Abstract

We have studied the transverse modes of a transient stimulated Raman signal generated in unsaturated Raman amplifiers with Fresnel numbers from one to seven, both with and without a seed Stokes pulse. In the absence of a seed Stokes pulse and for a pump Fresnel number greater than 1.5, the spatial intensity pattern of the stimulated Stokes signal is highly variable from shot to shot, reflecting the random nature of the quantum-noise source. However, when a separately generated and sufficiently strong seed Stokes pulse with a Gaussian spatial profile is injected into the amplifier, the spatial mode of the output Stokes beam assumes a smooth Gaussian spatial pattern that is significantly smaller in diameter than either the pump or the seed Stokes beam. This spatial mode control, which is due to the injected Stokes signal, persists down to a level of approximately 300 seed Stokes photons per spatial mode and, surprisingly, is observed to suppress the noise-initiated signal by at least a factor of 10 in the outer regions of the amplified Stokes beam. We have also studied the Stokes pulse-energy statistics over a range of Fresnel numbers. Data taken with systems having Fresnel numbers between 4 and 7 follow the same pattern as the spatial-mode-control results in that the statistical character of the Stokes pulse energies changes rapidly from that characteristic of a quantum-noise-initiated process to one characteristic of a stable source as the level of the injected seed Stokes is increased. However, for interaction regions with Fresnel numbers of 1 or smaller, the Stokes pulse-energy statistics show a gradual change as the level of the seed Stokes signal is increased and do not become stabilized until the seed Stokes is more than 100 times the total level needed to control the spatial character of the output Stokes in the larger-Fresnel-number cases. This slow change in the statistics for the Fresnel 1 system, and the suppression of the quantum-noise-initiated signal in the larger-Fresnel-number systems, is not fully understood at this time.

© 1990 Optical Society of America

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References

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  1. M. G. Raymer, K. Rzażewski, J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71 (1982).
    [CrossRef] [PubMed]
  2. I. A. Walmsley, M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382 (1986).
    [CrossRef] [PubMed]
  3. N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
    [CrossRef]
  4. K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
    [CrossRef]
  5. M. A. Henesian, 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 (1986).
  6. M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
    [CrossRef] [PubMed]
  7. J. Mostowski, B. Sobolewska, “Waveguide effects in super-fluorescence and stimulated Raman scattering,” Phys. Rev. A 34, 3109 (1986).
    [CrossRef] [PubMed]
  8. K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
    [CrossRef]
  9. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 769.
  10. S. J. Kuo, C. Radzewicz, M. G. Raymer, in Digest of the 1987 Annual Meeting (Optical Society of America, Washington, D.C., 1987), p. 29.
  11. M. G. Raymer, J. Mostowski, “Stimulated Raman scattering: unified treatment of spontaneous initiation and spatial propagation,” Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  12. M. Lewenstein, “Fluctuations in the nonlinear regime of stimulated Raman scattering,” Z. Phys. B 56, 69 (1984).
    [CrossRef]
  13. I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
    [CrossRef]
  14. M. D. Duncan, R. Mahon, L. L. Tankersley, J. Reintjes, “Transient stimulated Raman scattering in hydrogen,” J. Opt. Soc. Am. B 5, 37 (1988).
    [CrossRef]
  15. This software is published by Big Sky Software Corporation, P.O. Box 3220, Bozeman, Montana 59772.
  16. W. K. Bischel, M. J. Dyer, “Temperature dependence of the Raman linewidth and line shift for the Q(1) and Q(0) transitions in normal and para-H2,” Phys. Rev. A. 33, 3113 (1986).
    [CrossRef] [PubMed]

1988 (1)

1986 (5)

W. K. Bischel, M. J. Dyer, “Temperature dependence of the Raman linewidth and line shift for the Q(1) and Q(0) transitions in normal and para-H2,” Phys. Rev. A. 33, 3113 (1986).
[CrossRef] [PubMed]

I. A. Walmsley, M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382 (1986).
[CrossRef] [PubMed]

K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
[CrossRef]

M. A. Henesian, 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 (1986).

J. Mostowski, B. Sobolewska, “Waveguide effects in super-fluorescence and stimulated Raman scattering,” Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

1985 (2)

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

1984 (2)

N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
[CrossRef]

M. Lewenstein, “Fluctuations in the nonlinear regime of stimulated Raman scattering,” Z. Phys. B 56, 69 (1984).
[CrossRef]

1982 (2)

M. G. Raymer, K. Rzażewski, J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71 (1982).
[CrossRef] [PubMed]

K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
[CrossRef]

1981 (1)

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

Bischel, W. K.

