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Soviet Journal of Quantum Electronics

Accumulation effect in transient electronic stimulated Raman scattering accompanying pumping by a train of ultrashort pulses

V.M. Avakyan, Б. В. Крыжановский, David G. Sarkisyan

Published Sep 30, 1990• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qe1990v020n09abeh007412

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Annual Meeting Optical Society of America•Jan 1, 1985•0 citations
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.
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 results of numerical calculations of the transient stimulated Raman scattering reported previously have been verified experimentally under conditions where both linear dispersion and self-focusing effects were negligible. The existence of a delay between maxima of the laser and Stokes pulses is experimentally demonstrated for the first time, while the pulse shortening in time via Raman scattering is established more firmly than in previous work. The incident-laser-pulse duration, generated-Stokes-pulse duration, and delay between intensity maxima for the laser and Stokes pulses were measured with the two-photon absorption-fluorescence technique. The effective phonon-dephasing time is determined via spontaneous Raman scattering. By using these measured quantities, inferences are made as to the magnitude of the transient gain and the shape of the exciting picosecond laser pulse.
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.
The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.
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 .