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Physical Review A

Statistical theory of Raman amplification and spontaneous generation in dispersive media pumped with a broadband laser

A. T. Georges

Published Feb 1, 1989• 13 citations
Publisher

Abstract

We present a statistical theory of forward and backward Raman amplification and spontaneous generation in dispersive media pumped by a phase-diffusion field of arbitrary bandwidth. It is shown that, unless the Stokes input is correlated with the pump, the Stokes output and the pump are statistically orthogonal, even if the Stokes field builds up spontaneously. The growth of the average Stokes field amplitude is not affected by dispersion. A general expression is given for the average Stokes intensity which is valid both above and below the critical pump intensity for overcoming the decorrelating effects of group-velocity dispersion. If the length of the medium is much greater than the coherence length associated with the dephasing of the two waves, then the average intensity of stimulated Raman scattering (SRS) depends on the pump bandwidth. For relatively short medium lengths the average intensity of spontaneously initiated SRS is essentially independent of the bandwidth of a phase-diffusion pump field.

DOI
10.1103/physreva.39.1876

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Stimulated Raman scattering of colored chaotic light in dispersive media

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A theory is presented for forward- and backward-stimulated Raman scattering of colored chaotic light in dispersive media. Both amplification of a coherent Stokes seed and spontaneous generation are treated. It is shown that group-velocity dispersion reduces the gain for the average Stokes intensity, while the intensity fluctuations in the pump enhance it. For a given bandwidth, chaotic light is scattered more efficiently than coherent light when its average intensity exceeds the critical intensity for overcoming the decorrelating effects of group-velocity dispersion on the pump and Stokes waves. The figures presented demonstrate the asymmetry in the intensity of forward and backward Raman scattering of nonmonochromatic light.

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Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.

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Theory of stimulated Raman scattering in a dispersive medium

Igor' M Bel'dyugin, E M Zemskov, V. K. Orlov

An analysis is made of the laws governing amplification of the Stokes wave in stimulated Raman scattering (STRS) in a dispersive medium for different models of wide-band pump radiation. An accurate solution of the STRS equations is obtained for pump radiation having a quadratically time-modulated phase. It is shown that for pump radiation for which the width of the instantaneous frequency spectrum is much less than the Raman scattering line width, the laws governing amplification of the Stokes wave differ substantially from those predicted by statistical STRS theory. Solutions of STRS equations in a dispersive medium are found for a model of temporally periodic pump radiation having a high intermode beat frequency.

Soviet Journal of Quantum Electronics•Aug 31, 1980•2 citations
We present a statistical theory of forward and backward Raman amplification and spontaneous generation in dispersive media pumped by a phase-diffusion field of arbitrary bandwidth. It is shown that, unless the Stokes input is correlated with the pump, the Stokes output and the pump are statistically orthogonal, even if the Stokes field builds up spontaneously. The growth of the average Stokes field amplitude is not affected by dispersion. A general expression is given for the average Stokes intensity which is valid both above and below the critical pump intensity for overcoming the decorrelating effects of group-velocity dispersion. If the length of the medium is much greater than the coherence length associated with the dephasing of the two waves, then the average intensity of stimulated Raman scattering (SRS) depends on the pump bandwidth. For relatively short medium lengths the average intensity of spontaneously initiated SRS is essentially independent of the bandwidth of a phase-diffusion pump field.
A theory is presented for forward- and backward-stimulated Raman scattering of colored chaotic light in dispersive media. Both amplification of a coherent Stokes seed and spontaneous generation are treated. It is shown that group-velocity dispersion reduces the gain for the average Stokes intensity, while the intensity fluctuations in the pump enhance it. For a given bandwidth, chaotic light is scattered more efficiently than coherent light when its average intensity exceeds the critical intensity for overcoming the decorrelating effects of group-velocity dispersion on the pump and Stokes waves. The figures presented demonstrate the asymmetry in the intensity of forward and backward Raman scattering of nonmonochromatic light.
The authors have extended the theory of stimulated Raman scattering to include the effects of laser bandwidths, in both the transient and steady-state regimes. The case of two interacting laser beams, a pump laser and a probe (Stokes) laser, is treated. Using the phase-diffusion model for laser bandwidth, the authors demonstrate that in the absence of dispersion, the forward Raman gain is essentially independent of the laser bandwidths in the high-gain limit, while in the low-gain limit the gain coefficient is inversely proportional to the sum of the bandwidths. It is further shown that when the pump-laser bandwidth is much larger than the linewidth of the Raman medium, the stimulated Stokes output assumes the same spectrum as the pump laser in the high-gain limit. A possible interpretation of these results is discussed assuming a "phase-locking" of the Stokes phase to the fluctuations in the pump-laser phase, due to the nonlinear interaction of the two beams through the Raman medium.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.
A theoretical and experimental investigation was made of the amplification of a Stokes signal in a multimode pump field when the ratio of the spectral widths of the interacting fields was varied. In the pump intensity range I p < I cr ( I cr was a critical intensity) the gain increment was considerably less than the static value and it was governed entirely by the spectral distributions of the pump and Stokes signal. In the range I p > I cr the gain increment tended to the static value. An anomalous scatter of the Raman amplifier gain was observed experimentally for Δ ν s ≈Δ ν p ≫Δ ν l (Δ ν s ,Δ ν p , and Δ ν l were the line widths of the Stokes signal, pump, and spontaneous stimulated Raman scattering). A theory developed for the purpose indicated that the scatter was observed because the phase relationships between the interacting waves at the input into the medium varied from one measurement to another.
An analysis is made of the laws governing amplification of the Stokes wave in stimulated Raman scattering (STRS) in a dispersive medium for different models of wide-band pump radiation. An accurate solution of the STRS equations is obtained for pump radiation having a quadratically time-modulated phase. It is shown that for pump radiation for which the width of the instantaneous frequency spectrum is much less than the Raman scattering line width, the laws governing amplification of the Stokes wave differ substantially from those predicted by statistical STRS theory. Solutions of STRS equations in a dispersive medium are found for a model of temporally periodic pump radiation having a high intermode beat frequency.