Abstract

Many papers on semiconductor gain media have presented models for two-level homogeneously and inhomogeneously broadened media. In this paper, we show why and where these models become inadequate. The problems originate from the fact that the two-band semiconductor gain medium is an inhomogeneously broadened four-level medium with rapid cross relaxation due to carrier-carrier scattering, and all four levels have appreciable probability in gain media. The four states are given by |n_en_hk s>, where n_e (= 0 or 1) and n_h (= 0 or 1) are the number of electrons or holes, respectively, for momentum k and spin s. The two-level system is a one-electron system with no states corresponding to the partially excited semiconductor states |0_e1_hk> and |l_e0_hk>, which involve two electrons. The Pauli exclusion principle never gets a chance to enter the picture. In the absence of many-body effects, semiconductor gain can be fitted in an ad hoc fashion by a two-level model, but problems that involve the level probabilities individually, such as the laser photon statistics, elude a two-level description.

© 1992 Optical Society of America