Resonant Brillouin scattering in CdS. II. Theory

Numerical calculations are presented for the observable external scattering cross sections of resonant Brillouin scattering. The $A$ exciton in semiconducting CdS is taken as a concrete example with both the longitudinal-acoustic-phonon deformation potential and the transverse-acoustic-phonon piezoelectric potential scattering considered. Use is made of the factorization approximation for the external scattering cross section, and the internal cross section is formulated in detail quantum mechanically. Important factors contained in the scattering efficiency, exciton-polariton dispersion curves, scattered frequency, transmissivities (both from vacuum to medium and vice versa) with various additional boundary conditions, group and energy velocities, and exciton strength functions, are calculated separately, and are then combined to find the internal and the observable external scattering cross sections. While the internal cross section shows a monotonic increase as a function of incident frequency ${\omega }_I$, with strong growth near the transverse exciton frequency ${\omega }_0$ the curves describing the external cross sections are found to have characteristic structures around ${\omega }_0$ and the longitudinal exciton frequency ${\omega }_L$ which depend strongly on the choice of additional boundary conditions. They are also shown to exhibit a drastic profile change when the exciton damping constant $\Gamma$ approaches a threshold value ${\Gamma }_c$. Polariton effects are expected only for $\Gamma <{\Gamma }_c$, and the usual exciton "resonance" effects which are qualitatively different from those of the polariton are shown to occur for $\Gamma \gtrsim {\Gamma }_c$. The suitability of resonant Brillouin scattering for experimentally determining the proper additional boundary condition as well as values of the parameters of the exciton and exciton-polariton is discussed.