Sound amplification by stimulated emission of radiation was first experimentally demonstrated in the Gigahertz range in 2009. Announced in 2010, two independent groups came up with two different devices that produce coherent phonons at any frequency in the range megahertz to terahertz. One group from the University of Nottingham consisted of A.J. Kent and his colleagues R.P. Beardsley, A.V. Akimov, W. Maryam and M. Henini. The other group from the California Institute of Technology (Caltech) consisted of Ivan S. Grudinin, Hansuek Lee, O. Painter and Kerry J. Vahala from Caltech implemented a study on Phonon Laser Action in a tunable two-level system. The University of Nottingham device
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