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Journal of Experimental and Theoretical Physics

Optical rectification and frequency doubling in metal vapors

Victor P. Kochanov

Published Aug 1, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776108080037

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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.
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.
A saturated nonresonant two-photon absorption (TPA) theory of quasi-monochromatic radiation by an atom is developed in a model of a three-level cascade quantum system. It is shown that doubled-frequency radiation, arising from a multipole interaction of radiation with the dipole-forbidden transition, experiences spatial oscillations at arbitrary intensities of the pump. The influence of the total phase of the waves with the initial and doubled frequencies on TPA is considered under conditions of ring frequency mixing in a medium.
The fine-structure splitting of resonance atomic levels causes essential effects on the amplitude of a two-colour frequency mixing in a magnetic field. The fine-structure effects are analysed in the scattering cross section, and particularly in the circular dichroism phenomena, such as the elliptical polarization of the generated wave, when both incident waves are linearly polarized, and the dependence of the cross section on the helicity of one of the incident waves when the other one is linearly polarized. Together with general analytic expressions for the amplitude, the numerical data are presented for three different double-resonant routes involving two dipole and one quadrupole interactions of atoms with a field. The results may be useful for the polarization control of the process in an atomic vapour and for the frequency-mixing spectroscopic studies of atomic structure.
We analyze second harmonic generation in sodium vapor in a transverse magnetic field induced by the two-photon resonant excitation of the 3S-3D transition. The phenomenon is explained by the rotation of the two-photon induced quadrupole moment in the magnetic field. The analysis explains well the saturation of the intensity and rotation of the polarization of the second harmonic radiation in the higher magnetic field ≳0.5{\gtrsim}0.5≳0.5 kG. The collisional decay rate of the coherence of the E1 forbidden transition has been measured as an application of this SHG.