Nonlinear focal shift in medium Fresnel-number focused acoustic beams

The study of the acoustic field characteristics generated by focusing sources, both in linear and nonlinear regime, is an active field of research as they are relevant in most of the ultrasonic applications in medicine and industry. Particularly, the linear focal shift phenomenon (i.e. the distance between the geometrical focus of the focused source and the on axis maximum pressure position in linear regime, real focus) was explained in 1982 by Lucas and Muir. Also, the nonlinear focal shift phenomenon (the displacement of the pressure and intensity maxima position of focused acoustic beams under increasing driving voltages) has been related and interpreted in previous works. Nevertheless, till the moment it has not been published a specific experiment with the objective to study, experimentally and numerically, the focal region of medium Fresnel-number transducers, and the magnitude of the this shift. This is the purpose of this work. The nonlinear focal shift phenomenon is presented for the case of a medium Fresnel-number beam (N_F=6). The experimental results show the existence of a short nonlinear shift in the position of the on-axis maximum pressure (6 mm). These results are coherent with numerical KZK model predictions. It is shown that in the nonlinear regime and for this focusing degree the position of the on-axis maximum pressure can surpassing the geometrical focal length. Contrary, the on-axis minimum pressure approaches the transducer under increasing driving voltages, and at high excitation the distance between on-axis maximum and minimum pressure is closer to 1 cm.