Abstract

We describe a model for the stimulated Raman gain spectrum and the Raman response function in silica fiber using multiple vibrational modes. We base the model on previous spectroscopic data [J. Opt. Soc. Am. B 1, 652 (1984) and J. Opt. Soc. Am. B 6, 1159 (1989)] and extend an earlier proposed model [Appl. Opt. 21, 359 (1982)] by making use of an inhomogeneous distribution of damped oscillators. The model provides a simple analytical expression for the Raman response function and an expression for the Raman gain spectrum that is easy to evaluate numerically.

© 2002 Optical Society of America

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References

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  1. G. E. Walrafen and P. N. Krishnan, “Model analysis of the Raman spectrum from fused silica optical fibers,” Appl. Opt. 21, 359–360 (1982).
    [CrossRef] [PubMed]
  2. R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode silica fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984).
    [CrossRef]
  3. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
    [CrossRef]
  4. D. Hollenbeck, “Dynamics of a fiberoptic Raman amplifier,” Ph.D. dissertation (University of Texas at Dallas, Dallas, Tex., 2000).
  5. A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division-multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
    [CrossRef]
  6. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1997).
  8. R. J. Bell and P. Dean, “Atomic vibrations in vitreous silica,” Discuss. Faraday Soc. 50, 55–61 (1970).
    [CrossRef]
  9. A. G. Revesz and G. E. Walrafen, “Structural interpretations for some Raman lines from vitreous silica,” J. Non-Cryst. Solids 54, 323–333 (1983).
    [CrossRef]
  10. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1971), p. 100.
  11. A. Icsevgi and W. E. Lamb, Jr., “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969).
    [CrossRef]

1989 (2)

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
[CrossRef]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

1984 (2)

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division-multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

R. H. Stolen, C. Lee, and R. K. Jain, “Development of the stimulated Raman spectrum in single-mode silica fibers,” J. Opt. Soc. Am. B 1, 652–657 (1984).
[CrossRef]

1983 (1)

A. G. Revesz and G. E. Walrafen, “Structural interpretations for some Raman lines from vitreous silica,” J. Non-Cryst. Solids 54, 323–333 (1983).
[CrossRef]

1982 (1)

1970 (1)

R. J. Bell and P. Dean, “Atomic vibrations in vitreous silica,” Discuss. Faraday Soc. 50, 55–61 (1970).
[CrossRef]

1969 (1)

A. Icsevgi and W. E. Lamb, Jr., “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969).
[CrossRef]

Bell, R. J.

R. J. Bell and P. Dean, “Atomic vibrations in vitreous silica,” Discuss. Faraday Soc. 50, 55–61 (1970).
[CrossRef]

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Chraplyvy, A. R.

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division-multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

Dean, P.

R. J. Bell and P. Dean, “Atomic vibrations in vitreous silica,” Discuss. Faraday Soc. 50, 55–61 (1970).
[CrossRef]

Gordon, J. P.

Haus, H. A.

Icsevgi, A.

A. Icsevgi and W. E. Lamb, Jr., “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969).
[CrossRef]

Jain, R. K.

Krishnan, P. N.

Lamb Jr., W. E.

A. Icsevgi and W. E. Lamb, Jr., “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969).
[CrossRef]

Lee, C.

Revesz, A. G.

A. G. Revesz and G. E. Walrafen, “Structural interpretations for some Raman lines from vitreous silica,” J. Non-Cryst. Solids 54, 323–333 (1983).
[CrossRef]

Stolen, R. H.

Tomlinson, W. J.

Walrafen, G. E.

