Peculiarities of the fundamental mode structure in stable-resonator lasers upon spatially inhomogeneous amplification

The structure of the fundamental mode of a laser is calculated by the iteration Fox–Li method in the case of inhomogeneous unsaturated amplification produced by axially symmetric longitudinal pumping. The calculation is performed for different parameters g₁ and g₂ of the resonator within the entire stability region. It is shown that in the case of inhomogeneous amplification, the fundamental mode considerably deviates from the Gaussian mode of an empty resonator only in the so-called critical configurations of the resonator, when the quantity [arccos(g₁g₂)^1/2]/π is zero or takes a number of values expressed by irreducible fractions m/n. For the Fresnel number N_F = 9, configurations with m/n = 1/2, 2/5, 3/8, 1/3, 3/10, 1/4, 1/5, 1/6, 1/8, and 1/10 are pronounced. As N_F increases, the number of critical configurations increases. The expansion in a system of Laguerre – Gaussian beams shows that the fundamental mode in critical configurations is formed by a set of beams with certain radial indices p phased in the active medium.