Thermoelastic response of materials with thick-disk geometry excited by a ring-shaped laser beam

Abstract

The heat and thermoelastic equations are analytically solved for a material with low optical absorption. This set of equations shows profiles describing the temperature distribution, surface displacement, stresses and optical path for a sample with a thick-disk geometry when is excited by a ring-shaped laser beam. This is done by determining the steady-state because when a laser beam is used, it turns on for several minutes to stabilize before using it in experiments. It is shown that the temperature takes some seconds to reach the steady-state condition, then, this approximation is very useful and simplifies the data processing. These results were also compared with a Gaussian profile, showing that the Gaussian equations are a consequence of the ring-shaped laser beam equations. The finite element method is used as a form of validation of the equations found in this work, obtaining a good agreement between numerical results. Errors are calculated for the temperature, displacement and optical path difference at the center(edge) of the sample; these are around 0.14 %(0 %), 0.11 %(30.50 %) and 0.09 %(4.86 %), respectively, for a BK7 sample. The analytical results obtained could be of great help in the design of the optical components and different experimental configurations. Maybe the principal advantage of a ring-shaped laser beam is to produce a temperature profile with a top-hat form at steady-state, while that a top-hat laser beam does not.