Stability of planar ring lasers with mirror misalignment

We consider an active cavity defined by a geometrically symmetric ring of N mirrors, each of which may have an arbitrary radius. The beam steering imposed by all possible mirror misalignment parameters is shown to diverge if the radii of curvature R_i of the mirrors satisfy two constraints of the form |κ_N({R_i})| = 2. By comparison, the standard conditions for the stability of rays departing from the design path in a perfectly aligned ring have the form |κ_N({R_i})| ≤ 2, so that only approximately half of the critical radii for the latter stability conditions is also critical radii for the former. The detailed solutions identify the most sensitive misalignment parameters regarding beam steering. Certain beam steering effects vanish for resonators with κ_N = −2; this can be of practical importance, as, for example, the N = 2 confocal resonator.