Unified theoretical model for calculating laser-induced wavefront distortion in optical materials

Abstract

Laser-induced thermal lens in optical components causes wavefront distortion of the laser beam and may affect performance and stability of optical systems such as high-power lasers. The bulging of the heated area, the temperature dependence of the refractive index, and the photoelastic effects are responsible for phase shifts damaging beam quality. The theoretical background for laser-induced beam distortion is well understood and applies only for axially symmetric thermal loadings, with the assumptions that the stresses follow thin-disk or long-rod approximations. This, in fact, limits the overall applications of this model. In this work, we developed an unified theoretical model for the optical path change in optical materials regardless of its thickness. The modeling is based on the solution of the thermoelastic equation and has a real description of the surface deformation caused in the optical element. In the appropriated limits, as expected, the model retrieves the thin-disk and the long-rod type distributions. Furthermore, we provided time-dependent radial expressions for the temperature, surface displacement, and stresses. The theory presented in this paper provides simple analytical tools for designing laser systems, and complements previous work allowing one to access optical distortions of materials ranging from thin-disk to long-rod-like distributions.