Optical amplifier "erbium-doped waveguide amplifier" ("EDWA") is an optical amplifier that uses a waveguide to boost an optical signal. Amplification is achieved by stimulated emission of photons from dopant ions in the doped fiber. The pump laser excites ions into a higher energy from where they can decay via stimulated emission of a photon at the signal wavelength back to a lower energy level. The excited ions can also decay spontaneously (spontaneous emission) or even through nonradiative processes involving interactions with phonons of the glass matrix. These last two decay mechanisms compete with stimulated emission reducing the efficiency of light amplification. The
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