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Annual Meeting Optical Society of America

Response of stimulated Raman scattering to a pulse train

Bruce J. Herman, Marek J. Konopnicki

Published Jan 1, 1987• 0 citations
Publisher

Abstract

The high pulse repetition rates (~100 MHz) of radio-frequency free-electron lasers make possible the investigation of molecular response to a rapid pulse train.1 When the molecular decay time T2 is much larger than the time between pulses T, molecular memory is carried from pulse to pulse. For stimulated Raman scattering (SRS) the memory effect can lead to an increase in the size of the Raman dipole resulting in enhanced scattering. We analyze the 1-D SRS equations in the condition that the scattering under an individual pulse occurs in the transient regime (~10 ps). We obtain a general expression for the behavior of SRS which reduces to the following long-time limits: (1) When T2 ≪ T, the SRS from each pulse in the train develops independently from the others; (2) When T2 ≫ T, the transient SRS response is equivalent to the steady-state response to a constant pump at the time-averaged pump intensity. We also perform this analysis for a medium such as the atmosphere where the density of scatterers and Raman bandwidth decrease exponentially with distance.

DOI
10.1364/oam.1987.mi10

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The high pulse repetition rates (~100 MHz) of radio-frequency free-electron lasers make possible the investigation of molecular response to a rapid pulse train.1 When the molecular decay time T2 is much larger than the time between pulses T, molecular memory is carried from pulse to pulse. For stimulated Raman scattering (SRS) the memory effect can lead to an increase in the size of the Raman dipole resulting in enhanced scattering. We analyze the 1-D SRS equations in the condition that the scattering under an individual pulse occurs in the transient regime (~10 ps). We obtain a general expression for the behavior of SRS which reduces to the following long-time limits: (1) When T2 ≪ T, the SRS from each pulse in the train develops independently from the others; (2) When T2 ≫ T, the transient SRS response is equivalent to the steady-state response to a constant pump at the time-averaged pump intensity. We also perform this analysis for a medium such as the atmosphere where the density of scatterers and Raman bandwidth decrease exponentially with distance.
The nonlinear regime of stimulated Raman scattering (SRS) may be reached in two ways. The best known is that of depletion of the pump laser as a large number of photons are scattered into the Stokes field. There is, however, another way in which gain saturation can occur, that is, by depletion of the atomic population while the laser remains undepleted. The equations which describe SRS, including damping and population inversion,1 are remarkably similar to those of well-known theories of two-level superfluorescence, and it is possible by analogy to define a delay time τ D for cooperative Raman scattering (CRS). This delay time is inversely proportional to the spontaneous scattering rate, which depends on the pump laser intensity. A sufficient condition for CRS is that the spontaneous Stokes linewidth Γ is very much greater than τ D − 1 . The only other requirement is that there be more laser photons than scatterers, so that τ D is independent of the number of scatterers. The S(1) transition in molecular hydrogen, when excited by a short (≅ 100-ps) laser pulse, provides a possible system for observing pure CRS. Similar studies have been carried out previously2 for Γ ≅ τ D − 1 .
We consider transient stimulated Raman amplification of trains of picosecond pulses. In this regime the gain of a single pulse is reduced from its steady-state value because of the inability of the nonlinear polarization to follow the time variations of the pump pulse. In addition oscillatory behavior of the pump and Stokes pulse amplitudes have been predicted in the transient regime in conditions of high pump depletion. When the pump radiation is in the form of a train of pulses whose separation is comparable to or shorter than the dephasing time of the nonlinear medium, increased gain can be experienced by later pulses in the train because they can grow from the material polarization created by earlier pulses. We have analyzed this type of amplification as a function of pulse spacing, pump energy, and pump intensity in the regime of high pump depletion. In addition we have considered the effects of Stark shifts of the two-photon resonant Raman level on the Stokes conversion efficiency. We find that at constant pulse intensity the conversion efficiency increases with time through the pulse train, gradually approaching steady state at low conversion efficiencies at times long compared to T2. The maximum conversion efficiency increases as the pulse spacing is decreased. If the pump depletion is too high the peak conversion of the Stokes oscillates through the train in a manner similar to the oscillations of the intensity of a single pulse. A Stark shift of the resonant level can cause reduced gain as well as introduce phase shifts on the Stokes and pump beams. The effects of these processes on the conversion efficiency are discussed.
Investigations were made of the accumulation effect exhibited by transient electronic stimulated Raman scattering in atomic barium vapor pumped by a train of ultrashort pulses with a controlled time delay between the pulses. The essential feature of the accumulation effect is that the Stokes energy of a pulse is contributed to not only by its own exciting pump pulse, but also by the previous pump pulse, the influence of the latter depending strongly on the ratio of the transverse relaxation time T2 to the interpulse time interval. If one is to observe the accumulation effect in electronic stimulated Raman scattering, it is important to minimize the influence of depletion of the number of atoms. A method based on the accumulation effect for determination of T2 in one laser shot was developed.
A method is developed for studying transient stimulated Raman scattering in the quasi-steady-state regime when the input pump field consists of a repetitive periodic sequence of pulses. The method is most attractive for cases where the single-pulse duration is substantially shorter than the repetition time scale, making a straightforward numerical simulation very costly, time consuming, and potentially intractable. The method is applicable to any periodic electric field envelope including that generated by a finite number of longitudinal modes with arbitrary phase. A second numerically efficient method is developed for treating the buildup of the entire pulse train. In addition, an analytic solution is found in the undepleted-pump regime which illuminates the underlying physics of the process.
Systems that exhibit stimulated Raman scattering in the transient limit have long been the subject of theoretical and experimental study, and recent experimental developments have made possible the observation of the long-distance evolution of these systems. These systems are integrable using the inverse scattering method; however, in contrast to the usual behavior in integrable systems, solitons do not dominate the long-distance behavior. Instead, solitons are transient, and self-similarity appears in the long-distance limit. In this paper, the similarity solutions of the equations which describe stimulated Raman scattering are first reviewed from a physical standpoint. Inverse scattering theory is then used to show that given physically reasonable initial data in which the pump and Stokes waves have no linear frequency mismatch, the solution will converge toward a self-similar solution. These results are confirmed by a numerical comparison of the solution of the transient, stimulated Raman-scattering equations to the appropriate self-similar solutions. The length scale over which convergence occurs and the transient generation of solitons are observed. From a physical standpoint, the appearance of self-similarity rather than solitons in the long-distance limit can be attributed to the presence of memory in the Raman-active medium. Other systems with memory also exhibit self-similarity, and the results which are described here may have applications to a wide array of optical systems with memory. An experiment which could observe self-similarity is described.