W. K. Bischel, M. J. Dyer, “Temperature dependence of the Raman linewidth and line shift for the Q(1) and Q(0) transitions in normal and para-H2,” Phys. Rev. A. 33, 3113 (1986).
[CrossRef] [PubMed]

Duling, I. N.

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

Duncan, M. D.

Dyer, M. J.

W. K. Bischel, M. J. Dyer, “Temperature dependence of the Raman linewidth and line shift for the Q(1) and Q(0) transitions in normal and para-H2,” Phys. Rev. A. 33, 3113 (1986).
[CrossRef] [PubMed]

Fabricius, N.

K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
[CrossRef]

N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
[CrossRef]

Henesian, M. A.

M. A. Henesian, 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 (1986).

Kafka, J. D.

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

Kuo, S. J.

S. J. Kuo, C. Radzewicz, M. G. Raymer, in Digest of the 1987 Annual Meeting (Optical Society of America, Washington, D.C., 1987), p. 29.

Lewenstein, M.

M. Lewenstein, “Fluctuations in the nonlinear regime of stimulated Raman scattering,” Z. Phys. B 56, 69 (1984).
[CrossRef]

K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
[CrossRef]

Mahon, R.

Mostowski, J.

J. Mostowski, B. Sobolewska, “Waveguide effects in super-fluorescence and stimulated Raman scattering,” Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

M. G. Raymer, K. Rzażewski, J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71 (1982).
[CrossRef] [PubMed]

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

Nattermann, K.

K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
[CrossRef]

N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
[CrossRef]

Pennington, D. M.

M. A. Henesian, 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 (1986).

Radzewicz, C.

S. J. Kuo, C. Radzewicz, M. G. Raymer, in Digest of the 1987 Annual Meeting (Optical Society of America, Washington, D.C., 1987), p. 29.

Raymer, M. G.

I. A. Walmsley, M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382 (1986).
[CrossRef] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
[CrossRef]

M. G. Raymer, K. Rzażewski, J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71 (1982).
[CrossRef] [PubMed]

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

S. J. Kuo, C. Radzewicz, M. G. Raymer, in Digest of the 1987 Annual Meeting (Optical Society of America, Washington, D.C., 1987), p. 29.

Reintjes, J.

Rzazewski, K.

M. G. Raymer, K. Rzażewski, J. Mostowski, “Pulse-energy statistics in stimulated Raman scattering,” Opt. Lett. 7, 71 (1982).
[CrossRef] [PubMed]

K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 769.

Sizer, T.

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

Sobolewska, B.

J. Mostowski, B. Sobolewska, “Waveguide effects in super-fluorescence and stimulated Raman scattering,” Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

Tankersley, L. L.

von der Linde, D.

K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
[CrossRef]

N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
[CrossRef]

Walmsley, I. A.

I. A. Walmsley, M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382 (1986).
[CrossRef] [PubMed]

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

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

Opt. Commun. (3)

I. A. Walmsley, M. G. Raymer, T. Sizer, I. N. Duling, J. D. Kafka, “Stabilization of Stokes pulse energies in the nonlinear regime of stimulated Raman scattering,” Opt. Commun. 53, 137 (1985).
[CrossRef]

K. Nattermann, N. Fabricius, D. von der Linde, “Observations of transverse effects on quantum fluctuations in stimulated Raman scattering,” Opt. Commun. 57, 212 (1986).
[CrossRef]

K. Rzażewski, M. Lewenstein, M. G. Raymer, “Statistics of stimulated Stokes pulse energies in the steady state regime,” Opt. Commun. 43, 451 (1982).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

