Fractional Fresnel coefficients for optical absorption in femtosecond laser-induced rough metal surfaces

The surface morphology of metal influences its optical absorptivity. Recent experiments have demonstrated that the femtosecond laser induced surface structures on metals could be dynamically controlled by the fluence of laser and the number of pulses. In this paper, we formulate an analytical model to calculate the optical absorption of a rough metallic surface by modeling the roughness as a fractal slab. For a given experimental image of the surface roughness, we characterize the roughness with a fractal parameter by using box-counting method. With this parameter as input, we calculate the absorption of 800 nm laser pulse impinging on gold, copper and platinum, and the calculated results show excellent agreements. In terms of physics, our model can be viewed as a fractional version of the Fresnel coefficients, and it will be useful for designing suitable surface structures to tune the light absorption on metals from purely reflective to highly absorptive based on different applications.