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Optics Letters

Four-photon-resonant third-harmonic generation in Hg

Arlee V. Smith

Published Jul 1, 1985• 11 citations
Publisher

Abstract

A tunable resonant enhancement of third-harmonic and sum-frequency generation is observed at four-photon resonance with the 7(1)S, 6(1)D, and 6(3)D levels and at five-photon resonance with 9(1)P levels of atomic mercury. The causes of this resonant enhancement are examined and appear to include a nonlinear refractive index and nonlinear mixing of order 5 and higher. A perturbative treatment of the nonlinearities is found to be inadequate.

DOI
10.1364/ol.10.000341

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A tunable resonant enhancement of third-harmonic and sum-frequency generation is observed at four-photon resonance with the 7(1)S, 6(1)D, and 6(3)D levels and at five-photon resonance with 9(1)P levels of atomic mercury. The causes of this resonant enhancement are examined and appear to include a nonlinear refractive index and nonlinear mixing of order 5 and higher. A perturbative treatment of the nonlinearities is found to be inadequate.
The ability to introduce additional resonances in the nonlinear optical susceptibility of a medium by the injection of an additional radiation field is an attractive possibility from the standpoint of efficient tunable frequency mixing processes in the VUV. The possibility of such processes suggest themselves in previous observations in atomic mercury where an enhancement of several orders of magnitude in the third harmonic generation efficiency has been reported when the input frequency is four-photon resonant with the 6S → 6D transition(1).
This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.
A coherent continuous-wave Lyman-alpha source based on four-wave sum-frequency mixing in mercury vapor has been realized with solid-state lasers. The third-order nonlinear susceptibility is enhanced by the 6(1)S - 7(1)S two-photon resonance and the near 6(1)S-6(3)P one-photon resonance. The phase matching curve for this four-wave mixing scheme is observed for the first time. In addition we investigate the two-photon enhancement of the Lyman-alpha yield and observe that the maxima of Lyman-alpha generation are shifted compared to the two-photon resonances of the different isotopes.
A detailed model of two-photon-resonant four-wave mixing that includes the consideration of efficiency-limiting processes is presented. The model provides a generally applicable systematic approach for maximizing conversion efficiencies for both exact and near two-photon resonance. For exact two-photon resonance, an interference effect limits efficiency to a value determined by ratios of nonlinear susceptibilities and input intensities. For near two-photon resonance, nonlinear refractive indices limit efficiencies unless input intensities are properly balanced. For the specific case of 130.2-nm generation in Hg, we examine a number of potential additional efficiency-limiting processes, including amplified spontaneous emission, stimulated Raman and hyper-Raman gain, parametric gain, linear absorption, and population transfer. We include isotopic effects and Gaussian-profile beams. From our analysis, we conclude that efficiencies of approximately 10% should be feasible by using collimated light beams in an energy-scalable system.