A spatially nonuniform laser model

The Statz-deMars rate equations for a four-level laser are replaced by equations that allow for variation of the photon densities and inversion along the laser axis. Analytic solutions of these first order partial differential equations are found for the incubation region of the laser spike, i.e., for the time before stimulated emission can affect the inversion. Analytic solutions of the Statz-deMars equations are also derived for the incubation region. The spatially dependent equations are solved numerically in the spiking region for normal and
Q
-switched systems. After integration of these solutions to obtain the total photon number, comparison with the Statz-deMars solutions shows that there are differences if the cavity
Q
is low. The effect of stimulated scattering processes within the laser cavity is studied. It is found that these processes can be effective self-
Q
-switching mechanisms. The spatial variation plays a vital role in such
Q
-switching.