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Soviet Journal of Quantum Electronics

Theory of transient hyper-Raman scattering in gases

Yu. P. Malakyan

Published Sep 30, 1989• 2 citations
Publisher

Abstract

A theory is developed for transient hyper-Raman scattering and four-wave parametric processes in a gaseous medium subjected to an ultrashort pump pulse field. Investigations are made of the intensity and spectrum of the infrared and ultraviolet radiation generated in a medium as a result of these processes, bearing in mind the transient properties of the pump (phase modulation, pulse profile). It is shown that the initial nonlinearity of the pump field and the parametric processes result in new effects not observed in transient stimulated Raman scattering. For a large two-photon detuning, the hyper-Raman forward scattering is suppressed because of destructive interference with stimulated parametric generation of ultraviolet radiation. The gain of the infrared and ultraviolet radiation depends on the pump pulse profile. Under exact two-photon resonance conditions in the absence of any phase modulation of the pump, infrared and ultraviolet pulses are coherently split into various subpulses and a time-dependent Autler–Townes doublet is observed in their spectrum.

DOI
10.1070/qe1989v019n09abeh009120

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A theory is developed for transient hyper-Raman scattering and four-wave parametric processes in a gaseous medium subjected to an ultrashort pump pulse field. Investigations are made of the intensity and spectrum of the infrared and ultraviolet radiation generated in a medium as a result of these processes, bearing in mind the transient properties of the pump (phase modulation, pulse profile). It is shown that the initial nonlinearity of the pump field and the parametric processes result in new effects not observed in transient stimulated Raman scattering. For a large two-photon detuning, the hyper-Raman forward scattering is suppressed because of destructive interference with stimulated parametric generation of ultraviolet radiation. The gain of the infrared and ultraviolet radiation depends on the pump pulse profile. Under exact two-photon resonance conditions in the absence of any phase modulation of the pump, infrared and ultraviolet pulses are coherently split into various subpulses and a time-dependent Autler–Townes doublet is observed in their spectrum.
Investigations are made of hyper-Raman scattering and four-photon parametric processes in two-photon excitation of metal vapor. The laws of propagation of infrared and ultraviolet radiation generated in a metal vapor medium by these processes are found for the steady-state interaction. The nonlinear polarization of the medium is obtained in terms of elements of the atomic density matrix allowing for saturation by the pump field and for the influence of collisions. The spectral and tuning characteristics of the converted radiation are studied and a comparison is made with experimental data. A dip observed in the infrared radiation spectrum for hyper-Raman scattering and its broadening are explained. A detailed discussion is given of the role of collisions that substantially narrow the tuning range of the infrared radiation in hyper-Raman scattering.
Parametric instability induced by the medium saturation in stimulated Raman scattering is investigated theoretically via a generalized detuning (1) where ω p,s,o are the frequency of the pump, Stokes, and phonon, ϕ ˙ p s is the phase modulation, and the last term is the nonlinear correction of the highly excited anharmonic molecule with an amplitude Q.The steady-state gain and hence the Stokes efficiency, in the presence of the anharmonic term, are governed by a cubic equation of |Q|2which is to be solved from the Bloch and Maxwell equations including the pump depletion. Numerical results are shown for the transition diagram of Stokes efficiency vs input pump intensity at various system conditions at the steady-state. For the transient regime, with pulse duration shorter than the dephasing time, we analyze the temporal profiles of the Stokes and the depleted pump based on a transformed equation which combines Bloch and Maxwell equation as follows: (2) where Tis a nonlinear time, G s is the steady-state gain, l0is the input pump intensity, and Uis the real part of the phonon amplitude Q.For an input pulse intensity given by sech2(t/t p ), Eq. (2) is solved numerically to study the transient pulse profiles in the presence of pump depletion and medium saturation.
The self-induced suppression (SIS) of stimulated electronic Raman scattering (SERS) is discussed. The nature of SIS is that SERS induces in gaseous media the generation of new fields by a four-wave mixing (FWM) process which destructively interferes with SERS and results in its suppression. The behaviour of Stokes radiation is investigated under SIS of SERS, both in the steady-state case and in the non-stationary regime of interaction with an ultrashort pump pulse. The effect is shown to be absent in the non-stationary case. On the basis of this result the author is able to explain in a simple manner the 'strange' dependence of the Stokes wavelength on pump pulse duration observed experimentally in barium vapours. The author also discusses the possible application of SIS of SERS for Stokes frequency switching. This can be achieved by stimulation of destructive interference between SERS and FWM if, simultaneously with the pump pulse, a signal wave at a frequency of one of the parametrically generated fields is switched on. As a result the FWM is intensified leading to strong suppression of SERS on a given transition and the Stokes radiation is now generated on the other transition with a new frequency. The method can be used to convert the laser frequency into the far-IR region and for a new spectroscopic study of gaseous media.
A formalism suited for the study of two-photon resonant processes in atomic vapors is developed. Applications to the study of hyper-Raman scattering, four-photon parametric conversion and second-harmonic generation were carried out. Hyper-Raman scattering and four-photon parametric conversion were analyzed at steady state in the small-gain and saturation regimes. For the small-gain region, the results of perturbation theory are reproduced. The behavior of Stokes and idler fields in the saturation regime is shown to be in agreement with experimental results. Several characteristics of the line shapes experimentally observed are also qualitatively explained. A time-frequency analysis of the transients of the Stokes gain provides a method of studying the evolution of Stark shifts and dynamical Stark splittings, as well as constituting a valuable tool to distinguish between Raman-type and population-type lines.