Incubation models for under-threshold laser ablation with thermal dissipation

In laser incubation, the irradiated material reaches the ablation threshold after N pulses at a fluence (energy per unit area) lower than the one required for a single shot. In this work, a new unified picture of incubation is presented describing the growth rate of incubation sites in terms of an analytical expression having four parameters which can be fitted to the experimental data. Our model predicts two crossovers as a function of the pulse number N: and , describing the different incubation behaviors of materials under the action of 'below-threshold' laser pulses. For dielectric materials, and metals irradiated with short laser pulses, the first crossover indicates a transition from a dielectric type of surface response towards an increasingly 'metallic' behavior, consistent with the experimental observations. The second crossover determines the transition to the final stage of the modified surface. In this large N limit, the absorption coefficient of the surface achieves its saturation. For metals irradiated by long laser pulses, ae integral 0 and ae << 1, yielding an approximate power-law behavior of fluence versus N, over a broad range of N values, in agreement with the observations. It is found that one of the fitting parameters denoted here as the incubation exponent, delta, allows us to classify the material response as a dielectric (delta 1) or a metallic (delta << 1) one.