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LASER DIAGNOSTICS AND SPECTROSCOPY
Raman and hyper-Raman scatterings of light by TO phonons
in a CdS crystal
L. Semenova
Prokhorov General Physics Institute of the Russian Academy of Sciences, 38, Vavilov Str., 119991, Moscow, Russia sl@kapella.gpi.ru
In accordance with the selection rules, the Raman and hyper-Raman scatterings of light by E1 and A1 phonons in a CdS crystal with the wurtzite structure are allowed [1]. These optical phonon vibrations are split into longitudinal (LO) and transverse (TO) components. Resonant Raman scattering (RRS) by both LO and TO phonons was observed in CdS [2,3]. However, resonant hyper-Raman scattering (RHRS) by TO phonons was not found [4-6].
The present paper is devoted to a theoretical analysis of RRS and RHRS of light by TO phonons within the framework of the hydrogen-like Wannier exciton model. In so doing, for the valence band the wave functions, which were obtained in the work of Gutsche and Jahne [7], were considered.
The exciton-TO-phonon interaction leads to transitions between excitons with the same orbital quantum numbers. Thus, the main contribution in RRS is made by the sequence of intermediate virtual excitonic states s-s. For the scattering geometry used earlier in the experimental investigations [6], the hyper-Raman process involving two-photon transitions to the s-excitons of the A (the symmetry r6), B and C (the symmetry series can take a place. At the first sight, it is analogous to RRS and could lead to an increase in the cross section near the two-photon resonance with the lowest exciton levels.
But RHRS of light by A^TO) phonons with the participation of A excitons is forbidden. The absence of a noticeable increase in the contribution of the hyper-Raman process involving two-photon transitions to A excitons to RHRS by Ej(TO) phonons near two-photon resonance with the An=1 exciton level can be explained by analyzing the obtained expression describing the indirect transition from the dipole-forbidden A exciton state of the s-type (r6) [8].
The RHRS process involving two-photon transitions to the B and C excitons seems similar to RRS observed earlier [2,3]. However, the two-photon dipole transition can be described using both the two-band and three-band models [9]. And this can have a noticeable effect on the frequency dependence of the scattering cross section.
In general case, the RHRS process, which is described as two-photon dipole transition to a p-exciton state and then the indirect transition to the ground state, is also possible. The sequence of intermediate exciton states s-p-p conforms to it. However, an analysis of this process is difficult since it includes the weakly-forbidden dipole transitions. In this work, for RHRS by E1(TO) phonons the scattering process involving two-photon transitions to A excitons of the p-type was considered as an example.
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