The thermoelasticity of laser-based ultrasonics

The generation of ultrasound by heat deposition due to laser irradiation has several advantages over conventional generation by piezoelectric transducers. Ultrasound generation by focused laser beam irradiation is a problem of thermoelastodynamics. A mathematical analysis for focused laser beam heating of the surface of an elastic half-space can be carried out by the use of integral transform techniques. It is, however, well known that a point source of heat is mechanically equivalent to a center of expansion. Here we use, therefore, simpler thermoelastic arguments to determine the mechanical loading equivalent to heating by laser irradiation, and then proceed to determine the induced wave motion. This approach has the advantage that the surface center of expansion can be determined for a general class of elastic materials without the necessity of using integral transform techniques. As an example, we consider line-focused laser irradiation of a transversely isotropic material whose axis of symmetry is perpendicular to the free surface of the body. General calculations of ultrasound generated by laser irradiation have shown that by far the most significant part of the generated surface motion is a pulse propagating with the velocity of Rayleigh surface waves. In the approach presented here, the surface-wave pulse is determined for time-harmonic excitation by the use of the reciprocity theorem, whereby the two reciprocal solutions are the actually generated surface waves and a "virtual'' surface wave. The technique has general applicability for anisotropic and inhomogeneous materials, as long as the general form of the surface wave is known. Here we consider the case of a transversely isotropic material. In the last part, Fourier superposition of ultrasonic surface wave harmonics is used to obtain the surface wave pulse for arbitrary time dependence of the laser pulse.