Ultrasonic wave propagation in focussing tips with arbitrary geometries

Pulsed laser acoustic experiments have the advantage of very high temporal resolution. However, the lateral resolution amounts to several wavelengths of light. To improve the lateral resolution a focussing tip in which the mechanical waves are focussed is introduced. The combination of high resolution in time and space domain leads to a new potential time resolved scanning probe method. Therefore several axi-symmetric structures are investigated numerically using a finite difference method. The ultrasonic wave propagation in different tips is discussed. By varying the geometry of the tip, the displacement at the sharp end is maximized. The numerically calculated results are verified experimentally on structures having macroscopic dimensions. Scaling effects are considered in order to translate the results into the microscopic scale where arbitrary geometries are much more challenging to implement.