Abstract

A comparison of the theoretical predictions of a multimode broadband model with the experimentally measured gain enhancement in a Raman amplifier is presented. The results show that the multimode theory with fixed and totally random phases is in agreement with the data obtained from an excimer-laser-pumped Raman amplifier. Additionally, this theory indicates that the correlated gain can be larger than the gain for a monochromatic laser, as might be expected for a model with amplitude modulation.

© 1988 Optical Society of America

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References

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  1. S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).
  2. L. A. Westling and M. G. Raymer, “Quantum theory of Stokes generation with a multimode laser,” Phys. Rev. A 36, 4835 (1987);M. Trippenbach and C. L. Van, “Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 3, 879 (1986).
    [CrossRef] [PubMed]
  3. W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).
  4. E. A. Stappaerts, W. H. Long, and H. Komine, “Gain enhancement in Raman amplifiers with broadband pumping,” Opt. Lett. 5, 4 (1980).
    [CrossRef] [PubMed]
  5. M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
    [CrossRef]
  6. M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  7. G. G. Lombardi and H. Injeyan, “Phase correlation in a Raman amplifier,” J. Opt. Soc. Am. B 3, 1461 (1986).
    [CrossRef]
  8. J. Eggleston and R. L. Byer, “Steady-state stimulated Raman scattering by a multimode laser,” IEEE J. Quantum Electron. QE-16, 850 (1980).
    [CrossRef]
  9. G. S. Agarwal, “Stimulated Raman scattering in chaotic fields,” Opt. Commun. 35, 267 (1980).
    [CrossRef]
  10. A. T. Georges, “Theory of stimulated Raman scattering in a chaotic incoherent pump field,” Opt. Commun. 41, 61 (1982).
    [CrossRef]
  11. M. Trippenbach, K. Rzazewski, and M. G. Raymer, “Stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 1, 671 (1984).
    [CrossRef]
  12. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1972), p. 374.
  13. J. L. Carlsten, J. Rifkin, and D. C. MacPherson, “Spatial mode structure of stimulated Stokes emission from a Raman generator,” J. Opt. Soc. Am. B 3, 1476 (1986).
    [CrossRef]
  14. E. Hecht and A. Zajac, Options (Addison-Wesley, Reading, Mass., 1974).
  15. A. Owyoung, “High resolution cw stimulated Raman spectroscopy in molecular hydrogen,” Opt. Lett. 2, 91 (1978).
    [CrossRef]
  16. Actually, it has been shown by Westling and Raymer2 that the Stokes field will not have exactly the same linewidth and phase distribution as the pump except in the limit where the mode spacing is large compared with the Raman linewidth. In future studies we hope to be able to determine the effect of this lack of exact correlation.
  17. W. K. Bischel and M. J. Dyer, “Wavelength dependence of the absolute Raman gain coefficient for the Q(1) transition in H2,” J. Opt. Soc. Am. B 3, 677 (1986).For our calculation we used an average of the values given in this reference.
    [CrossRef]
  18. J. Ducuing and N. Bloembergen, “Statistical fluctuations in nonlinear optical processes,” Phys. Rev. A 133, 1493 (1964).

1987 (1)

L. A. Westling and M. G. Raymer, “Quantum theory of Stokes generation with a multimode laser,” Phys. Rev. A 36, 4835 (1987);M. Trippenbach and C. L. Van, “Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 3, 879 (1986).
[CrossRef] [PubMed]

1986 (3)

1984 (1)

1982 (1)

A. T. Georges, “Theory of stimulated Raman scattering in a chaotic incoherent pump field,” Opt. Commun. 41, 61 (1982).
[CrossRef]

1981 (1)

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

1980 (3)

J. Eggleston and R. L. Byer, “Steady-state stimulated Raman scattering by a multimode laser,” IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

G. S. Agarwal, “Stimulated Raman scattering in chaotic fields,” Opt. Commun. 35, 267 (1980).
[CrossRef]

E. A. Stappaerts, W. H. Long, and H. Komine, “Gain enhancement in Raman amplifiers with broadband pumping,” Opt. Lett. 5, 4 (1980).
[CrossRef] [PubMed]

1979 (1)

M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
[CrossRef]

1978 (2)

W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).

