Sound amplification by stimulated emission of radiation method of the pumping keeps the system electro-neutral and the dispersion laws of electrons and holes are assumed to be parabolic and isotropic. Also phonon dispersion law is required to be linear and isotropic too. Since the entire system is electro-neutral, the process of pumping creates electrons and holes with the same rate. A mathematical analysis, leads to an equation for the average number of electron-hole pairs per one phonon mode per unit volume. For a low loss limit, this equation gives us a pumping rate for the SASER that is rather moderate in comparison with usual phonon lasers on
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