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Optics Letters

Observation of resonantly enhanced sum-frequency generation involving sodium Rydberg states

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

Published Apr 1, 1983• 15 citations
Publisher

Abstract

A large, dc-electric-field-induced nonlinear optical susceptibility is exploited to produce ultraviolet radiation in the range 2453-2476 A by the process of sum-frequency generation in sodium. The interaction is resonantly enhanced at the first intermediate level by the 3 (2)P(3/2) state and at the second intermediate level by a Rydberg state. Conversion efficiencies of 10(-5) have been obtained; improvement of this value by a factor of 10(3) should be possible.

DOI
10.1364/ol.8.000211

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Physical Review A•Apr 1, 1992•83 citations
A large, dc-electric-field-induced nonlinear optical susceptibility is exploited to produce ultraviolet radiation in the range 2453-2476 A by the process of sum-frequency generation in sodium. The interaction is resonantly enhanced at the first intermediate level by the 3 (2)P(3/2) state and at the second intermediate level by a Rydberg state. Conversion efficiencies of 10(-5) have been obtained; improvement of this value by a factor of 10(3) should be possible.
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.
An experimental investigation was made of resonant nonlinear four-wave frequency mixing processes involving cw laser radiation in sodium vapor. It was found that, in spite of an increase in absorption, the use of resonant atomic nonlinearities can substantially improve the frequency conversion efficiency in the cw regime. The results of the measurements were compared with the theoretical conclusions. Ultraviolet radiation was generated at the sum frequency ( λ s = 268 nm) with the proportionality factor C = W s / W 1 W 2 W 3 ≈2W −2
The sum-frequency generation process using strong-field coupling and quantum interference is described systematically using atomic hydrogen both in theory and experiment. It is shown that strong coupling at the 3p-2s transition creates destructive interference to reduce the linear susceptibility at the resonant 3p\ensuremath{\leftarrow}1s transition. Simultaneously, two-photon coupling of the 2s and 1s states produces constructive interference to resonantly enhance the nonlinear susceptibility for sum-frequency generation at the 3p\ensuremath{\rightarrow}1s (Lyman-\ensuremath{\beta}) transition. Experimental results clearly demonstrate the theoretical predictions. When the Rabi frequency for the 3p-2s coupling exceeds the Doppler tail of the medium, the photoion signals on resonance are suppressed significantly because of induced transparency. The generated Lyman-\ensuremath{\beta} radiation grows rapidly by a factor of 250 at an atom density of 1015{10}^{15}1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and interaction length of 3.5 cm, resulting in a conversion efficiency of 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.
An experimental and theoretical study of magnetic-field-induced sum-frequency mixing in sodium vapor has been carried out using two single-frequency, continuous-wave dye lasers as the sources of the fundamental radiation. In addition to the usual two-photon resonant enhancement of the three-wave-mixing nonlinear-optical process, the use of near- or on-resonant single-photon transitions for further resonant enhancement was investigated. The macroscopic phase-matching behavior of the sum-frequency mixing was examined with the intermediate states off resonance. Experimental and theoretical results are presented to illustrate the differences that occur between the coherent quadrupole emission and the incoherent cascade fluorescence when the intermediate states in the two-photon absorption are resonant. Control over the single-photon resonant enhancement and the sum-frequency-mixing phase matching was achieved to increase the power conversion efficiency to 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$.