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IEEE Journal of Quantum Electronics

Resonant third-harmonic generation in a low-loss medium

Hans Junginger, H. B. Puell, H. Scheingraber, C. R. Vidal

Published Oct 1, 1980• 34 citations
Publisher

Abstract

The linear and nonlinear susceptibilities for resonant third-harmonic generation in an Mg-Kr system using the 3s2-3s 3d two-photon resonance at 431 nm are presented. The Mg-Kr system is shown to be a suitable low-loss medium because of its small one-photon and two-photon absorption cross section. A detailed quantitative analysis up to a power conversion efficiency of 1.2 . 10-4was carried out. The phase-matching curves and the intensity dependence are in excellent agreement with a nonstationary modification of the theory of resonant third-harmonic generation in high density, phase-matched systems recently presented by Puell et al. [4].

DOI
10.1109/jqe.1980.1070373

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Physical Review A•Apr 1, 1979•43 citations
The linear and nonlinear susceptibilities for resonant third-harmonic generation in an Mg-Kr system using the 3s2-3s 3d two-photon resonance at 431 nm are presented. The Mg-Kr system is shown to be a suitable low-loss medium because of its small one-photon and two-photon absorption cross section. A detailed quantitative analysis up to a power conversion efficiency of 1.2 . 10-4was carried out. The phase-matching curves and the intensity dependence are in excellent agreement with a nonstationary modification of the theory of resonant third-harmonic generation in high density, phase-matched systems recently presented by Puell et al. [4].
The linear and nonlinear susceptibilities for resonant third-harmonic generation in an Mg-Kr system using the3s^{2}-3s3dtwo-photon resonance at 431 nm are presented. The Mg-Kr system is shown to be a suitable low-loss medium because of its small one-photon and two-photon absorption cross section. A detailed quantitative analysis up to a power conversion efficiency of1.2 \cdot 10^{-4}was carried out. The phase-matching curves and the intensity dependence are in excellent agreement with a nonstationary modification of the theory of resonant third-harmonic generation in high density, phase-matched systems recently presented by Puell et al. [4].
The dependence of the third harmonic intensity on the medium length under completely phase-matched and resonant conditions is discussed. It is shown that the conversion efficiency in the coherent transient case is expected to exceed that in the steady state case in a long and/or dense medium when the incident light pulse has sufficient energy. The 3S-5S transition of sodium with a 602.3 nm light is studied experimentally as a model system. The efficiency as a function of the incident light frequency and intensity is in agreement with the predictions. By eliminating the phase-mismatching effect, the dependence on the medium density is also determined. It is demonstrated that the efficiency surely increases even in the higher density of sodium.
The saturation of resonant third-harmonic generation in absorbing and phase-matched high-density systems is investigated theoretically as well as experimentally. It is shown that the saturation is determined by the two-photon absorption [imaginary part of ${\ensuremath{\chi}}_{S}^{(3)}(\ensuremath{\omega})$]. It gives rise to a depletion of the fundamental wave and leads to a change of the level populations and of the effective refractive index destroying the phase matching. This has to be compared with nonresonant systems which are limited by the Kerr effect, the intensity-dependent changes of the refractive index [real part of ${\ensuremath{\chi}}_{S}^{(3)}(\ensuremath{\omega})$]. Optimum conditions for resonant systems are reported.
Three-photon resonantly enhanced third harmonic generation in a collisionally self-broadened gas of two-level atoms, appropriately buffered to allow phase matching, achieves maximum output when the input frequency is sufficiently detuned from exact resonance to avoid excessive self-absorption of the third harmonic. For a given active gas density or laser detuning there exists a relation between the buffer gas density, active gas density and laser detuning which maximizes the third harmonic intensity. The optimal combination depends only on the physical characteristics of the tripling medium and the buffer gas. When the third harmonic is maximized the absorption coefficient alpha and the sample length L combine so that alpha L is of order unity. The characteristics of three-photon resonantly enhanced third harmonic generation in a buffered gas are analysed in detail.
As a succession of two pulses propagates through a medium which exhibits a resonance (single or multiphoton), the resonant parts of the susceptibility will depend on the relative phase of the two pulses, provided the delay between the pulses is shorter than the phase relaxation time of the interaction. As a result of this "coherent interaction", the reradiation of the sample (the fluorescence, the absorption and the generation of harmonics) will be a periodic function of the phase difference and delay between the two pulses of the sequence 1. The study of these coherent effects is important, because one expect to find conditions under which the maximum harmonic conversion to much shorter wavelengths can be greatly enhanced 2. The presence of the multiphoton resonance enhances the nonlinear susceptibility responsible for the harmonic generation, but reduces also the maximum achievable conversion efficiency because of resonant losses (depletion of the fundamental by multiphoton absorption). The latter effect can be eliminated by a judicious choice of the pulse sequencing and phasing. In addition to demonstrating, for the first time, coherent interaction enhancement in harmonic generation, the data of third harmonic versus relative phase of the pulse sequences enable us to measure the phase angle of the third order susceptibility (hence the contribution of the continuum relative to that of the resonance).
The authors present a detailed theoretical analysis of two-photon resonant third- and fifth-harmonic generation in metal vapors with picosecond laser pulses. These processes are described by self-consistent Maxwell-Bloch equations which take into account the effects of optical Stark shifts, multiphoton ionization, Doppler broadening, two-photon absorption, the reaction of the third-harmonic field on the fundamental, and a nonlinear index of refraction. As an example, a quantitative analysis of third- and fifth-harmonic generation in lithium vapor ($2s\ensuremath{-}4s$ transition) is presented. The limitations on energy conversion efficiency and the temporal as well as spectral characteristics of the harmonic pulses are investigated for two kinds of low-loss propagation fundamental pulses. It is shown that 90\ifmmode^\circ\else\textdegree\fi{} phase-shifted fundamental pulses (zero area) are more efficient than $2\ensuremath{\pi}m$ pulses. Energy conversion efficiencies of 6.5% for third-harmonic (190 nm) and 0.07% for cascade fifth-harmonic (114 nm) pulses are predicted.