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Topical Meeting on Laser Techniques in the Extreme Ultraviolet

Continuously Tunable Sum-Frequency Generation Involving Rydberg States

Robert W. Boyd, Daniel J. Gauthier, Jerzy S. Krasiński, Michelle S. Malcuit

Published Jan 1, 1984• 0 citations
Publisher

Abstract

It has recently been shown1 that extremely large values of the second-order nonlinear suceptibility can be obtained through use of Rydberg atomic states perturbed by an external electric field.2 In these experiments a value of χ(2) = 10-9 esu was obtained using a sodium vapor of number density ~1014 atoms cm-3 and a dc electric field of magnitude 1 kV/cm. One laser was tuned close to the sodium D2 resonance line while a second laser completed the two-photon resonance with a Rydberg state. A strong coherent UV beam at the sum frequency was generated in the forward direction. The splitting of the highly excited atomic levels induced by the external electric field created a broad region of overlapping levels, leading to continuous tunability. This technique can be applied to any system displaying a Rydberg series, and should be capable of producing coherent, tunable radiation in the extreme ultraviolet.

DOI
10.1364/euv.1984.tud4

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It has recently been shown1 that extremely large values of the second-order nonlinear suceptibility can be obtained through use of Rydberg atomic states perturbed by an external electric field.2 In these experiments a value of χ(2) = 10-9 esu was obtained using a sodium vapor of number density ~1014 atoms cm-3 and a dc electric field of magnitude 1 kV/cm. One laser was tuned close to the sodium D2 resonance line while a second laser completed the two-photon resonance with a Rydberg state. A strong coherent UV beam at the sum frequency was generated in the forward direction. The splitting of the highly excited atomic levels induced by the external electric field created a broad region of overlapping levels, leading to continuous tunability. This technique can be applied to any system displaying a Rydberg series, and should be capable of producing coherent, tunable radiation in the extreme ultraviolet.
Broadly tunable sum-frequency generation has been observed in a vapor of atomic sodium in the presence of a dc electric field. This field induces a\chi^{(2)}nonlinearity which is resonantly enhanced when the sum frequency corresponds to the energy separation between the ground state and an atomic Rydberg state. In a vapor of number density4 \times 10^{14}cm-3, we obtain an energy conversion efficiency as large as3 \times 10^{-4}and a\chi^{(2)}as large as1.2 \times 10^{-8}ESU. We have also observed sum-frequency generation in the absence of an applied dc field, and we relate these observations to mechanisms that have been proposed to explain this effect.
Consider sum frequency generation (SFG) ω3 = 2 ω1 + ω2 in a phase matched metal-noble gas mixture, using two lasers ω1 and ω2, where 2 ω1 is tuned to a two photon transition Ωg2 and ω2 is shifted across Rydberg transitions Ω2n (g groundstate, 2 excited state, n Rydberg state of the metal atom). Then the intensity of the SFG spectrum I3 (ω3)~ |χ(3) (ω3)|2 displays resonances and related antiresonances, separated by (1) which are caused respectively by constructive and destructive interference of resonant and nonresonant parts of the 3. order nonlinear susceptibility χ(3) (ω3 ≃ Ωng) = χR(ω3)+ χNR (3) The products μ2nμng:= xn of the dipole transition matrix elements may then be obtained from a simple measurement of the frequency spacings Δωn at a large number of transitions Ωgn and solving iteratively the coupled equation system (1),(3); neither absolute radiation intensity nor vapour density deter mination is needed.
Measurements of radio-frequency (RF) electric fields in the MHz-to sub-THz range using EIT spectroscopy of Rydberg states in atomic vapors have garnered significant interest in recent years. Here we describe recent work extending the approach to measurements of coherent high-intensity RF electric fields above 1 kV/m and continuous-frequency RF measurement capability. The spectra are modeled using a non-perturbative Floquet model that accounts for higher-order interactions and state mixing. The spectroscopic data also reveal nonlinear amplifier behavior and noise.
Two tunable dye lasers have been used to generate coherent radiation at a tunable sum frequency in the vacuum-ultraviolet spectral region. Spectral ranges of \ensuremath{\sim}3500 ${\mathrm{cm}}^{\ensuremath{-}1}$ around 1895 \AA{} and \ensuremath{\sim}1200 ${\mathrm{cm}}^{\ensuremath{-}1}$ around 1798 \AA{} have been covered. These ranges may easily be extended. Large (\ensuremath{\sim}\ifmmode\times\else\texttimes\fi{}104{10}^{4}104) enhancements of $2{\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{2}$ sum mixing are seen when $2{\ensuremath{\nu}}_{1}$ is tuned to a double-quantum allowed transition from the ground state in Sr vapor.
Sum-frequency generation enhanced by electromagnetically induced transparency (EIT) has been extended to the production of extreme ultraviolet (XUV) radiation in the range 97.3--92.6 nm from $np\ensuremath{-}1s$ transitions (n=4−−8)(n=4--8)(n=4−−8) in atomic hydrogen. Pulsed radiation was generated by strong coupling of the np\mathrm{np}np and 2s2s2s levels with laser radiation at Balmer wavelengths, and simultaneously (weaker) coupling of the 2s2s2s and 1s1s1s levels by two-photon resonance with 243-nm laser radiation. Investigations were carried out over a range of laser intensities and products of interaction length and atomic density (NL).(\mathrm{NL}).(NL). As the product NL\mathrm{NL}NL increased, the XUV intensities were greatly enhanced by EIT, and at high NL\mathrm{NL}NL values, the spectral distributions of some of the generated signals were found to be distorted by the presence of molecular hydrogen. Calculated profiles, modified to incorporate the effects of nearby molecular resonances, were shown to be in good agreement with the observed spectra.