Self-induced transparency of excitons in semiconductors

Self-induced transparency of excitons is analysed in a model where intraband processes are described by density matrices and interband processes by coherent pair amplitudes. We determine the dispersion law of the carrier wave and the exciton wave function. The theory predicts: (a) a forbidden energy gap centered at the exciton line which broadens with increasing intensity, (b) a critical dependence of the effect on intensity, (c) a strong influence of intensity and carrier frequency on the exciton wave function.