Laser science the laser and maser in 1917, via a paper in which he re-derived Max Planck’s law of radiation using a formalism based on probability coefficients (Einstein coefficients) for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation. The existence of stimulated emission was confirmed in 1928 by Rudolf W. Ladenburg. In 1939, Valentin A. Fabrikant made the earliest laser proposal. He specified the conditions required for light amplification using stimulated emission. In 1947, Willis E. Lamb and R. C. Retherford found apparent stimulated emission in hydrogen spectra and effected the first demonstration of stimulated emission; in 1950, Alfred Kastler
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