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 . 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.