Sound amplification by stimulated emission of radiation to the statement that the levels on which the laser should operate, must be in the k-space relatively to each other. K-space refers to a space where things are in terms of momentum and frequency instead of position and time. The conversion between real space and k-space is a mathematical transformation called the Fourier transform and thus k-space can be also called Fourier space. We note that, the difference in energy of the photon lasing levels has to be at least smaller than the Debye energy in the semiconductor. Here we can think of the Debye energy as the maximum
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