The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.
Acknowledgements
FC acknowledge financial support from the AICO/2016-108 program of the Generalitat Valenciana. NJ acknowledge financial support from the FPI Grant PAID-2011 from the Universitat Politècnica de València. NGS acknowledge financial support from DPI2013-42236-R Project of the Spanish Ministry of Economy and Competitiveness, S2013/MIT-3024 of the Community of Madrid and from FPU Grant 12/02187 from the Spanish Ministry of Education, Culture and Sport.
