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Physical Review A

Sum-frequency generation via a resonant quadrupole transition in sodium

Donald S. Bethune, Robert W. Smith, Y. Ron Shen

Published Jan 1, 1978• 36 citations
Publisher

Abstract

We show that second-order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the electric-dipole approximation. A theoretical treatment of quadrupole sum- and difference-frequency generation is given, which includes the effects of spin-orbit and Zeeman splittings. The quadrupole nonlinear susceptibility is evaluated and expressions for phase matching and output power are found. We have generally confirmed the theoretical predictions by observing quadrupole sum-frequency generation of ultraviolet light in sodium vapor. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two-photon saturation, induced index of refraction changes, and single- and multi-photon absorption. Generalization of the dipole forbidden susceptibilities to the case of quadrupole-pumped processes is discussed, with difference-frequency generation in Cs vapor considered as an example.

DOI
10.1103/physreva.17.277

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 19, 1998•0 citations
We show that second-order nonlinear optical processes such as sum and difference generation can be observed in isotropic media, despite the fact that such processes are forbidden in the electric-dipole approximation. A theoretical treatment of quadrupole sum- and difference-frequency generation is given, which includes the effects of spin-orbit and Zeeman splittings. The quadrupole nonlinear susceptibility is evaluated and expressions for phase matching and output power are found. We have generally confirmed the theoretical predictions by observing quadrupole sum-frequency generation of ultraviolet light in sodium vapor. Deviations of the data from the simple theory can be satisfactorily accounted for by the effects of two-photon saturation, induced index of refraction changes, and single- and multi-photon absorption. Generalization of the dipole forbidden susceptibilities to the case of quadrupole-pumped processes is discussed, with difference-frequency generation in Cs vapor considered as an example.
Electric quadrupole transition enhanced tthree-wave difference-frequency generation in isotropic medium is investigated. Taking account of the contribution of electric quadrupole interaction, we derive the second-order nonlinear susceptibility. We also discuss the possibility of observation of collision induced second-order nonlinear optical processes. The experiments are performed with 3s→4d electric quadrupole transition in sodium vapor. The experimental results agree with theoretical predictions.
We have examined the effect of various phase-matching conditions on sum frequency generation in vapors. Using sodium vapor two resonant-enhancement routes for sum-frequency mixing (SFM) via a second-order magnetic-field-induced nonlinearity were explored. On one route the output is resonant with a quadrupole-allowed transition and the other a dipole-allowed resonance. We will show that the first route is preferential for SFM as phase matching on this route is easier to control and we present results detailing the important parameters and their effect in focused and unfocused cases. A second-order nonlinearity of 0.5--1 ${\mathrm{pmV}}^{\mathrm{\ensuremath{-}}1}$ is observed under optimum conditions. In the second route, variations in phase matching as one tunes across the transition may lead to a significant distortion of the spectroscopic line shapes. We show how the combination of different refractive-index sources can account for the different features seen.
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{}${10}^{\mathrm{\ensuremath{-}}5}$.
It is theoretically shown that, under conditions of two-photon absorption of radiation by metal vapors, the medium becomes considerably polarized and efficiently doubles the radiation frequency. Two physical mechanisms by which these effects can occur are detected. The first of them results from the ring frequency mixing, while the second one is caused by a polarization nonlinearity that is quadratic in the field amplitude and that is formed as a result of the electric quadrupole absorption due to the forbidden transition. The effects predicted can form the basis for new optical methods for measuring the electric quadrupole and magnetic dipole moments for forbidden atomic transitions.