Abstract

The transition between the transient and the stationary regimes of stimulated Raman scattering is examined computationally for pulses with a sharp initial rise. We find that the transient-regime predictions are useful for times less than T2 regardless of the pulse duration and that the stationary-regime predictions become useful only for times much greater than T2.

© 1996 Optical Society of America

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References

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  1. For a historical review that emphasizes self-similarity, see C. R. Menyuk, “Self-similarity in stimulated Raman scattering: an overview,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 1–27.
  2. J. G. Wessel, P. R. Battle, and J. L. Carlsten, “Stimulated Raman scattering in a multi-pass cell,” in Self-Similarity in Stimulated Raman Scattering, D. Levy, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 125–148.
  3. M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.
  4. D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
    [CrossRef]
  5. M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt. Soc. Am. B 5, 37–52 (1988).
    [CrossRef]
  6. C.-S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
    [CrossRef]
  7. C. R. Menyuk and T. I. Seidman, “Transient stimulated Raman scattering,” SIAM J. Math. Anal. 23, 346–363 (1992).
    [CrossRef]
  8. C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
    [CrossRef] [PubMed]
  9. G. Hilfer and C. R. Menyuk, “Stimulated Raman scattering in the transient limit,” J. Opt. Soc. Am. B 7, 739–749 (1990).
    [CrossRef]
  10. D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
    [CrossRef] [PubMed]

1994 (1)

D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
[CrossRef] [PubMed]

1992 (2)

C. R. Menyuk and T. I. Seidman, “Transient stimulated Raman scattering,” SIAM J. Math. Anal. 23, 346–363 (1992).
[CrossRef]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
[CrossRef]

1988 (1)

1969 (1)

C.-S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[CrossRef]

Battle, P. R.

J. G. Wessel, P. R. Battle, and J. L. Carlsten, “Stimulated Raman scattering in a multi-pass cell,” in Self-Similarity in Stimulated Raman Scattering, D. Levy, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 125–148.

Calame, G.

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Carlsten, J. L.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
[CrossRef]

J. G. Wessel, P. R. Battle, and J. L. Carlsten, “Stimulated Raman scattering in a multi-pass cell,” in Self-Similarity in Stimulated Raman Scattering, D. Levy, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 125–148.

Duncan, M. D.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt. Soc. Am. B 5, 37–52 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Hilfer, G.

G. Hilfer and C. R. Menyuk, “Stimulated Raman scattering in the transient limit,” J. Opt. Soc. Am. B 7, 739–749 (1990).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Levi, D.

D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
[CrossRef] [PubMed]

MacPherson, D. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
[CrossRef]

Mahon, R.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt. Soc. Am. B 5, 37–52 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Menyuk, C. R.

D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
[CrossRef] [PubMed]

C. R. Menyuk and T. I. Seidman, “Transient stimulated Raman scattering,” SIAM J. Math. Anal. 23, 346–363 (1992).
[CrossRef]

G. Hilfer and C. R. Menyuk, “Stimulated Raman scattering in the transient limit,” J. Opt. Soc. Am. B 7, 739–749 (1990).
[CrossRef]

For a historical review that emphasizes self-similarity, see C. R. Menyuk, “Self-similarity in stimulated Raman scattering: an overview,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 1–27.

Reintjes, J.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt. Soc. Am. B 5, 37–52 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Seidman, T. I.

C. R. Menyuk and T. I. Seidman, “Transient stimulated Raman scattering,” SIAM J. Math. Anal. 23, 346–363 (1992).
[CrossRef]

Swanson, R. C.

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
[CrossRef]

Tankersley, L. L.

M. D. Duncan, R. Mahon, L. L. Tankersley, and J. Reintjes, “Transient stimulated Raman amplification in hydrogen,” J. Opt. Soc. Am. B 5, 37–52 (1988).
[CrossRef]

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

Wang, C.-S.

C.-S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[CrossRef]

Wessel, J. G.

J. G. Wessel, P. R. Battle, and J. L. Carlsten, “Stimulated Raman scattering in a multi-pass cell,” in Self-Similarity in Stimulated Raman Scattering, D. Levy, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 125–148.

Winternitz, P.

