Rotating patterns in class-B lasers with cylindrical symmetry

We analyze two- and three-mode interactions in a cylindrically symmetric class-B laser with a low Fresnel number. Using the method of continued fractions, we derive the steady-state equations for two different kinds of rotating patterns, involving two or three modes. The threshold conditions for bistability in the first case and rotation in the second case are also found. The stability of the two dynamical solutions is investigated numerically. The results are compared with those obtained in some previous works.