A Continuum Mechanical Model for Laser-Induced Fracture in Transparent Media

Abstract

Theoretical investigations in the area of laser‐induced damage in transparent media have been primarily directed toward explaining the mechanism by which sufficient energy can be absorbed to cause the observed fracture. However, the work considered here is based on a theoretical investigation of damage from a macroscopic point of view, with the goal of developing a simple continuum mechanical model for the processes leading up to fracture. In this case, the energy absorbed and nonlinear absorption effects are related to the beam's total energy through an experimentally determined absorption parameter. The problem is formulated in terms of dynamic thermoelasticity theory, the energy absorbed from the laser beam being represented by a volume heat source with a physically reasonable space and time dependence based on diffraction theory and known parameters of the optical system. The nonhomogeneous, thermoelastic field equation is solved for the stress distribution by a Green's function technique. By introducing a tensile stress fracture criterion, conditions under which fracture can be initiated during the irradiation process are obtained. Initial numerical results based on an f/30 lens give a good explanation of the phenomenon of the pulverized region associated with laser damage and indicate that this region has a diameter of about 0.4 mm, which is in good agreement with experimental findings.