Asymptotic nature of threshold conditions and multimode laser emission

The multimode nature of the steady-state emission of a laser with a homogeneously broadened line is shown to be the direct consequence of the asymptotic character of the threshold conditions: Because of the spontaneous background the total losses in a laser are always slightly greater than the rate of supply of stimulated photons and the equilibrium between the losses and the stimulated emission in the resonator is reached only when the pumping rate becomes infinite. This is illustrated by a calculation of a multimode steady-state emission spectrum of a gallium arsenide injection laser. The dependence of the output power on the input current is also calculated for this laser.