Abstract

A common assumption that Raman-resonant four-wave mixing does not transfer energy between the light and the Raman medium is shown to be incorrect. The derivation of the correct energy-transfer picture is compared with those for stimulated Raman scattering and for nonresonant mixing. The physical mechanism for Raman-gain suppression due to Stokes/anti-Stokes coupling under phase-matched conditions is clarified by this understanding of the energy transfer. An experimental demonstration of the nature of the energy transfer is proposed.

© 1990 Optical Society of America

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References

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  1. M. D. Duncan, R. Mahon, J. Reintjes, and L. L. Tankersley, “Parametric Raman gain suppression in D2 and H2,” Opt. Lett. 11, 803–805 (1986).
    [CrossRef] [PubMed]
  2. K. Leung, M. Oron, D. Klimek, R. Holmes, and A. Flusberg, “Observation of parametric gain suppression in rotational Raman transitions of N2 and H2,” Opt. Lett. 13, 33–35 (1988).
    [CrossRef] [PubMed]
  3. A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
    [CrossRef] [PubMed]
  4. M. A. Henesian and D. M. Pennington, “Diffraction properties of laser speckle generated by stimulated rotational Raman scattering in long air paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 874, 2–16 (1988).
  5. B. J. Herman, “Numerical investigation of stimulated Raman scattering,” in Technical Digest of the Optical Society of America 1988 Annual Meeting (Optical Society of America, Washington, D.C., 1988).
  6. R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).
  7. C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859–1864 (1989).
    [CrossRef]
  8. N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
    [CrossRef]
  9. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
  10. B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjunction (Springer-Verlag, New York, 1985).
    [CrossRef]
  11. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).
  12. E. A. Stappaerts, W. H. Long, and H. Komine, “Gain enhancement in Raman amplifiers with broadband pumping,” Opt. Lett. 5, 4–6 (1980).
    [CrossRef] [PubMed]
  13. A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
    [CrossRef]
  14. J.-P. Taran, “CARS techniques and applications,” in Tunable Lasers and Applications, A. Mooradian, T. Jaeger, and P. Stokseth, eds. (Springer-Verlag, Berlin, 1976), pp. 378–388.
    [CrossRef]

1989 (2)

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859–1864 (1989).
[CrossRef]

1988 (3)

K. Leung, M. Oron, D. Klimek, R. Holmes, and A. Flusberg, “Observation of parametric gain suppression in rotational Raman transitions of N2 and H2,” Opt. Lett. 13, 33–35 (1988).
[CrossRef] [PubMed]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

M. A. Henesian and D. M. Pennington, “Diffraction properties of laser speckle generated by stimulated rotational Raman scattering in long air paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 874, 2–16 (1988).

1986 (1)

1985 (1)

A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
[CrossRef]

1980 (1)

1964 (1)

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[CrossRef]

Bischel, W. K.

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

Bloembergen, N.

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[CrossRef]

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

Duncan, M. D.

Duzy, C.

A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
[CrossRef]

Flusberg, A.

K. Leung, M. Oron, D. Klimek, R. Holmes, and A. Flusberg, “Observation of parametric gain suppression in rotational Raman transitions of N2 and H2,” Opt. Lett. 13, 33–35 (1988).
[CrossRef] [PubMed]

A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
[CrossRef]

Heinrichs, R. M.

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

Henesian, M. A.

M. A. Henesian and D. M. Pennington, “Diffraction properties of laser speckle generated by stimulated rotational Raman scattering in long air paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 874, 2–16 (1988).

Herman, B. J.

B. J. Herman, “Numerical investigation of stimulated Raman scattering,” in Technical Digest of the Optical Society of America 1988 Annual Meeting (Optical Society of America, Washington, D.C., 1988).

Hickman, A. P.

C. Reiser, T. D. Raymond, R. B. Michie, and A. P. Hickman, “Efficient anti-Stokes Raman conversion in collimated beams,” J. Opt. Soc. Am. B 6, 1859–1864 (1989).
[CrossRef]

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

Holmes, R.

Klimek, D.

Komine, H.

Korff, D.

A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
[CrossRef]

Leung, K.

Long, W. H.

Mahon, R.

Michie, R. B.

Oron, M.

Pennington, D. M.

M. A. Henesian and D. M. Pennington, “Diffraction properties of laser speckle generated by stimulated rotational Raman scattering in long air paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 874, 2–16 (1988).

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjunction (Springer-Verlag, New York, 1985).
[CrossRef]

Raymond, T. D.

Reintjes, J.

Reiser, C.

Shen, Y. R.

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[CrossRef]

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjunction (Springer-Verlag, New York, 1985).
[CrossRef]

Smith, W. W.

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

Stappaerts, E. A.

Tankersley, L. L.

Taran, J.-P.

J.-P. Taran, “CARS techniques and applications,” in Tunable Lasers and Applications, A. Mooradian, T. Jaeger, and P. Stokseth, eds. (Springer-Verlag, Berlin, 1976), pp. 378–388.
[CrossRef]

Tedroe, M. M.

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

Winkler, I. C.

