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and Autoionizing Atomic States

Nikolai I Koroteev, Aleksandr N. Naumov, Aleksei M. Zheltikov

Published Jan 1, 2017• 0 citations
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Abstract

Koroteev, A. N. Naumov, and A. M. ZheltikovInternational Laser Center,Moscow State University, Moscow, 119899 RussiaABSTRACTCoherent four-photon scattering oflight due to excited and autoionizing states of atomic systems isconsidered. We analyze the influence of one-photon resonances at the frequency of the anti-Stokes signaland at the frequency of the pump wave on the shape of the spectrum of four-photon scattering. We deriveanalytical expressions for the line shapes of four-photon scattering involving one-photon resonances withallowance for phase-matching conditions and variation in the populations of excited states for limitingregimes of tight focusing and sirong absorption in a medium with a cubic nonlinearity. The calculatedspectra of four-photon scattering include the interference of resonant and nonresonant components of thethird-order nonlinear susceptibility with allowance for one-photon saturation. We develop a method fornormalizing experimental spectra of four-photon scattering with one-photon resonances that takes into

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Koroteev, A. N. Naumov, and A. M. ZheltikovInternational Laser Center,Moscow State University, Moscow, 119899 RussiaABSTRACTCoherent four-photon scattering oflight due to excited and autoionizing states of atomic systems isconsidered. We analyze the influence of one-photon resonances at the frequency of the anti-Stokes signaland at the frequency of the pump wave on the shape of the spectrum of four-photon scattering. We deriveanalytical expressions for the line shapes of four-photon scattering involving one-photon resonances withallowance for phase-matching conditions and variation in the populations of excited states for limitingregimes of tight focusing and sirong absorption in a medium with a cubic nonlinearity. The calculatedspectra of four-photon scattering include the interference of resonant and nonresonant components of thethird-order nonlinear susceptibility with allowance for one-photon saturation. We develop a method fornormalizing experimental spectra of four-photon scattering with one-photon resonances that takes into
Coherent four-photon scattering of light due to excited and autoionizing states of atomic systems is considered. We analyze the influence of one-photon resonances at the frequency of the anti-Stokes signal and at the frequency of the pump wave on the shape of the spectrum of four-photon scattering. We derive analytical expressions for the line shapes of four-photon scattering involving one-photon resonances with allowance for phase-matching conditions and variation in the populations of excited states for limiting regimes of tight focusing and strong absorption in a medium with a cubic nonlinearity. The calculated spectra of four-photon scattering include the interference of resonant and nonresonant components of the third-order nonlinear susceptibility with allowance for one-photon saturation. We develop a method for normalizing experimental spectra of four-photon scattering with one-photon resonances that takes into account distortion of spectral lines due to the influence of phase mismatch and one- photon absorption.
An analysis is made of the influence of the phase matching conditions on the four-photon scattering spectrum at a one-photon resonance under various focusing conditions. An analytic expression is obtained for the phase matching integral in the limiting cases of hard focusing and strong absorption in a medium with the cubic nonlinearity. A study is made of the influence of one-photon resonances on the form of the spectrum of four-photon scattering by excited and preionisation states of atoms. Calculations are reported of the four-photon scattering spectra in which allowance is made for the interference of the resonant and nonresonant components of the third-order nonlinear susceptibility. A method for the normalisation of the experimental four-photon scattering spectra under one-photon resonance conditions is proposed; this method allows for the distortions associated with the influence of the phase mismatch and of one-photon absorption.
The effect of atomic collisions on the optical characteristics of an ensemble of excited atoms is well known [ 1 , 2 ]. The evolution of laser techniques and the resulting interest in various nonlinear-spectroscopy methods have suggested that atomic collisions have a significant effect on the lasing mode of gas lasers and the shape and width of various nonlinear signals. For a long time attention has been focused on the important role of elastic collisions, among other things, and various methods have been proposed for describing such collisions [ 3 ].
The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of T1{T}_{1}T1​ or T2{T}_{2}T2​. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.
It is shown that in order to obtain a correct interpretation of experiments on four-photon nonlinear spectroscopy within the absorption line, it is necessary to allow not only for a coherent four-photon process due to a resonant electronic nonlinearity but also for a similar process involving generation of optically induced diffraction gratings followed by the diffraction of one of the probe beams from these gratings. It is also necessary to allow for the contribution of highly excited molecular states to the resonant electronic nonlinearity. General expressions are derived and investigated for the cubic susceptibility in an isotropic medium. It is found that all nonzero components of this tensor may be expressed in terms of a single scalar function of the interacting wave frequencies. The explicit form of this function is determined in the lowest order of perturbation theory.