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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical quadropole sum-frequency generation of polarized waves via dipole-forbidden atomic transition

É. G. Kanetsian, G. G. Adonts

Published Aug 19, 1998• 0 citations
Publisher

Abstract

The process of collinear mixing of two frequencies in an external magnetic field in resonant systems is studied theoretically. It is suggested to provide the interacting wave phase matching by corresponding choice of sum-frequency between doublet splitting second excited state. The numerical estimations demonstrate the possibility of 1 - 5% power conversion.

DOI
10.1117/12.320977

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Physical Review A•Feb 1, 1993•14 citations
The process of collinear mixing of two frequencies in an external magnetic field in resonant systems is studied theoretically. It is suggested to provide the interacting wave phase matching by corresponding choice of sum-frequency between doublet splitting second excited state. The numerical estimations demonstrate the possibility of 1 - 5% power conversion.
Application of a steady magnetic field allows sum-frequency radiation generated via dipole-forbidden mixing of two-colour fields in an atomic medium to be emitted in the (otherwise forbidden) forward direction. As a result of resonance tuning at low-field strength (not exceeding 0.1 T) a fourth-order magnetic-dipole-induced amplitude for the sum-frequency process can be made comparable to the third-order field-free amplitude. We show that the interference between different terms of the field-dependent amplitude may cause the circular dichroism of the forward-scattering cross section for one of the two incident waves or the sum-frequency wave when the other two waves are linearly polarized. The dichroism effect is due to the dissipation processes determined by the resonant level width Γ and depends strongly both on Γ and the resonance detuning Δ. The effect may be used to control the frequency conversion process or to make possible a frequency mixing laser spectroscopy of excited atomic levels.
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.
The relative contributions of the magnetic dipole interaction ( M 1) and the electric quadrupole interaction ( E 2) in the dipole-forbidden three-wave process of mixing two-colour radiation in free atoms may be determined from the dependence of the frequency-conversion efficiency on the incident-wave polarization. Analytical expressions are derived for the polarization dependence of amplitudes and cross sections of a double-resonant scattering of the sum- and difference-frequency photons. Numerical estimates are presented for the ratio of E 2 and M 1 three-photon amplitudes in ground-state indium and thallium atoms.
Coherent radiation at the 1.28-\ensuremath{\mu}m electric-dipole-forbidden $6^{2}P_{\frac{3}{2}}\ensuremath{-}6^{2}P_{\frac{1}{2}}$ transition in thallium vapor has been produced by the simultaneous application of a magnetic field and two collinear, overlapping laser beams nearly resonant with the $6^{2}P_{\frac{1}{2}}\ensuremath{-}7^{2}S_{\frac{1}{2}}$ and $6^{2}P_{\frac{3}{2}}\ensuremath{-}7^{2}S_{\frac{1}{2}}$ transitions, respectively. The effect of the magnetic field is to mix hyperfine levels---atomic polarization effects are negligible. The optical difference-frequency power generated at low magnetic field varies as the square of the magnetic-field component normal to the laser-beam propagation direction.
Polarization dependence of amplitude for resonant magnetic-field-induced coherent mixing of two collinear laser waves may be used for separating M1 and E2 contributions to n1 2P1/2(3/2) - n2 2P3/2(1/2) dipole-forbidden transition in atoms. The interference between E2 and Ml terms of the amplitude may cause linear polarization and circular dichroism effects. The dependencies of the two effects on the width and splitting of resonance levels, on resonance detuning, on relative directions of steady and alternating field vectors are determined. Numerical data are presented for frequency summation of two laser waves on Cs, Rb and K atoms.
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{}${10}^{\mathrm{\ensuremath{-}}5}$.