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Soviet Journal of Quantum Electronics

Theory of frequency addition under resonance conditions

V. I. Anikin, Dariusz Gora, Konstantin N. Drabovich, A. N. Dubovik

Published Feb 28, 1976• 14 citations
Publisher

Abstract

An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.

DOI
10.1070/qe1976v006n02abeh010882

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An expression is obtained for the nonlinear susceptibility governing the addition of frequencies under resonance conditions. Allowance is made for the Stark shift, changes in populations, and transient response of the medium. Analysis is made of the stimulated emission of the third harmonic as a result of two-photon resonance in parallel and focused beams. It is shown that the saturation effect limits seriously the conversion coefficient of a nonlinear medium of fixed length. Optimal intensities of the fundamental-frequency radiation are found. It is shown that when a beam is focused sharply in a nonlinear medium, the saturation effect and Stark shift make it possible to add frequencies in media with normal dispersion. The relationship between four-photon parametric effects and coherent resonant processes such as self-induced transparency is established for ultrashort pulses.
A numerical investigation is made of third harmonic generation (THG) under conditions of two-photon resonance between the fundamental frequency and a selected transition in the atoms of a medium. It is shown that under conditions of coherent interaction between the pump pulse and the medium, a THG efficiency of ∼20% or higher may be achieved. In this case, THG in the form of high-power ultrashort pulses may be obtained. It is shown that experimental observation of similar effects in specific media should not present particular difficulties.
A theoretical analysis is made of the influence of the pump intensity on the nonlinear susceptibility of the third harmonic excited under conditions of two-photon resonance between the pump wave and the Doppler-broadened transition. Pumping by both traveling and standing waves is considered. For traveling wave pumping, an expression for the nonlinear harmonic susceptibility in an arbitrary field is derived and analyzed. The optimal detunings of twice the pump frequency relative to the two-photon transition frequency are determined. For standing wave pumping an expression for the nonlinear harmonic susceptibility is obtained from perturbation theory up to and including the third order. It is shown that an important factor in the reduction of the harmonic susceptibility is the saturation of the transition due to Doppler-free two-photon absorption of opposite traveling waves.
An investigation is made of four-photon sum and difference frequency generation under two-photon resonance conditions allowing for population migration accompanying incoherent processes and for the possibility of a one-photon quasiresonance with the emitted radiation in inverted and uninverted media. A study is made of parametric bleaching of the medium and phase locking of the interacting waves, their stability, and influence on the conversion quantum efficiency η . It is established that resonant parametric processes have a larger region of stability than nonresonant ones. An analysis is made of bifurcation, typical of resonant processes, that strongly influences η . Accurate analytic expressions are derived for the maximum attainable values of η and it is shown that there is an optimum frequency detuning from a one-photon resonance.
Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-\AA{} radiation by a five-photon mixing process in Li+{\mathrm{Li}}^{+}Li+ is considered.
An experimental investigation was made of the dispersion of the cubic susceptibility of sodium vapor in the region of two- and three-photon resonances with the 3s-4s and 3s-7p transitions. A compensation of the contributions to the nonlinear susceptibility of two- and three-photon resonances was observed. A theory was developed for the generation of the third harmonic in a nonmonochromatic field under resonance conditions and this theory was found to be in good agreement with the experimental results. A reduction in the effective susceptibility occurred in a strong field and this was due to saturation and Stark shift of the levels.
A review is given of recent theoretical investigations on coherent propagation and nonlinear interaction of multifrequency ultrashort radiation pulses in resonantly absorbing media. An analysis is made of frequency conversion by parametric interaction and stimulated Raman scattering of laser pulses in resonant three-level media. New ways of controlling the parameters of coherent pulses and the use of multifrequency pulses in the spectroscopy of multilevel media are discussed. The experimental capabilities of the investigated effects are considered.