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Physical Review A

Growth from spontaneous emission in a Raman multipass cell

Philip R. Battle, Jim G. Wessel, John L. Carlsten

Published May 1, 1993• 9 citations
Publisher

Abstract

Previous investigations of stimulated Raman scattering in a multipass cell have considered the amplification of a Stokes input pulse. They found that a simple plane-wave transient theory, appropriately scaled to include the multiple passes and focusing, matched experimental data well. In this paper, we investigate growth from spontaneous emission in a ${\mathrm{H}}_{2}$ Raman multipass cell. We find that a fully-quantum-mechanical scaled plane-wave theory describes the growth from spontaneous emission well in the high-gain limit. However, in the low-gain regime there is a significant increase in the Stokes output which is not predicted by the scaled plane-wave theory.

DOI
10.1103/physreva.47.4308

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Measurements of the output of a Raman amplifier when there is no input Stokes seed are presented.It is shown that a fully quantum mechanical scaled planewave theory describes the growth from spontaneous emission well in the high gain limit.However, in the low gain regime there is a significant increase in the amount of Stokes output which is not predicted by the plane wave theory.To account for the deviation from planewave growth observed at low gain, a fully quantum mechanical theory of amplification in a focused gain geometry is presented.The theory is based on a non-orthogonal mode expansion of the amplified field and incorporates the effects of both gain-guiding and diffraction.In addition to accounting for the observed Stokes output at low gain the non-orthogonal mode theory predicts that the Stokes field cart experience enhanced gain as well as have excess noise.Results from an experiment are presented which verify the existence of enhanced gain in a multipass Raman amplifier.Though the experiment does not give a direct measure of the excess noise factor the results

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Previous investigations of stimulated Raman scattering in a multipass cell have considered the amplification of a Stokes input pulse. They found that a simple plane-wave transient theory, appropriately scaled to include the multiple passes and focusing, matched experimental data well. In this paper, we investigate growth from spontaneous emission in a H2{\mathrm{H}}_{2}H2​ Raman multipass cell. We find that a fully-quantum-mechanical scaled plane-wave theory describes the growth from spontaneous emission well in the high-gain limit. However, in the low-gain regime there is a significant increase in the Stokes output which is not predicted by the scaled plane-wave theory.
Measurements of the output of a Raman amplifier when there is no input Stokes seed are presented.It is shown that a fully quantum mechanical scaled planewave theory describes the growth from spontaneous emission well in the high gain limit.However, in the low gain regime there is a significant increase in the amount of Stokes output which is not predicted by the plane wave theory.To account for the deviation from planewave growth observed at low gain, a fully quantum mechanical theory of amplification in a focused gain geometry is presented.The theory is based on a non-orthogonal mode expansion of the amplified field and incorporates the effects of both gain-guiding and diffraction.In addition to accounting for the observed Stokes output at low gain the non-orthogonal mode theory predicts that the Stokes field cart experience enhanced gain as well as have excess noise.Results from an experiment are presented which verify the existence of enhanced gain in a multipass Raman amplifier.Though the experiment does not give a direct measure of the excess noise factor the results
Previous investigations of Raman amplification in a multipass cell showed that a plane-wave transient theory matched the experimental data. In this work the output energy of a Raman amplifier was measured when no input was present. To model the output we initially used a fully quantum mechanical plane wave theory, which was scaled to take into account both the focusing and the multiple passes with the noise source being the usual one photon per mode. While the theory adequately describes the exponential growth for large gain, for gz < 10 there is a substantial deviation between the theory and experiment. To account for this excess noise the Stokes output is modeled by using a set of non-power-orthogonal modes. These modes arise naturally from the non-Hermitian nature of the gain guided process. It is the inherent non-power-orthogonality of these modes that can lead to excess noise, as noted first by Petermann. We find that the output from this model matches qualitatively the observed experimental output.
The semiclassical theory of spontaneous Raman scattering is reviewed. From the semiclassical theory we identify the parameters and dynamical variables involved in Raman scattering. A classical theory of stimulated Raman scattering is constructed. It is an extension of the theory of Shen and Bloembergen. We show that the system is a weakly coupled system. Because the driving term contains dynamical variables, the linewidth of the stimulated Stokes wave should be smaller than that of the spontaneous Stokes wave. Using Riemann's method, we obtain Kroll's solution rigorously, in a more general form. The steady-state limit is also derived rigorously. The conditions for the transient and steady-state gains are discussed. It is shown that for the transient case one may have an abrupt change of the Stokes gain versus incident laser power.
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.
A theory of nonstationary stimulated Raman scattering is developed, allowing for the coupling between the Stokes and anti-Stokes waves. The main equations are solved in the asymptotic approximation, which is valid for large values of the gain. The dependences of the gain on the phase mismatch Δ k , pulse duration τ p , and cell length l are discussed and the optimal angle for the observation of the anti-Stokes rings is calculated. Moreover, the spectral distributions of the Stokes and anti-Stokes waves are considered.
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.