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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spectrum of Stokes component of the resonant stimulated Raman scattering in a multimode pump field

Anatoly A. Afanas'ev, B. A. Samson, N. B. Gubar

Published Jan 2, 1995• 0 citations
Publisher

Abstract

The theory of RSRS in a multi-mode pump field with a symmetric spectrum is developed. The spectral dependences of a RSRS-gain coefficient for the different values of distance between modes and amplitudes of pump modes are studied. The conditions of an arising of narrow resonances with width approximately (gamma) are defined.
DOI
10.1117/12.197737

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The development of the Stokes spectrum and the dependence of Raman gain upon pump laser bandwidth in a narrow linewidth Raman medium are analyzed in terms of a closed set of multimode equations. The analysis predicts that the Stokes gain coefficient takes on its maximum value, which is independent of bandwidth, when the Stokes spectrum replicates the pump spectrum. It is also shown that in the absence of dispersion the spectrum of a weak Stokes wave is driven to duplicate the pump spectrum, and that for noise input the average power generated in the Stokes wave is independent of the pump bandwidth.
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.
We conduct a theoretical analysis of the Stokes component mode structure of the Raman scattering. The Raman scattering is excited in a multimode waveguide with pump radiation having statistics corresponding to the model of the narrow-band Gaussian noise. We obtain an analytical relation connecting the number of spatially coherent modes of the Stokes component, characteristics of the waveguide and conditions of the Raman scattering excitation. It follows from the obtained relation that the Raman scattering spatial coherency degree at the waveguide's exit is determined by the number of the spatial modes of pump radiation and the amplification of the Stokes radiation throughout the waveguide's length. There exists a threshold in the amplification corresponding to the unlimited increase of the number of the spatially coherent modes of the Raman scattering and therefore to a zero of spatial coherency. Conducted estimations show that at the Raman scattering threshold value of the radiation intensity the number of the spatially coherent modes of the Raman scattering Stokes component should be comparable to that of the thermal source. Experimentally, measured dispersion of the spatial intensity fluctuations of the Stokes component isolated with an interference filter (spectral bandwidth ~ 1nm, λ = 620nm) is three time smaller than that of the luminescent lamp radiation.
An analysis is made of the influence of the width of the pump line on the stimulated scattering in Fabry–Perot and ring resonators which are tuned both to the pump frequency and to the frequency of the Stokes component. It is shown that the excitation threshold of the stimulated scattering in dispersion-free media is independent of the width of the pump line, because of the parametric interaction between the modes, whereas in media with a considerable dispersion the threshold is Δω p /Δω sp greater than the stimulated emission threshold under monochromatic pumping conditions (the subscripts "p" and "sp" refer to the pump wave and to the spontaneous Raman scattering). Analytic expressions are given for the amplitudes of the pump and Stokes fields at the excitation threshold and under steady-state conditions.
The mode structure of the Stokes component of stimulated Raman scattering (SRS) in a multimode fibre excited by a pump field with statistics corresponding to a narrowband Gaussian noise model is theoretically analysed. The relation is obtained between the number of spatially coherent radiation modes of the Stokes wave and fibre parameters and SRS excitation conditions. It follows from this relation that the degree of spatial coherence of the Stokes radiation at the fibre output is determined by the number of spatial modes of pump radiation and the averaged gain of the Stokes radiation over the interaction length. It is established that there exists the threshold gain at which the number of spatially coherent radiation modes of the Stokes component increases infinitely and, therefore, its spatial coherence tends to zero. The estimates of the number of spatially coherent radiation modes of the Stokes component showed that already at the Raman scattering excitation threshold their number is so great that the degree of spatial coherence of the Stokes component radiation corresponds to the degree of coherence of a thermal source radiation. The measured dispersion of spatial intensity fluctuations of the Stokes component sepa-rated by using an interference filter (with the transmission bandwidth ≈1 nm at 620 nm) proved to be approximately three times higher than the dispersion of radiation intensity fluctuations of a luminescent lamp. The large dispersion of spatial intensity fluctuations of the Stokes component is caused most likely by individual intensity spikes in a small-scale (unresolved by a detector with a spatial resolution of ≈14 μm) speckle pattern produced in the detection plane by monochromatic Stokes radiation.
The quantum theory-of Stokes generation by stimulated Raman scattering of a multimode laser is developed and analyzed. For large laser-mode spacing, the generated Stokes intensity is found to be independent of the number of laser modes for both high and low gains. The result applies to both free-running and mode-locked lasers and is in contrast to that in the Raman amplifier, in which gain is found to depend on the number of modes. The Stokes light is generated with mode amplitudes and phases in perfect correlation with those of the laser. Also, in steady state the instantaneous Stokes intensity is found to follow exactly the rapid fluctuations of the laser intensity.