Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams

TL;DR

This paper investigates the complex nonlinear focal shift phenomena in amplitude modulated acoustic beams, revealing how pressure, intensity, and force maxima shift dynamically in water and tissue, with implications for shear wave generation.

Contribution

It demonstrates the coexistence of linear and nonlinear effects in amplitude modulated beams and explains the dynamic behavior through harmonic generation and absorption in lossy nonlinear media.

Findings

Nonlinear focal shift causes maxima to shift along the axis dynamically.

Amplitude modulation introduces complex coexistence of linear and nonlinear effects.

Potential application in shear wave generation using focused transducers.

Abstract

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 behaviour, 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 with an amplitude modulated signal.