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjunction (Springer-Verlag, New York, 1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Flusberg, D. Korff, and C. Duzy, “The effect of weak dispersion on stimulated Raman scattering,” IEEE J. Quantum Electron. QE-21, 232–236 (1985).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. A (1)

A. P. Hickman and W. K. Bischel, “Theory of Stokes and anti-Stokes generation by Raman frequency conversion in the transient limit,” Phys. Rev. A 37, 2516–2523 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

N. Bloembergen and Y. R. Shen, “Coupling between vibrations and light waves in Raman laser media,” Phys. Rev. Lett. 12, 504–507 (1964).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

M. A. Henesian and D. M. Pennington, “Diffraction properties of laser speckle generated by stimulated rotational Raman scattering in long air paths,” Proc. Soc. Photo-Opt. Instrum. Eng. 874, 2–16 (1988).

R. M. Heinrichs, W. W. Smith, M. M. Tedroe, and I. C. Winkler, “Effect of intensity scintillation on the stimulated rotational Raman threshold in hydrogen,” Proc. Soc. Photo-Opt. Instrum. Eng. 1060, 34–40 (1989).

Other (5)

J.-P. Taran, “CARS techniques and applications,” in Tunable Lasers and Applications, A. Mooradian, T. Jaeger, and P. Stokseth, eds. (Springer-Verlag, Berlin, 1976), pp. 378–388.
[CrossRef]

B. J. Herman, “Numerical investigation of stimulated Raman scattering,” in Technical Digest of the Optical Society of America 1988 Annual Meeting (Optical Society of America, Washington, D.C., 1988).

N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).

B. Ya. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjunction (Springer-Verlag, New York, 1985).
[CrossRef]

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (5)

Fig. 1
Fig. 1

Misconceived energy diagram for Raman-resonant four-wave mixing. Reverse all arrows for the reverse process. Medium energy is unchanged for both forward and reverse processes.

Fig. 2
Fig. 2

Correct energy diagram for the Raman-resonant four-wave mixing process that de-excites the medium. Reverse all arrows for the reverse process, which excites the medium.

Fig. 3
Fig. 3

Transition from (a) the spectrum for two-line Raman amplification to (b) the spectrum for Stokes/anti-Stokes coupling.

Fig. 4
Fig. 4

Energy diagram for nonresonant four-wave mixing. Reverse all arrows for the reverse process. Medium energy is unchanged for both forward and reverse processes.

Fig. 5
Fig. 5

Numerical integration results for Stokes and anti-Stokes intensities I = |E|2 (given in units of 10−6 times the pump intensity) as a function of amplifier cell length z. The inputs are Is = 0 and Ia = 10−5, the e-fold gain length is 1.0 cm, and the phase-mismatch factor is = exp(−i5z) for z measured in centimeters.

Equations (33)

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2 ω p ω s + ω a .
E z = i 2 π ω 2 k c 2 P NL .
i k a c 2 2 π ω a 2 E a z = χ a a * | E p | 2 E a + χ s a * E p 2 E s * ,
i k p c 2 2 π ω p 2 E p z = χ a a | E a | 2 E p + χ s s * | E s | 2 E p + * ( χ s a + χ s a * ) E p * E s E a ,
i k s c 2 2 π ω s 2 E s z = χ s s | E p | 2 E s + χ s a E p 2 E a * .
exp [ i ( 2 k p k s k a ) z ] .
χ ( ω a , ω p , ω s ) = C ( ω a , ω p , ω s ) ω p ω s ω Q i Γ
N = n 2 | E | 2 / ( 4 π h ω ) .
R a ( n / 2 h c ) i ( χ a a χ a a * ) | E p E a | 2 ,
R s ( n / 2 h c ) i ( χ s s χ s s * ) | E p E s | 2 ,
F r ( n / 4 h c ) i ( χ s a χ s a * ) ( E p 2 E s * E a * + c.c. ) ,
F n r ( n / 4 h c ) i ( χ s a + χ s a * ) ( E p 2 E s * E a * c.c. ) .
N a z = R a F r + F n r ,
N p z = R a R s 2 F n r ,
N s z = R s + F r + F n r .
N Q z = N s z N a z = R a + R s + 2 F r .
N a z = R a F r ,
N p z = R a R s ,
N s z = R s + F r ,
ω s + 2 ω Q ω a .
k a = k s + 2 k Q ,
k Q = k p k s
k a + k s = 2 k p
d 2 Q d t 2 + Γ d Q d t + ω Q 2 Q = 1 2 m E α ¯ ¯ q E .
q = i 4 m Γ ω Q α ( Ω ) q ( E p E s * + E a E p * ) .
P N L = N Q α q E ,
c π N ω s E s z = ( α q ) 2 ( E p * E s + E a * E p ) E p .
2 E s j z = g k = 1 2 E p k E p j * E s k exp [ i ( k j ) γ ν z ] ,
p 1 a ; p 2 p ; s 1 p ; s 2 s
N a z = F n r ,
N p z = 2 F n r ,
N s z = F n r ,
N Q z = 0 .

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