Two-photon spectroscopy between states of opposite parities

Abstract

Magnetic and electric dipole two-photon absorption (MED-TPA), recently introduced as a spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. An approximation referred to as weak quasiclosure approximation is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric dipole two-photon absorption. PRELIMINARIES Two-photon spectroscopy is now an experimental technique widely used in various domains, as for instance transition ions in crystals and excitons in semiconductors and insulators. Two-photon spectroscopy experiments on excitons were first achieved by Hopfield and Worlock. ' Recently, Frohlich et al. reported two-photon absorption measurements for the three alkali halides RbI, NaI, and NaBr. These authors considered nonlinear processes where two photons are simultaneously absorbed, one photon by magnetic dipole transition and the other by electric dipole transition. The resulting magnetic and electric dipole two-photon absorption (MED-TPA) has to be distinguished from the following.(i) The classical electric dipole two-photon absorption (ED-TPA) where the two photons are simultaneously absorbed by electric-dipole transition between states of the same parity. The standard theory for parity-allowed ED-TPA was given by Axe and the corresponding selection rules arising from the point symmetry group G of the absorbing site were derived by Inoue and Toyazawa and by Bader and Gold. Further investigations of parity-allowed ED-TPA were conducted in Refs. 6 -11 on the basis of microscopic models and symmetry adaptation methods' for the chain of groups SU(2)ZG* (where G* is the double group of the group G). (ii) The forced ED-TPA where the two photons are simultaneously absorbed by electric dipole transition between states of opposite parities. Several parity-violation mechanisms were introduced' ' for explaining parity-forbidden ED-TPA, especially for partly-filled shell ions in crystals. Selection rules based on the SU(2) D G* symmetry were obtained in Refs. 10, 11, and 17 for parity-forbidden ED-TPA. Of course, MED-TPA and (parity-allowed and parityforbidden) ED-TPA differ as far as simple considerations on spin are concerned. We may also a priori expect some differences regarding the selection rules coming from the point symmetry of the site. In this connection, the selection rules for MED-TPA used in Ref. 2 were obtained in the spirit of the pioneer work by Inoue and Toyazawa. However, it is to be realized that the selection rules introduced in Ref. 4 and extended by Bader and Gold were developed, on the basis of symmetry considerations only, for (parity-allowed) ED-TPA.It is the aim of this paper to show that the SU(2) DG* selection rules for parity-forbidden ED-TPA hold for MED-TPA when the two absorbed photons in both processes are different. We sh...

Femtosecond Two-Photon Absorption Spectroscopy of Poly(fluorene) Derivatives Containing Benzoselenadiazole and Benzothiadiazole

“…Since both polymers do not present an inversion center, the 1Ag-like → 1Bu-like transition that is strongly 1PA-allowed (related to lowest energy band) may also be accessed via 2PA. This is possible because, for noncentrosymmetric molecules, the electric dipole selection rules are relaxed [ 31 ].…”

Polarization dependence of two-photon absorption and electronic Raman scattering intensitiesin crystals

“…37 Two-photon absorption processes in which one photon is absorbed by a magnetic dipole transition and the other by electric dipole transition have also been investigated by Frohlich et al 38 and Daoud and Kibler 39 as possible mechanisms contributing to interconfigurational excitonic transi-tions observed in RbI, NaI, and NaBr. Daoud and Kibler's prediction using symmetry adaptation technique, 39 however, disagreed with Frohlich et al's assignments of the observed transitions. 38 Except the derivations proposed by Makhanek et al 33,34 and Daoud et al,37,39 all of two-photon studies up to the fourth order mentioned above have been applied in the framework of the Cartesian coordinates or circular polar coordinates.…”

“…Daoud and Kibler's prediction using symmetry adaptation technique, 39 however, disagreed with Frohlich et al's assignments of the observed transitions. 38 Except the derivations proposed by Makhanek et al 33,34 and Daoud et al,37,39 all of two-photon studies up to the fourth order mentioned above have been applied in the framework of the Cartesian coordinates or circular polar coordinates. The general study of polarization dependence behavior of the thirty two crystallographic point groups was initiated by Inoue and Toyozawa.…”

“…The theory of static and dynamic contributions to the two-photon f -d transitions has been developed by Leavitt, 32 Daoud and Kibler,37,39 and Sztucki and Strek. 18 Their polarization dependent expressions can be derived by using methods described in the previous section.…”

The Master thesis of Moshé Flato

“…In 1995, with the advent of strong technological progress in two-photon absorption spectroscopy of rare earth ions doped materials, part of the above-mentioned works were revived in view of the elaboration of a model for analysing intensities of two-photon transitions between states of opposite parities for an ℓ N ion in finite symmetry [32].…”