Analysis of second harmonic generation at a free boundary for oblique incidence

Abstract

This thesis investigates the generation of second harmonic bulk waves in the presence of a free boundary. Second harmonic waves have proven to be useful in the field of nondestructive evaluation to detect fatigue in a material at an early stage. Since most experimental setups include a free surface, the influence of such a boundary is of significant practical interest. As a result, the objective of this research is to develop a quantitative understanding of the complete process of second harmonic generation at a free boundary. This research shows that the interaction of primary waves (with each other) in the nonlinear framework leads to the generation of second harmonic bulk waves. We distinguish between self-interaction of a single primary wave and the cross-interaction of two different primary waves. The proposed approach uses the perturbation method to solve the nonlinear equations of motion, and shows two fundamentally different solutions. In the case of resonance, the secondary waves grow with propagation distance. This is the most important practical case, since the growing amplitudes of these waves should be easier to experimentally measure. In the second, non-resonant case, the amplitudes of the secondary waves are constant. The complete process of second harmonic generation is analyzed for an incident Pand an incident SV-wave, with the primary and secondary fields given. Finally, the degenerate case of normal incidence is presented. Normal and oblique incidence are compared with regard to their feasibility in experimental setups. The specific behavior of second harmonic waves propagating in aluminum is numerically determined. These results enable a variety of physical insights and conclusions to be drawn from the analytical and numerical investigations.