Definition of invariant molecular tensors in an origin change. II. Refraction and Faraday effect

Abstract

AbstractsIn the previous paper, a global tensor invariant under origin changes was introduced for all optical phenomena. By applying the results obtained, we determine invariant partial tensors which characterize refraction and the Faraday effect.Dans I'article pricedent un tenseur global, invariant par rapport a un changement d'origine, a ttC introduit pour tous les phenomenes optiques. Utilisant ces resultats nous dtterminons les tenseurs invariants partiels, qui caracttrisent la refraction et l'effet de Faraday.Im vorigen Artikel wurde ein globaler Tensor fur alle optische Phanomene eingefuhrt, der unter Transformationen des Koordinatenursprungs invariant ist. Durch Anwendung dieser Ergebnisse bestimmen wir den invarianten Partialtensor, der die Refraktion und den Faradayeffekt charakterisiert.

Invariance of molecular response properties under a coordinate translation

“…A few studies on the invariance of the molecular tensor used to rationalize the Faraday effect, in a shift of origin, Eq. , have appeared . However, the first proof of the translational invariance the Verdet tensor has been reported only recently …”

“…(305), have appeared. [137][138][139][140] However, the first proof of the translational invariance the Verdet tensor has been reported only recently. [111] The third-rank tensors needed to rationalize contributions quadratic in the external fields and intramolecular perturbations are expressed, within the quadratic response scheme, by the response function A;B;Ĉ x1;x2 5…”

On the origin independence of the Verdet tensor†

“…A few studies on the invariance of the molecular tensor used to rationalise the Faraday effect, in a shift of origin r → r = r + d of the coordinate system, have been reported [5,[40][41][42] …”

Definition of invariant molecular tensors in an origin change. III. Comparison of the methods suitable for the obtainment of invariant tensors for refraction and the Faraday effect

“…In a recent paper, denoted I [l] we determined global tensors which account for all linear and nonlinear optics and are invariant under an origin change locating the electrons in the molecule or in the cell. Then, in a paper denoted I1 [2], we pointed out, in two particular cases, refraction and Faraday effect, how to obtain the partial invariant tensors accounting for these two effects. The formaiism used in Papers I and 11, that facilitates the demonstration of the invariance, leads, for global and partial tensors, to matrix elements where we find quantum averages of operators different from those used in the previous studies of the phenomena mentioned (see, for example, Refs.…”