Modes of a plano — spherical laser resonator with the Gaussian gain distribution of the active medium

Modes of a laser with plano–spherical degenerate and nondegenerate resonators are calculated upon diode pumping producing the Gaussian gain distribution in the active medium. Axially symmetric and off-axis pumpings are considered. It is shown that in the first case the lowest Hermite–Gaussian mode is excited with the largest weight both in the degenerate and nondegenerate resonator if the pump level is sufficiently high or the characteristic size w_g of the amplifying region greatly exceeds the mode radius w₀. The high-order Ince–Gaussian modes are excited upon weak off-axis pumping in the nondegenerate resonator both in the absence and presence of the symmetry of the gain distribution with respect to the resonator axis. It is found that when the level of off-axis symmetric pumping of the resonator is high enough, modes with the parameters of the TEM₀₀ mode periodically propagating over a closed path in the resonator can exist. The explanation of this effect is given.