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 given by where the proportionality constant "B" is known as the "Einstein B coefficient" for that particular transition, and "ρ"("ν") is the radiation density of the incident field at frequency "ν". The rate of emission is thus proportional to the number of atoms in the excited state "N", and to the density of incident photons. At the same time, there will be a process of atomic absorption which "removes" energy from the field while raising electrons from the lower state to the upper state. Its rate is given by an essentially identical equation, The rate of absorption is thus proportional