Abstract

Equations governing the Raman effect in birefringent optical fibers are derived. Both the parallel and perpendicular Raman effects are taken into account. The evolution of solitons is discussed.

© 1991 Optical Society of America

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References

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  1. C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef] [PubMed]
  2. M. N. Islam, C. D. Poole, J. P. Gordon, Opt. Lett. 14, 1011 (1989).
    [CrossRef] [PubMed]
  3. M. N. Islam, Opt. Lett. 14, 1257 (1989); M. N. Islam, C. E. Soccolich, D. A. B. Miller, Opt. Lett. 15, 909 (1990).
    [CrossRef] [PubMed]
  4. R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  5. Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
    [CrossRef]
  6. See, e.g., E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), p. 480, for a discussion of this concept.
  7. C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987); IEEE J. Quantum Electron. 25, 2674 (1989).
    [CrossRef]
  8. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]

1990 (1)

Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
[CrossRef]

1989 (2)

1987 (2)

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987); IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

1986 (1)

1977 (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Gordon, J. P.

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Islam, M. N.

Menyuk, C. R.

C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987); IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

Merzbacher, E.

See, e.g., E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), p. 480, for a discussion of this concept.

Poole, C. D.

Stegeman, G. I.

Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
[CrossRef]

Wabnitz, S.

Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
[CrossRef]

Wright, E. M.

Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. R. Menyuk, IEEE J. Quantum Electron. QE-23, 174 (1987); IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

Some previous discussions have neglected the term that yields cross-polarized gain in the continuous-wave limit. See, e.g., S. Wabnitz, E. M. Wright, G. I. Stegeman, Phys. Rev. A 41, 415 (1990).
[CrossRef]

Prog. Quantum Electron. (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Other (1)

See, e.g., E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), p. 480, for a discussion of this concept.

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Figures (1)

Fig. 1
Fig. 1

Schematic illustration of the molecular transitions that create the positive frequency component of the polarizability in the Kerr and Raman effects. The virtual levels at −ħω0, ħω0, and 2ħω0 are shown as dashed lines. The nuclear levels are shown as solid lines. The electronic levels are not shown. In process a, in which the system never returns to the nuclear levels, the whole process is essentially instantaneous. By contrast, in processes b and c, where the system returns to the nuclear levels, there can be a finite time delay.

Equations (10)

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P = - t d t 1 - t d t 2 - t d t 3 χ ( t - t 1 , t - t 2 ; t - t 3 ) × [ E ( t 1 ) · E ( t 2 ) ] E ( t 3 ) ,
P Raman ( z , t ) = E ( z , t ) - t ϕ 1 ( t - t ) E ( z , t ) · E ( z , t ) d t + E ( z , t ) · - t E ( z , t ) ϕ 2 ( t - t ) E ( z , t ) d t ,
E ( z , t ) = [ U ( z , t ) exp ( i k 0 z - i ω 0 t ) + U * ( z , t ) × exp ( - i k 0 z + i ω 0 t ) ] e ^ x + [ V ( z , t ) exp ( i l 0 z - i ω 0 t ) + V * ( z , t ) exp ( - i l 0 z + i ω 0 t ) ] e ^ y ,
P Raman ( z , t ) = [ ρ ( z , t ) exp ( i k 0 z - i ω 0 t ) + ρ * ( z , t ) exp ( - i k 0 z + i ω 0 t ) ] e ^ x + [ σ ( z , t ) × exp ( i l 0 z - i ω 0 t ) + σ * ( z , t ) exp ( - i l 0 z + i ω 0 t ) ] e ^ y ,
2 i k 0 U z | Raman = - 4 π ω 0 2 c ρ ,
i u ( s ) ξ | Raman = u ( s ) - s f 1 ( s - s ) u ( s ) 2 d s + u ( s ) - s f 2 ( s - s ) v ( s ) 2 d s + v ( s ) - s f 3 ( s - s ) u ( s ) v * ( s ) d s + v ( s ) - s f 4 ( s - s ) u * ( s ) v ( s ) exp ( i R δ ξ ) d s ,
i u ξ + i δ u s + 1 2 2 u s 2 + ( u 2 + 2 3 v 2 ) u + i u ξ | Raman = 0 , i v ξ - i δ v s + 1 2 2 v s 2 + ( 2 3 u 2 + v 2 ) v + i v ξ | Raman = 0.
I = - d s u 2 = 1 2 π - d ω u ˜ 2 , ω I = i 2 - d s ( u * u s - u * s u ) = 1 2 π - d ω ω u ˜ 2 ,
i u ξ | Raman = u ( r 10 + c 1 s ) u 2 + u ( r 20 + c 2 s ) v 2 + v ( r 30 + c 3 s ) u v * .
d I d ξ | Raman = 4 c 3 Θ A sech 2 ( Θ ξ + δ ξ ) , d ω I d ξ | Raman = 8 c 2 A sech 2 ( Θ ξ + δ ξ ) tanh 2 ( Θ δ + δ ξ ) - 2 ( 2 c 2 + c 3 ) A sech 4 ( Θ ξ + δ ξ ) .

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