mixing in ruby. Light from a laser is split into two beams (pump and probe) that interfere in a ruby crystal. The probe beam is frequency shifted by a mirror (M2) mounted to a PZT and measured by detector D. A voltage source applies a triangular wave to the PZT.

Fig. 4
Fig. 4

Photograph from oscilloscope (see Fig. 3) showing two-wave mixing attenuation and gain. Traces a and b show the transmitted probe power as measured by detector D with the pump beam blocked and unblocked, respectively, but no frequency shift. Trace c shows the voltage applied to the PZT to produce a frequency shift, and trace d shows the corresponding attenuation and gain for the probe. Zero is indicated by the cross in the lower left, one horizontal division corresponds to 20 msec, and the vertical axis gives relative intensity.

Fig. 5
Fig. 5

Measurements of the nondegenerate two-wave mixing gain in ruby as a function of frequency detuning between the two waves for various wavelengths. At 488 nm the gain is antisymmetric, indicating an index grating, while at 580 nm there is a departure from antisymmetry, indicating a mixed grating (index and absorption).

Fig. 6
Fig. 6

Measurements of the nondegenerate two-wave mixing gain in ruby as a function of the intensity of the pump wave at 515 nm.

Equations (6)

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

n = n 0 + n 2 I ,
n 2 = n 2 i n 2 .
I 2 ( L ) = I 2 ( 0 ) exp ( γ δ r 1 + δ 2 α ) L ,
γ = 2 π λ cos ( θ / 2 ) ( 1 e α L α L ) n 2 I 1 .
Γ 1 ln I 2 ( L , δ ) I 2 ( L , 0 ) = γ L δ + r δ 2 1 + δ 2 ,
Γ 2 ln I 2 ( L , δ = + 1 ) I 2 ( L , δ = 1 ) = γ L I 1 ( 1 + I 1 / I s ) 2 ,

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