General dispersion formulae for atomic third-order non-linear optical properties

Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.

Dispersion formulas for real- and imaginary-frequency-dependent hyperpolarizabilities

The dynamic second hyperpolarizability for real frequencies, [Formula: see text] in the limit ωi → 0 can be expressed as [Formula: see text] where ωL2 = ωσ2 + ω12 + ω22 + ω32 and [Formula: see text] is the frequency-independent (static) quantity; the parallel sutsscript [Formula: see text] indicates that the polarization and electric fields all lie along the same axis. In this paper the coefficient [Formula: see text] is evaluated exactly for the H atom and very accurately for H−, He, and Li+. A similar analysis is carried out for [Formula: see text] in the limit ω → ∞. Key words: nonlinear optics, hyperpolarizabilities, dispersion formulas.On peut exprimer la deuxième hyperpolarisabilité dynamique de fréquences réelles, [Formula: see text] dans la limiteωi → 0, peut être exprimée sous la forme [Formula: see text], dans laquelle ωL2 = ωσ2 + ω12 + ω22 + ω32 et [Formula: see text] est la quantité (statique) indépendant de la fréquence; l'indice parallèle [Formula: see text] indique que la polarisation et les champs électriques sont situés dans le même axe. Dans ce travail, on a fait une évaluation exacte de [Formula: see text] pour l'atome d'hydrogène et d'une façon précise pour H−, He et Li+. On a effectué une analyse semble pour [Formula: see text]dans la limite ω → ∞. Mots clés : optique non linéaire, hyperpolarisabilités, formules de dispersion. [Traduit par la rédaction]