Influence of slit width on harmonic generation in ultrasonic surface waves excited by masking a laser beam with a line arrayed slit

Abstract

Masking an expanded laser beam with a line-arrayed slit is an effective and easy way to produce line arrayed illumination sources in order to excite a laser-generated surface wave within a narrowband of frequencies. The objective of this study is to identify the slit width dependency of the magnitude of harmonic waves generated by this technique. The frequency response of the generated surface wave is presented first under the assumption that the spatial energy profile of each line beam is a simple one-dimensional square pulse and the temporal profile is a delta function. Then the magnitude ratio A2/A1 (A1: magnitude of the fundamental wave, A2: magnitude of the second-order harmonic wave) is obtained as a function of the duty ratio to show that it has a minimum of zero at a specific duty ratio; that is, the initial generation of the second-order harmonic wave can be fully suppressed at this duty ratio. This is comparable with the conventional Gaussian line beam model, in which the initial generation of the second-order harmonic wave is inevitable. Next, we carried out a two-dimensional thermo-elastic analysis using FEM in order to model a practical situation, where thermal conduction and a Gaussian temperature profile are factors. Naturally, the frequency response obtained from this numerical analysis does not perfectly match that of the one-dimensional analysis; however, we prove that the magnitude ratio A2/A1 has a minimum at a specific duty ratio. Additionally, the dependency of A2/A1 on the duty ratio obtained from the numerical analysis showed very good agreement with the experimental results.