The temperature-dependent linewidths of excitons in semiconductors due to the interaction of the exciton with both LO phonons and with acoustic phonons are studied with use of a Green sfunction approach in which the exciton-phonon interaction is treated perturbatively.The interaction between the excitons and the LO phonons is taken to be of the Frohlich form, and the contribution to the linewidth is obtained in closed form. In this case it is found that scattering of the exciton to both bound and continuum states is important and that it is important to treat the continuum states fully as Coulomb scattering states. In describing optical-absorption processes, the fact that absorption occurs from polariton states, which are states composed of excitons coupled to light, is taken into account. The linewidths due to the exciton-LO-phonon interaction are evaluated for a series of II-VI and III-V compound semiconductors, and are shown to account for the existing experimental results for temperatures~80 K. The contributions to the linewidth due to the interaction of excitons with acoustic phonons via both the deformation potential and the piezoelectric couplings are treated, and it is found that the deformation-potential coupling dominates for all of the materials considered. Because of the small velocity of sound, scattering to only intraband intermediate states, i.e. , those in which the internal exciton quantum numbers do not change, is found to contribute to the linewidth. In the case of acoustic phonons, it is found to be important to treat optical absorption as originating from polariton states in order to evaluate properly the magnitude of this contribution to the linewidth. The acoustic-phonon contribution to the linewidths is compared with experiment for temperatures 80 K, for which it dominates the temperature dependence.

The vacuum-field Rabi splitting of an optical mode in a cavity interacting with a system of N excitations ͑atomic or electronic͒ represented by harmonic oscillators is obtained quantum mechanically both without and with coupling to dissipation. The optical lineshapes and the scaling of the Rabi splitting with the number of oscillators and its dependence on the damping parameters are given. Corresponding results are given for a classical treatment of the oscillators, and it is shown that to the leading order in the dissipation, the quantum mechanical results for absorption are the same as the classical ones. ͓S0163-1829͑99͒09515-6͔ PHYSICAL REVIEW B 15 APRIL 1999-I VOLUME 59, NUMBER 15 PRB 59

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