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

M. G. Raymer, I. A. Walmsley, J. Mostowski, B. Sobolewska, “Quantum theory of spatial and temporal coherence properties of stimulated Raman scattering,” Phys. Rev. A 32, 332 (1985).
[CrossRef] [PubMed]

J. Mostowski, B. Sobolewska, “Waveguide effects in super-fluorescence and stimulated Raman scattering,” Phys. Rev. A 34, 3109 (1986).
[CrossRef] [PubMed]

I. A. Walmsley, M. G. Raymer, “Experimental study of the macroscopic quantum fluctuations of partially coherent stimulated Raman scattering,” Phys. Rev. A 33, 382 (1986).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

W. K. Bischel, M. J. Dyer, “Temperature dependence of the Raman linewidth and line shift for the Q(1) and Q(0) transitions in normal and para-H2,” Phys. Rev. A. 33, 3113 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

N. Fabricius, K. Nattermann, D. von der Linde, “Macroscopic manifestation of quantum fluctuations in transient stimulated Raman scattering,” Phys. Rev. Lett. 52, 113 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. A. Henesian, 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 (1986).

Z. Phys. B (1)

M. Lewenstein, “Fluctuations in the nonlinear regime of stimulated Raman scattering,” Z. Phys. B 56, 69 (1984).
[CrossRef]

Other (3)

This software is published by Big Sky Software Corporation, P.O. Box 3220, Bozeman, Montana 59772.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 769.

S. J. Kuo, C. Radzewicz, M. G. Raymer, in Digest of the 1987 Annual Meeting (Optical Society of America, Washington, D.C., 1987), p. 29.

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Figures (5)

Fig. 1
Fig. 1

Spatial modes imaged at the output window of a transient Raman amplifier: (a) the 683-nm seed Stokes has a radius of 2.1 mm and a Fresnel number of 7, (b) the 532-nm pump has a radius of 1.9 mm and a Fresnel number of 7, (c) two examples of the randomly generated spontaneous stokes signal after stimulated amplification to a level of 109 to 1010 photons, (d) two examples of the amplified Stokes signal when 1400 seed Stokes photons are injected into the Raman interaction, (e) two examples of the amplified Stokes signal when 1.4 × 104 seed Stokes photons are injected into the Raman interaction.

Fig. 2
Fig. 2

Spatial modes imaged at the output window of a transient Raman amplifier: (a) the 683-nm seed Stokes has a radius of 1.0 mm and a Fresnel number of 1.5, (b) the 532-nm pump has a radius of 1.9 mm and a Fresnel number of 7, (c) two examples of the randomly generated spontaneous Stokes signal after stimulated amplification to a level of 109 to 1010 photons, (d) two examples of the amplified Stokes signal when 325 seed Stokes photons are injected into the Raman interaction, (e) two examples of the amplified Stokes when 860 seed btokes photons are injected into the Raman interaction.

Fig. 3
Fig. 3

Stokes pulse-energy statistics for (a) an unseeded amplifier pumped by a Fresnel 4 beam in the unsaturated regime, (b) the seed-Stokes produced in a saturated self-generator.

Fig. 4
Fig. 4

Pulse-energy statistics and spatial modes of the amplified Stokes: (a) for 102 seed Stokes photons, (b) for 103 seed Stokes photons, (c) for 104 seed Stokes photons. The 532-nm pump beam was collimated to a Fresnel number of 4 and the seed Stokes beam to an effective Fresnel number of 6.5 over the 1-m length of the amplifier cell.

Fig. 5
Fig. 5

Pulse-energy statistics of a Fresnel-number-0.7 system for various levels of seed Stokes: (a) no seed Stokes, (b) 30 seed Stokes photons, (c) 150 seed Stokes photons, (d) 104 seed Stokes photons, (e) 106 seed Stokes photons, (f) 109 seed Stokes photons.

Equations (3)

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P ( W ) = W 1 exp ( W / W ) ,
P N ( W T ) = 1 ( N 1 ) ! W T N 1 W N exp ( W T / W ) ,
S N = N d σ d Ω d Ω z 0 ν S ν P P N ,

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