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Conference on Lasers and Electro-Optics

Theory for optimization of two-photon-resonant sum-frequency mixing in Hg

Arlee V. Smith, W. J. Alford, George Ronald Hadley

Published Apr 25, 1988• 0 citations
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Abstract

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.

Related papers

Efficient two-photon-resonant frequency conversion in mercury: the effects of amplified spontaneous emission

Arlee V. Smith, George Ronald Hadley, P. Esherick +1 more

Numerical modeling of two-photon-resonant sum-frequency mixing in mercury vapor predicts efficiencies >10% for generation of 130.2-nm oxygen resonance light. The modeling indicates that power broadening of the two-photon resonance due to amplified spontaneous emission from the pumped level strongly influences the mixing process. Measurements of the broadening and the efficiencies for difference-frequency mixing are presented as a check of the model calculations.

Optics Letters•Sep 1, 1987•8 citations

Optimization of two-photon-resonant four-wave mixing: application to 1302-nm generation in mercury vapor

Arlee V. Smith, W. J. Alford, George Ronald Hadley

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.

Journal of the Optical Society of America B•Jul 1, 1988•28 citations

High-efficiency, energy-scalable, coherent 130-nm source by four-wave mixing in Hg vapor

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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

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.

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Resonant sum-difference frequency mixing enhanced by electromagnetically induced transparency in krypton

C. Franklin Dorman, J. P. Marangos

We report experiments that investigate the generation of coherent VUV radiation at 123.6 nm via a resonant sum-difference frequency mixing scheme in Kr. One of the mixing fields at 212.55 nm was in two-photon resonance with the transition between the ${4p}^{6}{}^{1}S$ ground state and the ${4p}^{5}5p[0,\frac{1}{2}]$ excited state $(94093.7 {\mathrm{cm}}^{\ensuremath{-}1}).$ The second field (the coupling field) at 759 nm was in single-photon resonance with the transition between the ${4p}^{5}5p[0,\frac{1}{2}]$ state and the ${4p}^{5}5s[1,\frac{1}{2}]$ state at $80917.6 {\mathrm{cm}}^{\ensuremath{-}1}.$ The presence of the coupling field leads to electromagnetically induced transparency (EIT) at the wavelength of the generated field, 123.6 nm. This is predicted to enhance the four-wave-mixing efficiency by a large factor. We have studied the dependence of the four-wave mixing process on the detuning and strength of the coupling field. The efficiency for four-wave mixing was found to be enhanced by a significant factor (>5) by the EIT effect when the resonant coupling field strength exceeded about half the Doppler width $(0.1 {\mathrm{cm}}^{\ensuremath{-}1}).$ A calculation for monochromatic fields and a uniform slab of gas provided qualitative agreement with the results of experiment. The relative conversion efficiency for this resonant mixing scheme is found to be ${10}^{4}$ times greater than that for a similar scheme where the coupling laser is tuned far $(1270 {\mathrm{cm}}^{\ensuremath{-}1})$ off resonance. A substantial part of this resonant enhancement can thus be attributed to the EIT effect.

Physical Review A•Nov 1, 1998•18 citations

Femtosecond-pulse two-photon resonant difference-frequency mixing in gases: A technique for tunable vacuum-ultraviolet femtosecond-pulse generation and a spectroscopic tool for studying atoms in strong laser fields

A. Nazarkin, G. Korn, Olaf Kittelmann +2 more

Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.

Physical Review A•Jul 1, 1997•19 citations
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.
Coherent vacuum-ultraviolet (VUV) pulses with energy of 1.1 mJ, 2.2-nsec pulse length (2 MW cm−2 unfocused), and measured bandwidth ≤0.1 cm−1 have been achieved at 130 nm from four-wave mixing in Hg vapor. Conversion efficiencies of 5% have been demonstrated in a collimated beam geometry over 1-m interaction lengths. These high efficiencies are made possible by using two-photon-resonant sum-frequency mixing through the Hg 71S level. The experimental facility assembled to produce this efficient VUV source is described, and a comparison between experimental measurements and theory is provided.
We report experiments that investigate the generation of coherent VUV radiation at 123.6 nm via a resonant sum-difference frequency mixing scheme in Kr. One of the mixing fields at 212.55 nm was in two-photon resonance with the transition between the 4p61S{4p}^{6}{}^{1}S4p61S ground state and the 4p55p[0,12]{4p}^{5}5p[0,\frac{1}{2}]4p55p[0,21​] excited state $(94093.7 {\mathrm{cm}}^{\ensuremath{-}1}).$ The second field (the coupling field) at 759 nm was in single-photon resonance with the transition between the 4p55p[0,12]{4p}^{5}5p[0,\frac{1}{2}]4p55p[0,21​] state and the 4p55s[1,12]{4p}^{5}5s[1,\frac{1}{2}]4p55s[1,21​] state at $80917.6 {\mathrm{cm}}^{\ensuremath{-}1}.$ The presence of the coupling field leads to electromagnetically induced transparency (EIT) at the wavelength of the generated field, 123.6 nm. This is predicted to enhance the four-wave-mixing efficiency by a large factor. We have studied the dependence of the four-wave mixing process on the detuning and strength of the coupling field. The efficiency for four-wave mixing was found to be enhanced by a significant factor (>5) by the EIT effect when the resonant coupling field strength exceeded about half the Doppler width $(0.1 {\mathrm{cm}}^{\ensuremath{-}1}).$ A calculation for monochromatic fields and a uniform slab of gas provided qualitative agreement with the results of experiment. The relative conversion efficiency for this resonant mixing scheme is found to be 104{10}^{4}104 times greater than that for a similar scheme where the coupling laser is tuned far $(1270 {\mathrm{cm}}^{\ensuremath{-}1})$ off resonance. A substantial part of this resonant enhancement can thus be attributed to the EIT effect.
Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time ${T}_{2}^{\ensuremath{'}}$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102--124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.