Spectral hole burning and carrier-heating effect on the transient optical nonlinearity of highly carrier-injected semiconductors

An improved density-matrix theory is developed that can treat both spectral hole burning and carrier heating self consistently. Various intraband and interband relaxation terms characterized by different relaxation times and quasi-equilibrium distributions are introduced into the density-matrix equations within a relaxation-time approximation. Conservation of total number and energy densities of carrier systems in each band is considered to determine the quasi-equilibrium distributions. Formalism is applied to the calculation of the transient optical nonlinearity of highly carrier-injected semiconductors. Spectral hole burning and carrier-heating effects on the spectral and temporal characteristics are then clarified. In particular, the significant four-wave-mixing effect due to carrier heating is pointed out. An experiment that can be used to directly prove the existence of the carrier-heating effects on gain nonlinearity is also proposed.>