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.

Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry

“…where is approximately the phase difference of the probe beam at rϭ0 and rϭ(2 1/2 e ) induced by the thermal lens, P(W) is the excitation laser power, A e (cm Ϫ1 ) is the absorption coefficient at the excitation beam wavelength, K(W K Ϫ1 cm Ϫ1 ) is the thermal conductivity, p (cm) is the probe beam wavelength, L ͑cm͒ is the sample thickness and ds/dT (K Ϫ1 ) is the optical path-length change with temperature, which is given by 9,20 …”

Temperature and wavelength dependence of the thermo-optical properties of tellurite and chalcogenide glasses

“…[23][24][25] Since the thermal expansion coefficient is independent of the wavelength, then the wavelength dependence of dS / dT at a fixed temperature provides information on the wavelength dependence of the electronic polarizability of the glass. The dispersion curves of dS / dT at 65°C are shown in Fig.…”

Thermal Lensing in Infrared Laser Window Materials

“…For a fixed time, the temperature and the strains depend only on p. Therefore, for a small change in ni, and following the development given by Quelle (1966) and Sparks (1971) ,,( o# z)…”

“…In this paper we extend previous treatments of thermal lensing (Quelle, 1966;Foster et al, 1970;Sparks, 1971) to include window aberrations to all orders and (Received for publication 23 March 1972) 2A…”

“…Theoretical treatments of some problems quite close to the one examined in this paper have also been given (Tien et al, 1965;Quelle, 1966;Foster et al, 1970). In fact, Sparks (1971) showed that a significant amount of thermal lensing will occur in an infrared window well before it fails due to other causes. For a discussion of other modes of failure see Horrigan et al (1969).…”