Thermal shock damage may be a precursor to the melting and disordering of metallic reflector surfaces. A number of investigators have reported in these proceedings the phenomena of slip fracture on the surfaces of both polished and diamond turned optics. In this paper, a model is presented using elastic-plastic technique coupled with the transient thermal response of an optical surface. Equations are presented to reflect the thermal shock threshold for major metals that are commonly used for high power laser reflective optics. The models for the continuous wave and repetitive pulsed conditions have some similarities in evaluating the strain and rupture. However, because of the two cycle nature of the Repetitive Pulse condition, the thresholds are demonstrably lower than those that are shown for the Continuous Wave situation.

The direction of this paper is to provide a theoretical model and supporting empirical data for evaluation of laser damage to optical thin films subjected to high power Continuous Wave laser irradiation. Basically, there has been a seeming anomaly in the maximum temperature that optical thin films can withstand before they fail to perform their function. On the one hand, a paper was presented to the Laser Boulder Damage Symposium that clearly provided empirical data that a number of oxide coating materials could reach 59°C to 680°C before failure set ia On the other hand, many investigators have found that coatings have failed at temperatures of 200°C to 300°C. In this paper we set out to demonstrate that both conditions could be correct, rather than just one or the other. The equations for the absorption and subsequent temperature rise in the multilayer stacks are provided. The temperature rise of the substrate is evaluated and the equations for the actual thermal shock resulting from the conditions in the optical thin films, the substrate, and sensitivity of both to the materials that comprise the optical thin films and the substrates combination. Several coating chemistry combinations and three diverse substrate materials are evaluated and plotted based on measurements made and reported some years ago.

This is the companion paper to the Reverse Thermal Wave Approximations for High Power Continuous Wave Lasers. The purpose of this paper is to provide equations that will allow the optical designer to evaluate the temperature gradient in optical thin films and substrates under transient conditions. The semi-infinite plate models have been described rather extensively in other publications. However, the problem that is treated in this paper is that set of boundary conditions that do not satisfy the semi-infinite plate condition. It is not uncommon to have coated reflective optics that have very thin substrates. For those conditions it is necessary to evaluate the temperature transient much differently than one would if the substrates were of sufficient thickness to satisfy the semi-infinite plate boundary. One finds that the temperature rise and gradients are substantially different for very thin substrate conditions. The Reverse Thermal Wave Modelwill provide the ability to evaluate the temperature gradients during the transient with closed form approximations. The repetitive pulsed case has a substantially different characteristic temperature profile from that of the continuous wave and in this paper the equations and figures are provided to reflect the unique character of the temperature gradients in the optical thin films and substrates as a function of the hertz rate and pulse width. It becomes clear that the duel cycle of heating and cooling coupled with the thermal shock play important roles in the damage thresholds of many optical components in high power laser systems.

There are a number of requirements in high energy laser systems to provide optical elements that are not integrally cooled. However, there are many instances where a cooling gas, such as helium or nitrogen, may be used to cool the front and back surfaces in order to reduce optical distortion. In order to evaluate the response of an optic to this type of cooling, first order analytical techniques have been generated to determine transient and steady-state temperature distributions through a fully irradiated optic, an irradiated spot on a large optic, and a toroidal shaped beam (i.e., hole in the beam), on a large optical element. Cooling temperatures and damage relationships coupled with optical path differences of the flowing gas are treated for evaluation. Optical distortion of the element due to radial and axial temperature gradients are treated for both transient and steady-state conditions and for various gas flow dynamics.

A theoretical model has been developed which provides for evaluating both pulse and continuous wave laser damage on metal mirrors. The model technique employs the three-dimensional Palmer-Bannett model as a base. Using the fullwidth, half-band temporal profile for the pulse time constant and the thermal diffusivity of copper as a baseline, the time constant is corrected for other materials by the ratio of thermal diffusivities. Basically, the theoretical concept rests on the premise that neither the Drude theory nor the Jakob-Kelvin theory are completely correct for short-pulsed (i.e., less than a microsecond) time constants. The heat sink below the first few angstroms acts as a dampening coefficient. The metal does not appear to be able to respond to the very short time constants and, as a consequence, the temperature versus reflectivity does not hold in straight-forward fashion. As the time constants extend into the microsecond regime, and longer, the relationships of temperature versus reflectivity become more representative. Melt and Slip thresholds for copper, silver and gold have been presented previously [1]. The data have been generated for wavelengths of 1.06 μm, 2.7 μm, 3.8 μm, and 10.6 μm. Varying spot-sizes and different pulse widths were used. The theoretical model has been applied against this datum with excellent results ranging from 99.8% to 82% agreement. Based on the relationship suggested by the three-dimensional Palmer-Bennett model and the unifying theory suggested, spot size dependence may be determined for given metal diamond turned mirror substrates. The basis for damage, selected for the theory, is the point where slip phenomena occurs in the metal surface. This selection is more than arbitrary. Slip phenomena becomes the first indication that there is a permanent disruption to the optical surface. Further, slip and melt would seem to be the most thermally dependent manifestations of disruption.