Critical analysis and correction of the rate equation for the injection laser

A critical examination of the conventional rate equation connecting the photon density, the spontaneous emission and the gain parameter reveals an internal inconsistency; while the first two quantities are pro-rated over the spectrum of the mode, the last is evaluated at the mode centre. Because interference between incident and reflected waves rapidly reduces the rate of stimulation as the optical frequency departs from resonance, pro-rating the net gain parameter over the spectral line gives a power-dependent first-order correction to its effective value. Examination of treatments of the optical noise amplifier as a lumped-element classical device and as a classical travelling-wave amplifier suggests ways to modify the conventional rate equation. If the usual concept of the spontaneous emission factor is retained in the equation, the net gain parameter is replaced by its square root. Alternative modifications redefine the dependent variable describing the output or the spontaneous emission factor. One result of the correction of the rate equation is a strong reduction in the predicted damping of the noise amplifier.