D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

D. C. MacPherson, R. C. Swanson, and J. L. Carlsten, “Stimulated Raman scattering in the visible with a multipass cell,” IEEE J. Quantum Electron. 25, 1741–1746 (1989).
[CrossRef]

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

Phys. Rev. (1)

C.-S. Wang, “Theory of stimulated Raman scattering,” Phys. Rev. 182, 482–494 (1969).
[CrossRef]

Phys. Rev. A (1)

D. Levi, C. R. Menyuk, and P. Winternitz, “Similarity reduction and perturbation solution of the stimulated-Raman-scattering equations in the presence of dissipation,” Phys. Rev. A 49, 2844–2852 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

C. R. Menyuk, D. Levi, and P. Winternitz, “Self-similarity in transient stimulated Raman scattering,” Phys. Rev. Lett. 69, 3048–3051 (1992); C. R. Menyuk, “Long-distance evolution in transient stimulated Raman scattering,” Phys. Rev. A 47, 2235–2248 (1993).
[CrossRef] [PubMed]

SIAM J. Math. Anal. (1)

C. R. Menyuk and T. I. Seidman, “Transient stimulated Raman scattering,” SIAM J. Math. Anal. 23, 346–363 (1992).
[CrossRef]

Other (3)

For a historical review that emphasizes self-similarity, see C. R. Menyuk, “Self-similarity in stimulated Raman scattering: an overview,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 1–27.

J. G. Wessel, P. R. Battle, and J. L. Carlsten, “Stimulated Raman scattering in a multi-pass cell,” in Self-Similarity in Stimulated Raman Scattering, D. Levy, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 125–148.

M. D. Duncan, R. Mahon, L. L. Tankersley, G. Calame, G. Hilfer, and J. Reintjes, “Transient stimulated Raman scattering,” in Self-Similarity in Stimulated Raman Scattering, D. Levi, C. R. Menyuk, and P. Winternitz, eds. (Les Publications CRM, Montreal, 1994), pp. 149–172.

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Figures (9)

Fig. 1
Fig. 1

Pump (solid curve) and Stokes (dashed curve) amplitudes as a function of time (τ) at a distance χ=50.

Fig. 2
Fig. 2

Same as Fig. 1 but for χ=100.

Fig. 3
Fig. 3

Same as Fig. 1 but for χ=200.

Fig. 4
Fig. 4

Pump (solid curve) and Stokes (dashed curve) amplitudes, after transformation by Eqs. (7) and (8), as a function of time (τ) at a distance χ=50. Note that the distance is χ=50, not χ = 50, to permit comparison with Fig. 1.

Fig. 5
Fig. 5

Same as Fig. 4 but for χ=100. Note that the distance is χ=100, not χ=100, to permit comparison with Fig. 2.

Fig. 6
Fig. 6

Same as Fig. 4 but for χ=200. Note that the distance is χ=200, not χ=200, to permit comparison with Fig. 3.

Fig. 7
Fig. 7

Pump amplitude (solid curve) as a function of time (τ), compared with the prediction of the stationary-regime theory (dashed curve) at a distance χ=50.

Fig. 8
Fig. 8

Same as Fig. 7 but for χ=100.

Fig. 9
Fig. 9

Same as Fig. 7 but for χ=200.

Equations (16)

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1c E1t+E1x=-i k1k2 κ2E2Q,
1c E2t+E2x=-iκ2E1Q*,
Qt+1T2 Q=-iκ1E1E2*,
χ=x/L,τ=t/Tpulse,γ=Tpulse/T2,
A1=E1Emax,A2=k1k21/2 E2Emax,
X=ik1k21/2 Qκ1Emax2Tpulse,
A1χ=-A2X,
A2χ=A1X*,
Xτ+γX=A1A2*.
A1=A1,0(τ)×K(τ)exp[-K2(τ)χ/γ]{|A1,0(τ)|2 exp[-2K2(τ)χ/γ]+|A2,0(τ)|2}1/2,
A2=A2,0(τ)×K(τ){|A1,0(τ)|2 exp[-2K2(τ)χ/γ]+|A2,0(τ)|2}1/2.
A1,0(τ)=αH(τ)sech(τ),
A2,0(τ)=βH(τ)sech(τ),
X(χ,τ)=-τA1(χ,τ)A2*(χ,τ)exp[-γ(τ-τ)]dτ.
τ=1T 0τK2(τ)dτ,χ=Tχ,
A1=A1K(τ), A2=A2K(τ), X=XT.

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