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Journal of the Optical Society of America B

Practical guide for 7S resonant frequency mixing in mercury: generation of light in the 230–185-and 140–120-nm ranges

A. V. Smith, W. J. Alford

Published Nov 1, 1987• 32 citations
Publisher

Abstract

We present recent measurements of refractive indices, nonlinear susceptibilities, and isotope shifts important for sum- and difference-frequency mixing through the 71,3S two-photon resonances of Hg. These data are presented in a form that makes it possible to make quick and accurate calculations of index-matching and mixing efficiencies in the low-intensity limit.

DOI
10.1364/josab.4.001765

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Optics Letters•Jul 1, 1985•11 citations
We present recent measurements of refractive indices, nonlinear susceptibilities, and isotope shifts important for sum- and difference-frequency mixing through the 71,3S two-photon resonances of Hg. These data are presented in a form that makes it possible to make quick and accurate calculations of index-matching and mixing efficiencies in the low-intensity limit.
Previously we showed1 that two-photon-resonant sum- and difference-frequency mixing in Hg vapor is a practical means of generating coherent light over the 140-120- and 230-185-nm wavelength ranges. Here we consider optimization of the conversion efficiency for such a two-photon-resonant mixing process in general and for generation of 130.2-nm atomic oxygen resonance light in particular. We predict that conversion efficiencies (defined as the energy of the sum frequency divided by the total input light energy) of 5-10% should be possible for 130.2-nm production using unfocused mixing beams. This prediction is being tested in experiments at Spectra Technologies, Inc. Their results are described in a companion paper.
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.
We have measured the null positions in the third-order susceptibility for two-photon resonant (6 17^{1}717 1^{1}1,3S) sum-frequency mixing in atomic mercury. In addition, we have made measurements of some 7S-nP oscillator strengths using a fluorescence-dip technique. Combined with earlier results we are able to obtain a set of 7S-nP (n=7--13) oscillator strengths which gives a good description of the third-order susceptibility. The uncertainty in the 7S-nP oscillator strengths is typically 35--50%. The absolute third-order susceptibility has been determined for energies less than 83 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with an uncertainty of typically 20--30%.
We have developed new techniques based on four-wave mixing for the accurate determination of oscillator strengths and applied them to measure 61S - n1,3P and 71S - n1,3P (n = 6 - 13) matrix elements of atomic Hg. For transitions from the 61S ground state, index matching conditions were used to determine refractive indicies and thus f-values, while the frequency dependence of the nonlinear susceptibility was used to deduce matrix elements for transitions involving 71S. For all measurements, two-photon resonance with the 71S state was maintained.