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LASER DIAGNOSTICS AND SPECTROSCOPY
Resonant hyper-Raman scattering of light by 2LO 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 experimental investigations of multiphonon resonant Raman scattering in a CdS crystal under excitation below excitonic resonances an intensity alternation with increasing number of excited longitudinal optical (LO) phonons was found where the even-order lines dominated [1]. This feature was qualitatively explained within the framework of the exciton model in accordance with which the odd-order lines could expect to dominate in hyper-Raman spectra [1,2]. It was later reported that resonant hyper-Raman scattering (RHRS) of light by 1LO and 3LO phonons was observed in CdS [2]. And in a study of RHRS in CdS with the use of a tunable laser an appearance of the 2LO line in hyper-Raman spectra under excitation near two-photon resonance with the 1s exciton state of the A series was found, and its intensity has grown with increasing the incident photon energy [3]. This RHRS by 2LO phonons was explained by the scattering mechanism involving two-photon dipole transitions to the B and C excitons of the s-type [4].
In present work, RHRS by 2LO phonons is considered, taking into account the valence band wave functions obtained by Gutsche and Jahne [5], i.e. mixing the p- and d-like wave functions is assumed to take a place in the top sub-band A and the deeper valence band v' of the symmetry r9. The hydrogen-like Wannier excitons are supposed to be intermediate virtual states of an electronic system. The Fröhlich mechanism of the exciton-phonon interaction is taken into account.
The two-phonon RHRS process considered here involves two-photon dipole transitions to s-excitons of the B and C series and is, at first sight, analogous to Raman scattering by 2LO phonons. But, in accordance with the two-photon absorption theory [6,7], the two-photon dipole transitions to B and C excitons of the s-type can be occur via the intermediate virtual states which can be p-excitons belonging to same pair of the bands and s-excitons associated with the higher-lying conduction band or the deeper valence band v' (r9). Values of the matrix elements of the dipole transitions in these bands are unknown.
The rough estimations performed has shown that taking into account the dipole transitions to the deeper valence band v' can affect the frequency dependence of the two-phonon RHRS cross section (dc/dQ) and, under certain conditions, can lead to the fact that dc/dQ begins to increase sharply at excitation slightly below the two-photon resonance with the lowest exciton level.
[1] A.A. Klyuchikhin, S.A. Permogorov, and A.N. Reznitskii, Multiphonon processes in resonant scattering and exciton luminescence of crystals, Sov. Phys. JETP, vol. 44, pp. 1176-1186 (1976).
[2] L.E. Zubkova, K.K. Ondriash, Yu. N. Polivanov, and K.A. Prokhorov, Multiphonon resonant hyper-Raman scattering, JETP Lett., vol. 57, pp. 348-351 (1993).
[3] V.A. Maslov, K.K. Ondriash, Yu.N. Polivanov, K.A. Prokhorov, L.E. Semenova, Yu.L. Chuzavkov, Observation of resonant hyper-Raman scattering of light in a CdS crystal using a tunable optical parametric oscillator, Laser Phys., vol. 6. pp. 132-143 (1996).
[4] L.E. Semenova and K.A. Prokhorov, Two-phonon resonant hyper-Raman scattering treatment in a CdS crystal, Laser Phys. Lett., vol. 2, pp. 262-266 (2005).
[5] E. Gutsche and E. Jahne, Spin-orbit splitting of the valence band of wurtzite type crystals, phys. stat. sol., vol. 19, pp.823-832 (1967).
[6] G.D. Mahan, Theory of two-photon spectroscopy in solids, Phys. Rev., vol. 170, pp. 825-838 (1968).
[7] K.C. Rustagi, F. Pradere, and A. Mysyrowicz, Two-photon absorption in Cu2O, Phys, Rev. B, vol. 8, pp. 2721-2732 (1973).
