Simplifications for the calculation of surface wave pulses generated by laser-irradiation

In this paper a simplified approach is presented to determine the ultrasonic surface wave motion generated by laser irradiation of a linearly elastic solid. It combines three novel ideas. The first is a way to directly determine the mechanical loading equivalent to laser irradiation by considering local thermoelastic effects in the area that is heated by the laser. The second idea is the use of a new formulation for surface waves which considers a surface wave as a carrier wave that satisfies Helmholtz' equation in surface coordinates and that supports depth-dependent motions that are the same for any kind of carrier wave. The third idea is to directly determine the surface wave motion generated by the equivalent mechanical loading by applying the elastodynamic reciprocity relation for the generated surface wave motion and an appropriately selected "virtual" wave motion. The analysis based on the reciprocity relations is carried out for the time-harmonic case, but Fourier superposition is used to obtain the surface wave pulses corresponding to pulsed laser irradiation. The approach based on these ideas is taken through several steps for an isotropic and a transversely Isotropic solid whose mechanical properties may depend on the distance from the surface. For a homogeneous isotropic solid the details have been worked out for the surface wave pulses generated by the laser irradiation of arbitrary time dependence at a point, an infinitely long line, and a line of finite length.