Beam steering in confocal unstable resonators

The effects of mirror misalignment in a confocal unstable resonator are interpreted in terms of beam steering or deflection in the output beam. Exact mode solutions for a resonator with a Gaussian output mirror lead to an expression for the far-field beam-steering angle as a function of the magnification and Fresnel number of the resonator. This solution reduces to the geometric result when the Fresnel number exceeds 10, for output couplings greater than 50 percent. An expression is derived that relates the beam diameter, the mirror vibration amplitude, and the far-field beam divergence. Numerical values are presented that show that in order to prevent the far-field intensity of a 10.6-μm laser beam from being degraded by a factor of two, the product of the mirror vibration angle and the beam diameter should typically not exceed 220 μrad-cm.