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Soviet Journal of Quantum Electronics

Spectral-temporal effects in resonant harmonic generation in gases

A. Z. Zhmudskii, A. M. Steba, V. L. Strizhevskiǐ

Published Mar 31, 1978• 0 citations
Publisher

Abstract

A theoretical investigation is made of unsteady quasiresonant optical third-harmonic generation in a gaseous nonlinear medium pumped by amplitude-modulated pulses of constant collimated radiation. It is shown that two effective unsteadiness mechanisms exist: wave unsteadiness, associated with the difference between the propagation velocities of the pump and harmonic waves, and local unsteadiness caused by the finite relaxation time of the appropriate nonlinear component of the polarization of the medium. In spectral terms these correspond to the resonant dispersion of the phase matching and the dispersion of the nonlinear polarizability of the medium, respectively. The output pulse profile is determined and the influence of the main parameters on its profile is analyzed. The stimulated emission spectrum is also studied for conditions when the pump field is a steady-state random Gaussian process.

DOI
10.1070/qe1978v008n03abeh010018

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A theoretical investigation is made of unsteady quasiresonant optical third-harmonic generation in a gaseous nonlinear medium pumped by amplitude-modulated pulses of constant collimated radiation. It is shown that two effective unsteadiness mechanisms exist: wave unsteadiness, associated with the difference between the propagation velocities of the pump and harmonic waves, and local unsteadiness caused by the finite relaxation time of the appropriate nonlinear component of the polarization of the medium. In spectral terms these correspond to the resonant dispersion of the phase matching and the dispersion of the nonlinear polarizability of the medium, respectively. The output pulse profile is determined and the influence of the main parameters on its profile is analyzed. The stimulated emission spectrum is also studied for conditions when the pump field is a steady-state random Gaussian process.
A theoretical analysis is made of generation and amplification of Stokes and anti-Stokes waves in gaseous media allowing for Raman and parametric processes and saturation effects. Allowance is also made for any difference between the Raman polarizabilities of the Stokes and anti-Stokes waves which may be caused in particular by the occurrence of one-photon quasiresonances of the interacting waves. Assuming that pump and Stokes (or anti-Stokes) waves are applied at the entrance to a medium (inverted or uninverted), a general solution is found for the amplitudes of the interacting waves under exact resonance and phase-matching conditions. This is used as the basis to investigate their spatial evolution (in particular, for inverse Raman light scattering) and expressions are found for the maximum efficiencies for conversion of the pump to Stokes and/or anti-Stokes waves. It is shown that depending on the relationship between the Raman polarizabilities and also on the input parameters of the waves, conditions of parametric bleaching of the medium with nonzero amplitudes of all the waves or conditions of complete conversion of the pump to the Stokes and anti-Stokes waves or to one of these are established asymptotically. An investigation is made of the stability of these solutions.
The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.
Several extensions are made in theoretical studies of multiphoton ionization associated with third-harmonic fields that are generated near three-photon resonances in gaseous media. The treatment includes the strong coherent cancellation effect which occurs between three-photon pumping of a resonant level and pumping by the third-harmonic field that is generated in the same medium. The incomplete spoiling of the cancellation effect with counterpropagating beams is quantitatively described. Also, treatment of the multiphoton-ionization problem involving phase-matched, third-harmonic fields is generalized to include quantitative effects of index changes due to a buffer gas, absorption due to dimers, and collisional dephasing of coherent excitations. Finally, we show how measurements of linewidths, phase-matching positions, and pressure dependences of ionization yields associated with third-harmonic generation and subsequent absorption can be used to determine oscillator strengths of a resonant level, absorption coefficients for a resonant species and a buffer-gas species, and the refractive index of the buffer gas at the third-harmonic frequency.
An investigation is reported of the characteristic features of a four-wave mixing of a chirped signal with bandwidth- limited pump waves in a resonant medium modeled by a two- level scheme. Analytic estimates are obtained and a numerical analysis is made of the combined influence of various mechanisms (spatial phase matching, a finite nonlinear response time, and phase cross-modulation) on the spectral composition and on the temporal behavior of the fourth pulse. Conditions are found for achieving, with practically undetectable distortions, phase conjugation of a chirped signal accompanied by shortening of the pulse envelope and narrowing of the spectrum of the phase- conjugate wave.
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.
The review systematizes the experimental material and reports the fundamental theoretical results on the study of nonlinear resonance effects in spectra of atomic systems situated in the radiation field of lasers. The theoretical part explains the topics of greatest importance and significance for understanding of the experimental studies: the Stark effect in an optical field; the nonequilibrium velocity distribution of the atoms; the shape of the spectral line for a transition adjacent to a transition combining with a strong field; the simultaneous manifestation of the Stark effect and of Doppler broadening in the form of a very sharp structure on the line contour; a brief mention of the influence of collisions, recoil, and other factors on the sharp structure in spectra. The experimental part reports the results of experiments on the observation of the Stark effect in the optical region of the spectrum, the fine structure of the profile of a Doppler-broadened line and its properties, namely the dependence on the observation direction, the anisotropy in the field of a standing wave, the polarization properties, etc. in spectra of spontaneous or stimulated emission, absorption, and generation.