Phase Relation of Harmonics in Nonlinear Focused Ultrasound**Supported by the National Natural Science Foundation of China under Grant Nos 41274134 and 81527901, and the ‘12th Five-Year Plan’ Period for Informatization Project in Supercomputing Key Demonstration of Chinese Academy of Sciences under Grant No XXH12503-02-02-2(07).

Abstract

The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimentally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately (n — 1)π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.