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IEEE Journal of Quantum Electronics

Continuously tunable sum-frequency generation involving sodium Rydberg states

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

Published Sep 1, 1984• 13 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1984.1072522

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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.

Topical Meeting on Laser Techniques in the Extreme Ultraviolet•Jan 1, 1984•0 citations
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.
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.
A unique set of circumstances makes the Rydberg states of atoms ideal for mediating tunable, resonantly enhanced, nonlinear optical interactions. The application of a dc electric field to a vapor of such atoms can induce a second-order or\chi^{(2)}nonlinear susceptibility, which in the absence of the applied field would be forbidden by reasons of symmetry. This paper presents an exact expression, valid within the hydrogenic approximation for field strengths that produce a linear Stark effect, for the resonant contribution to the dc-electric-field-induced\chi^{(2)}susceptibility. Numerical evaluation of this expression for field strengths of the order of 103V/cm predict\chi^{(2)}susceptibilities hundreds of times larger than those of conventional mixing crystals.
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{}${10}^{\mathrm{\ensuremath{-}}5}$.
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.