Sound amplification by stimulated emission of radiation this scheme with a rather moderate pumping rate can hold against the fact that excitons in coupled quantum wells have low dimensionality in comparison to phonons. Hence, phonons not confined in the coupled quantum well are considered. An example is longitudinal optical (LO) phonons that are in AlGaAs/GaAs heterostructure and thus, phonons presented in this proposed system are three-dimensional. Differences in dimensionalities of phonons and excitons cause upper level to transform into many states of phonon field. By applying this information to specific equations we can conclude to a desired result. There is no additional requirement for the laser pumping
Stimulated emission of energy levels 1 and 2, respectively. The intensity (in watts per square meter) of the stimulated emission is governed by the following differential equation: as long as the intensity "I"("z") is small enough so that it does not have a significant effect on the magnitude of the population inversion. Grouping the first two factors together, this equation simplifies as where is the "small-signal gain coefficient" (in units of radians per meter). We can solve the differential equation using separation of variables: Integrating, we find: or where The saturation intensity "I" is defined as the input intensity at which the