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Journal of Physics B Atomic Molecular and Optical Physics

Optimizing third harmonic generation in gases

Richard M. Friedberg, Sven R. Hartmann, Jamal T. Manassah

Published Jun 28, 1991• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/24/12/011

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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.
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.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
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.
The destructive interference between the three-photon and the third-harmonic one-photon absorption in the vicinity of the 6s[3/2]1{]}_{1}]1​ state of Xe has been studied in the resonantly enhanced multiphoton ionization via nf states, through the cancellation of the nf, J=2 resonances of the spectrum, accessible by four-photon absorption. The gas-pressure, i.e., phase-matching, dependence of the three-photon detuning range from the 6s[3/2]1{]}_{1}]1​ state for which cancellation occurs has been investigated in one- and two-color experiments, including positive detuning from this state in positively dispersive regions. For obtaining cancellation, the theoretically predicted requirement of optically thick medium at the third-harmonic frequency is corroborated by present observations for negative detunings. The different cancellation behavior of the nf[3/2]2{]}_{2}]2​ and nf[5/2]2{]}_{2}]2​ states observed indicates the dependence of the effect on the atomic parameters of the coupled four-photon resonance. The experimental results are found to be in partial agreement with existing theoretical models.
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].
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).