A. Owyoung, “High resolution cw stimulated Raman spectroscopy in molecular hydrogen,” Opt. Lett. 2, 91 (1978).
[CrossRef]

1974 (1)

S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).

1964 (1)

J. Ducuing and N. Bloembergen, “Statistical fluctuations in nonlinear optical processes,” Phys. Rev. A 133, 1493 (1964).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1972), p. 374.

Agarwal, G. S.

G. S. Agarwal, “Stimulated Raman scattering in chaotic fields,” Opt. Commun. 35, 267 (1980).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).

Bischel, W. K.

Bloembergen, N.

J. Ducuing and N. Bloembergen, “Statistical fluctuations in nonlinear optical processes,” Phys. Rev. A 133, 1493 (1964).

Byer, R. L.

J. Eggleston and R. L. Byer, “Steady-state stimulated Raman scattering by a multimode laser,” IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

Carlsten, J. L.

J. L. Carlsten, J. Rifkin, and D. C. MacPherson, “Spatial mode structure of stimulated Stokes emission from a Raman generator,” J. Opt. Soc. Am. B 3, 1476 (1986).
[CrossRef]

M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
[CrossRef]

D’yakov, Yu. E.

S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).

Ducuing, J.

J. Ducuing and N. Bloembergen, “Statistical fluctuations in nonlinear optical processes,” Phys. Rev. A 133, 1493 (1964).

Dyer, M. J.

Eggleston, J.

J. Eggleston and R. L. Byer, “Steady-state stimulated Raman scattering by a multimode laser,” IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

Georges, A. T.

A. T. Georges, “Theory of stimulated Raman scattering in a chaotic incoherent pump field,” Opt. Commun. 41, 61 (1982).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Options (Addison-Wesley, Reading, Mass., 1974).

Injeyan, H.

Komine, H.

Lombardi, G. G.

Long, W. H.

MacPherson, D. C.

Mostowski, J.

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
[CrossRef]

Nikitin, I. V.

W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).

Odinstsov, V. I.

W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).

Owyoung, A.

Pavlov, L. I.

S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).

Raymer, M. G.

L. A. Westling and M. G. Raymer, “Quantum theory of Stokes generation with a multimode laser,” Phys. Rev. A 36, 4835 (1987);M. Trippenbach and C. L. Van, “Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 3, 879 (1986).
[CrossRef] [PubMed]

M. Trippenbach, K. Rzazewski, and M. G. Raymer, “Stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 1, 671 (1984).
[CrossRef]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
[CrossRef]

Rifkin, J.

Rzazewski, K.

Stappaerts, E. A.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1972), p. 374.

Trippenbach, M.

Vokhnik, W. M.

W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).

Westling, L. A.

L. A. Westling and M. G. Raymer, “Quantum theory of Stokes generation with a multimode laser,” Phys. Rev. A 36, 4835 (1987);M. Trippenbach and C. L. Van, “Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 3, 879 (1986).
[CrossRef] [PubMed]

Zajac, A.

E. Hecht and A. Zajac, Options (Addison-Wesley, Reading, Mass., 1974).

IEEE J. Quantum Electron. (1)

J. Eggleston and R. L. Byer, “Steady-state stimulated Raman scattering by a multimode laser,” IEEE J. Quantum Electron. QE-16, 850 (1980).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

G. S. Agarwal, “Stimulated Raman scattering in chaotic fields,” Opt. Commun. 35, 267 (1980).
[CrossRef]

A. T. Georges, “Theory of stimulated Raman scattering in a chaotic incoherent pump field,” Opt. Commun. 41, 61 (1982).
[CrossRef]

Opt. Lett. (2)

Opt. Spectra (1)

W. M. Vokhnik, I. V. Nikitin, and V. I. Odinstsov, “Delay of broad-band-pumped stimulated Raman gain,” Opt. Spectra 45, 47 (1978).

