Klein C A, Dorschner T A
Appl Opt. 1989 Mar 1;28(5):904-14. doi: 10.1364/AO.28.000904.
Faraday rotation isolators for CO(2) laser radars must be capable of handling substantial average power loads without degrading the beam quality or experiencing thermal runaway. For this reason, the semiconductorbased isolators, which are of promise for applications at 10.6 microm, must be cooled. This creates radial temperature gradients and, in conjunction with a nonuniform beam pattern, may lead to severe wavefront aberrations. It is the purpose of this paper to formulate simple procedures for assessing the impact of such aberrations in a cw regime and to provide a prescription on how to proceed in the context of designing or evaluating Faraday rotators for CO(2) laser systems. If it is a good approximation to describe the beam-induced temperature rise by means of a fourth-order even polynomial, the degradation in beam quality originates entirely from the quartic term deltaT(4)rho(4). Specifically, it is the spherical aberration factor S = deltaT(4) radicalvar[rho(4)] that best describes the combined impact of temperature profile and beam shape. The heat flow equation for cw-loaded, edge-cooled, or face-cooled cylindrical Faraday rotator elements can be formulated in a simple nondimensional manner, which demonstrates that (a) temperature variations causing optical distortion scale with betaP/K, i.e., linearly with the deposited power per unit path length and inversely with the thermal conductivity; (b) in a transmission mode of operation with edge cooling and no thermal runaway, the power handling capability is independent of the aperture diameter; and (c), in a double-pass reflection mode of operation that takes advantage of a face-cooled back surface, a significant reduction of the distortion requires Nusselt numbers of at least 10, which leads to a new figure of merit for characterizing the performance of Faraday rotator material candidates. Edge-cooled optical isolators described in the published literature then provide cases for exercising the formalism and demonstrating its effectiveness. Finally, the authors examine the InSb free-carrier Faraday rotator developed at Case Western Reserve University and evaluate its surface-cooling requirement in light of specific design objectives.
