Optical gain in materials with indirect transitions

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Abstract
Based on a simple two-level system, we discuss optical gain in materials with indirect optical transitions. We show that contrary to direct materials the absolute value of the negative absorption coefficient, which describes the optical gain, can be orders of magnitude larger in indirect semiconductors than the positive absorption coefficient measured under equilibrium conditions. These results are in contrast to previously published work and suggest that the question as to whether laser operation based on band–band transitions in bulk crystalline silicon is possible or not, in principle, needs to be readdressed. In addition, it is shown that indirect optical transitions can provide negative absorption, i.e., optical gain without an electronic population inversion.