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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theory of spectra of coherent four-photon scattering with one-photon resonances due to excited and autoionizing atomic states

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

Published May 10, 1996• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.239788

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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.
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
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.
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.
An investigation was made of the spectral properties of four-photon parametric oscillation when the frequency of the generated field is tunable near an atomic resonance line. An ω4 = ω1–ω2+ω3 generation process involving coherent anti-Stokes scattering in thallium vapor was achieved experimentally. Biharmonic pumping was provided by resonant excitation of a 6P1/2–6P3/2 two-photon transition at the frequency ω1–ω2. Measurements were made of the oscillation power when the frequency ω3 was tunable near the frequency of a 6P3/2–7D3/2 transition at various thallium vapor pressures. It was found that the spectral properties of resonant parametric oscillation depend strongly on the concentration of active-mixture atoms and also on various saturation effects.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
A quantum theory of coherent four-photon spectroscopy of electron resonances in molecular systems is developed. A model allowing for real properties of the dispersion of perturbations modulating electron transitions in complex molecules is considered. New relationships are established between the characteristics of spectra of one-photon absorption and the law governing the dispersion of a signal obtained in steady-state four-photon spectroscopy, conditions for excitation of this signal, its dispersion, etc. It is shown that the theory agrees with the available experimental data.