Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams

Abstract

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

Dynamic nonlinear focal shift in amplitude modulated moderately focused acoustic beams

“…The agreement between experiments and simulations in the quasi-linear region (low and medium input voltages) is good, but they differ slightly at high power levels (nonlinear regime), being the maximum pressure nonlinear focal shift effect slightly higher in the simulation. A similar discrepancy was also detected in Camarena et al 11 and explained according to several reasons: first, the frequency response of the hydrophone is bounded to 20 MHz, which limits the number of harmonics detected by the hydrophone. Second, the sound field does not present a flat and uniform distribution over the active area of the receptor (200 µm active diameter), thus the measure is underestimated after the spatial averaging of the measurement region, which does not happen in the simulation.…”

“…They also provided an interpretation of the phenomenon based on the self-defocusing effect due to the asymmetrical distortion of the wave profile and to the increase in propagation velocity of the compressive phase of the wave close to the beam axis. Recently, Camarena et al 11 proved experimentally that at high amplitudes and for moderately focusing (G = 18.8) the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length.…”

Prediction of HIFU Propagation in a Dispersive Medium via Khokhlov–Zabolotskaya–Kuznetsov Model Combined with a Fractional Order Derivative

“…In previous studies, shifts between the predicted and observed focal regions have been frequently reported in HIFU-related studies. Usually, the shift was measured to be around 1-3 mm for 1-MHz HIFU transducers [24], 4-5 mm for~2.2-MHz excitation [51], and an empirical formula was also used to calculate the focus shift [22]. Although different possible mechanisms have been proposed and a series of correlation studies have been carried out [21][22][23][24][25][26][27], detailed theoretical proof that could quantitatively explain the inherent mechanisms of the observed focal shifts is still lacking.…”

Optimization of a label‐free biosensor vertically characterized based on a periodic lattice of high aspect ratio SU‐8 nano‐pillars with a simplified 2D theoretical model

“…the focal displaces towards the source. Both effects can be related to nonlinear self-refraction of the beam in the focal spot (Camarena et al, 2013a). However, due to the low focal size of this strongly focused device (Camarena et al, 2010) these effects are minor and the total displacements are not longer that λ/4.…”

“…(Camarena et al, 2013b). Thus, the heating pattern will be different using directly Q v = 2αI, or by estimating the energy deposition rate using the momentum transfer, i.e.…”