Onset threshold analysis of defect-driven surface and bulk laser damage

Surface and bulk laser damage probability distribution functions are derived for a Gaussian laser beam and a power-law defect damage ensemble. Closed-form solutions are derived and plotted for six and three values of the defect ensemble parameter p in the surface and bulk damage distribution functions, respectively. The derived degenerate (p = 1) and nondegenerate (p = 0) bulk damage equations are least-squares fitted to measured laser damage statistics in polymethyl methacrylate. The results show that the power-law defect ensemble is a reasonable description of the laser-damageable defects in the damage-tested polymethyl methacrylate and that the ensemble is more degenerate in character than uniform.