Dynamic ADI computations of thermoelastic stresses in crystalline laser media

This article considers thermoelastic effects which influence both the thermal engineering design and optical propagation in solid state high average power laser (HAPL) systems. The methods and computations described were developed for applications, ultimately, to crystalline slabs with arbitrary symmetry properties and with arbitrary spatial orientations between crystalline axes and slab configurations. For this, accurate numerical solutions are required simultaneously for the heat equation and Hooke's law in their most general tensor forms. Prompted by the optical problem requirements in HAPL systems, this work utilizes implementations of Eulerian discretizations and dynamic ADI methods for solving general fourth order elliptic partial differential equations (PDE's) which describe stress potentials in anisotropic media. These formulations can provide both steady state and transient PDE solutions. Computed results for trigonal Al2O3 crystal deformations in various crystal axes/slab orientations are presented.