A. G. Revesz and G. E. Walrafen, “Structural interpretations for some Raman lines from vitreous silica,” J. Non-Cryst. Solids 54, 323–333 (1983).
[CrossRef]

G. E. Walrafen and P. N. Krishnan, “Model analysis of the Raman spectrum from fused silica optical fibers,” Appl. Opt. 21, 359–360 (1982).
[CrossRef] [PubMed]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Appl. Opt. (1)

Discuss. Faraday Soc. (1)

R. J. Bell and P. Dean, “Atomic vibrations in vitreous silica,” Discuss. Faraday Soc. 50, 55–61 (1970).
[CrossRef]

Electron. Lett. (1)

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division-multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

J. Non-Cryst. Solids (1)

A. G. Revesz and G. E. Walrafen, “Structural interpretations for some Raman lines from vitreous silica,” J. Non-Cryst. Solids 54, 323–333 (1983).
[CrossRef]

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

Phys. Rev. (1)

A. Icsevgi and W. E. Lamb, Jr., “Propagation of light pulses in a laser amplifier,” Phys. Rev. 185, 517–545 (1969).
[CrossRef]

Other (3)

D. Hollenbeck, “Dynamics of a fiberoptic Raman amplifier,” Ph.D. dissertation (University of Texas at Dallas, Dallas, Tex., 2000).

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, New York, 1971), p. 100.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1997).

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Figures (13)

Fig. 1
Fig. 1

Raman gain spectrum of silica fiber, after Stolen et al.3

Fig. 2
Fig. 2

Raman response function of silica fiber, after Stolen et al.3

Fig. 3
Fig. 3

Response function in the single-damped-oscillator model [relation (6)].

Fig. 4
Fig. 4

Gain spectrum in the single-damped-oscillator model [relation (8)].

Fig. 5
Fig. 5

Gaussians used in the intermediate-broadening model of the Raman gain spectrum.

Fig. 6
Fig. 6

Representation of the convolution of Lorentzians with a Gaussian.

Fig. 7
Fig. 7

Best fit achieved for the Raman response function in the intermediate-broadening model [Eq. (9)] and the data from Table 1.

Fig. 8
Fig. 8

Best fit achieved for the Raman gain spectrum gR(ω)s(ω) with the intermediate-broadening model [Eq. (11)] and the data given in Table 1.

Fig. 9
Fig. 9

Real component of the Raman transfer function in the intermediate-broadening model [Eq. (12)] and the data from Table 1.

Fig. 10
Fig. 10

Raman gain spectrum in the limit of purely inhomogeneous broadening.

Fig. 11
Fig. 11

Raman response function in the limit of purely inhomogeneous broadening.

Fig. 12
Fig. 12

Raman response function in the limit of purely homogeneous broadening (Γi=0).

Fig. 13
Fig. 13

Raman gain spectrum in the limit of purely homogeneous broadening (Γi=0).

Tables (1)

Tables Icon

Table 1 Values of the Parameters Used in the Intermediate-Broadening Modela

Equations (18)

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z+β1 t+i 12β2 2t2-16β3 3t3ES(z, t)
=-α2 ES(z, t)+2πiω02β0c2 PS(z, t),
βj=djβdωjω=ω0,
PS=PS,i+PS,R.
PS,i(1-fR)ES[|ES|2+2|EL|2],
PS,R(t)ifREL(z, t)×-hR(t-t, 0)exp[-i(ωL-ωS)(t-t)]×EL*(z, t)ES(z, t)dt,
hR(t)exp(-t/τ2)sin(t/τ1).
gR(ω)=ω0cn0fRχ(3) Im[h˜R(ω)],
gR(ω)2ωγ(ω2-ωv2)2+(2ωγ)2.
hR(t)=i=113 Aiωv,i exp(-γit)exp(-Γi2t2/4)sin(ωv,it)θ(t),
θ(t)=1ift00ift<0.
s(ω)==113 A2ωv, 0{cos[(ωv,-ω)t]-cos[(ωv,+ω)t]}exp(-γt)exp(-Γ2t2/4)dt,
r(ω)==113 A2ωv, 0{sin[(ωv,-ω)t]+sin[(ωv,+ω)t]}exp(-γt)exp(-Γ2t2/4)dt,
gR(ω)i=113 Ai2ωv,i exp[(ω-ωv,i)2]/Γi2
hR(t)=i=113 Aiωv,i exp(-Γi2t2/4)sin(ωv,it)θ(t),
θ(t)=1,ift00,ift<0.
hR(t)=i=113 Aiωv,i sin(ωv,it)exp(-γit),
gr(ω)i=113 Ai2ωv,i×2ωv,iγiωγi4+(ω2-ωv,i2)2+2γi2(ω2+ωv,i2),

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