Calculation of the fundamental mode of a resonator cavity with an extended thermal lens

An analysis is made of the conditions for stable operation of a laser in which the active element has focusing properties (forms a thermal lens) and the length of this element $L$ is comparable with the focal length of the lens. The change in the dimensions of a laser mode inside the active element (extended lens) is taken into account. It is shown that such a resonator cavity has a section (arm) in which the dimensions and curvature of the wavefront of a mode remain stable for a certain value of the optical power $P$ of the active-element lens. Expressions are deduced for the case when the optical power of a thermal lens corresponds to the stable dimensions of a mode in various intracavity components. The thick-lens approximation is shown to be suitable for design calculations of cavities with an extended lens when $PL\ll1$ and also when $PL\sim1$.