Definition of invariant molecular tensors in an origin change. I. General formalism

Abstract

AbstractsAmong the tensors used in the published literature to characterize a phenomenon of nonlinear optics, some are not invariant under a change of origin. In this paper, we show that this invariance can be obtained in a general manner, if the densities of electric and magnetic polarization are not separated but replaced by a density of magnetoelectric polarization whose quantum calculation is performed for a molecular crystal.Parmi les tenseurs utilisis dans la litterature pour caracteriser un phenomene de I'optique non-lineaire, certains-uns ne sont pas invariants par rapport a un changement d'origine. Dans le prCsent article nous montrons que cette invariance peut &[re obtenue de fason generale, si les densites de polarisat ion tlectrique et magnktique ne sont pas separees mais remplacees par une densite de polarisation magneto-electrique, dont le calcul quantique est effectue pour un cristal moleculaire.Unter den in der Litteratur vorkommenden Tensoren fur die Charakterisierung eines Phanomens der nichtlinearen Optik, sind einige unter Transformationen des Koordinatenursprungs nicht invariant. In diesem Artikel zeigen wir, dass diese Invarianz in einer allgemeinen Weise erhalten werden kann, wenn die elektrische und magnetische Polarisierungsdichten nicht separiert werden, aber von einer magneto-electrischen Polarisierungsdichte ersetzt wird, die fur einen Molekulkristall berechnet wird.

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] …”