Classical derivation of the laser rate equation

In this paper, the rate equation for the energy (photon) density inside the resonant cavity of a laser oscillator is derived from Maxwell's equations. By comparison to the familiar photon rate equation, this classical derivation can be used to obtain the well-known expression for the ratio of the power that is spontaneously emitted into a single laser mode relative to the total amount of spontaneous emission. This independent derivation does not require mode counting procedures and settles the following question: what fraction of the total power that is spontaneously emitted into the wavelength range of the fluorescent linewidth is utilized for increasing the energy in a given laser mode?