Analysis of Surface Wave Generation by Laser Interference

An analytical solution for thermal excitation of elastic waves in an homogeneous, isotropic, elastic half-space resulting from a pulsed laser interference pattern incident on the solid surface is presented. The spacially-periodic laser field absorbed by the surface causes rapid heating within the optical penetration depth. Thus, a temperature field is generated which can be modeled as being spacially harmonic along the free edge, decaying exponentially with depth, and having a Heaviside dependence on time. Transform techniques yield expressions for the resulting transverse and normal displacements within the laser interference region in terms of infinite integrals over frequency. The integrands contain poles indicating the expected Rayleigh waves propagating along the surface, as well as branch points corresponding to the bulk longitudinal and transverse wave speeds. The solution is obtained by integrating numerically in the complex frequency plane with an appropriate contour around the poles and branch cuts. Normal and transverse displacements are plotted as functions of time and depth for various materials and temperature fields.