Phys. Rev. A (4)

M. G. Raymer, J. Mostowski, and J. L. Carlsten, “Theory of stimulated Raman scattering with broad-band lasers,” Phys. Rev. A 19, 2304 (1979).
[CrossRef]

M. G. Raymer and J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
[CrossRef]

L. A. Westling and M. G. Raymer, “Quantum theory of Stokes generation with a multimode laser,” Phys. Rev. A 36, 4835 (1987);M. Trippenbach and C. L. Van, “Intensity cross-correlation functions in stimulated Raman scattering of colored chaotic light,” J. Opt. Soc. Am. B 3, 879 (1986).
[CrossRef] [PubMed]

J. Ducuing and N. Bloembergen, “Statistical fluctuations in nonlinear optical processes,” Phys. Rev. A 133, 1493 (1964).

Sov. Phys. JETP (1)

S. A. Akhmanov, Yu. E. D’yakov, and L. I. Pavlov, “Statistical phenomena in Raman scattering stimulated by a broad-band pump,” Sov. Phys. JETP 39, 249 (1974).

Other (3)

Actually, it has been shown by Westling and Raymer2 that the Stokes field will not have exactly the same linewidth and phase distribution as the pump except in the limit where the mode spacing is large compared with the Raman linewidth. In future studies we hope to be able to determine the effect of this lack of exact correlation.

E. Hecht and A. Zajac, Options (Addison-Wesley, Reading, Mass., 1974).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1972), p. 374.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the gain-enhancement experiment.

Fig. 2
Fig. 2

Schematic of the Mach–Zehnder interferometer used to measure the linewidths of the input Stokes and pump beams.

Fig. 3
Fig. 3

Spatial profile of the input Stokes beam at (a) cell entrance, (b) cell center, and (c) cell exit.

Fig. 4
Fig. 4

Spatial profile of the input pump beam at (a) cell entrance, (b) cell center, and (c) cell exit.

Fig. 5
Fig. 5

Temporal profile of the XeCl laser pulse.

Fig. 6
Fig. 6

Interference profile generated with the Mach–Zehnder interferometer. The solid curve is the actual data, and the dashed curve is a least-squares fit to Eq. (4). For this data |γ| was 0.91.

Fig. 7
Fig. 7

Magnitude of the normalized autocorrelation function γ for (a) the Stokes beam and (b) the laser beam versus the path-length difference in the interferometer. The crosses represent specific values of |γ| for different interferometer path lengths and were generated as parameters from fitting a series of interference profiles similar to Fig. 6. The solid curve is an exponential fit to |γ|.

Fig. 8
Fig. 8

Comparison of the experimental (solid curve) and theoretical (dashed curve) values of the gain enhancement as a function of optical delay. The energy of the injected Stokes and input pump was 0.43 μJ and 0.42 mJ, respectively.

Fig. 9
Fig. 9

Correlated (×’s) and uncorrelated (○’s) gain-enhancement data as a function of input pump energy. Superimposed upon the data is the theoretical result (solid curve). Also shown are the theoretical data for the monogain (dashed line).

Fig. 10
Fig. 10

Distribution of laser modes used in theoretical calculation. Distance between laser modes (vertical lines) is 0.0035 cm−1, which is small compared with the Raman linewidth (solid curve).

Fig. 11
Fig. 11

Lorentzian frequency distribution of the laser given by the dashed curve was chopped at 1.12 cm−1 and is large compared with the Raman linewidth of 0.08 cm−1 plotted as the solid curve.

Fig. 12
Fig. 12

Laser field intensities for a 4.685-psec pulse length results from the superposition of 640 longitudinal modes with fixed but random phases.

Equations (5)

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d d z E S = i k 2 Q * E L , d d τ Q * = Γ Q * + i k 1 E L * E S .
k 1 = d 12 d 23 / 2 2 Δ , k 2 = N π d 21 d 23 ω S υ S / c 2 Δ ,
E S ( z , τ + τ D ) = E S ( 0 , τ + τ D ) + ( k 1 k 2 z ) 1 / 2 × 0 τ exp [ Γ ( τ τ ) ] [ p ( τ ) p ( τ ) ] 1 / 2 × I 1 ( { 4 k 1 k 2 z [ p ( τ ) p ( τ ) ] } 1 / 2 ) × E L ( τ ) E L * ( τ ) E S ( 0 , τ + τ D ) d τ .
E L ( τ ) = n E L n exp [ i ( n δ τ + ϕ L n ) ] , E S ( 0 , τ ) = m E S m ( 0 ) exp { i [ m δ τ + ϕ S m ( 0 ) ] } ,
I ( ξ ) = I 1 + I 2 + 2 ( I 1 I 2 ) 1 / 2 γ cos ( α ξ ϕ ) .

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