Abstract

Faraday rotation isolators for CO₂ laser radars must be capable of handling substantial average power loads without degrading the beam quality or experiencing thermal runaway. For this reason, the semiconductor-based isolators, which are of promise for applications at 10.6 μm, 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 CO₂ 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 δT₄ρ⁴. Specifically, it is the spherical aberration factor $S=\delta {{\rm T}}_4\sqrt{\mathrm{var}[{\rho }^4]}$ 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 βP/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.

© 1989 Optical Society of America

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