Optical Distortion by Heated Windows in High-Power Laser Systems

Abstract

In a typical long-focal-length laser system, the distortion of the laser beam by the heated exit window can significantly reduce the intensity at the target at power levels well below those required to melt or fracture the window. The spatially inhomogeneous incident laser intensity causes a temperature gradient which changes the thickness and the index of refraction n of the window, causing it to become a lens having, in general, aberration and birefringence in addition to a finite focal length. Expressions are derived for the thermally induced optical distortion in terms of measurable parameters such as n, dn/dT, the strain-optical coefficients p11 and p12, and the thermal-expansion coefficient α. Since the values of all these parameters are not known for most materials of interest, alternate expressions are derived for use in obtaining rough estimates of the amount of distortion. The temperature differential ΔTcrit across the radius of the window which causes a factor of 1/q reduction in target intensity is derived and tabulated (for the case of q=2). Figures of merit for rating materials are derived and tabulated for various materials. The distortion is smaller in general for ionic crystals than for covalent crystals. The briefringence is expected to be larger for the ionic materials than for the covalent ones. In typical systems, rather large increases, say an order of magnitude, in the value of ΔTcrit can be obtained by changing the focal length of the optical system. Other methods of reducing the optical distortion are discussed briefly. Since the optical distortion is expected to be the factor which determines the limit of the target intensity in long-focal-length systems, a large heat capacity and small values of α, dn/dT, p11, p12, and n are important, while the melting point, tensile strength, and Young's modulus are less important, within obvious limits. Experiments are suggested for studying the thermally induced optical distortion.