Nonlinear fields of focused acoustic-vortex beams

• Published in: Applied acoustics 2024-05, Vol.221, p.110022, Article 110022
• Main Authors: Guo, Ge-pu, Li, Xiao-fei, Chen, Zhen-hua, Meng, Ting-hui, Li, Yu-zhi, Ma, Qing-yu
• Format: Article
• Language: English
• Subjects: 3-D iterative solution; Focused acoustic-vortex; Harmonic pressure; Nonlinear KZK equation; Topological characteristics
• ISSN: 0003-682X; 1872-910X
• DOI: 10.1016/j.apacoust.2024.110022

•An improved 3-D solution of the nonlinear KZK equation is developed based on the Gauss-Seidel iterative algorithm and the fourth-order Runge-Kutta method.•Harmonic-FAVs can be generated in the focal region with the harmonic topological charge of the product of that of fundamental and the harmonic-order.•The vortex-radius of harmonic-FAVs is almost identical to that of the fundamental, being independent of the harmonic-order.•The nonlinear effects of FAVs can advance combined applications of the large-OAM-based drug particle manipulation and high-intensity focused-ultrasound therapy. Benefiting from the excellent performance of energy focusing and orbital angular momentum (OAM) transferring, the focused acoustic-vortex (FAV) exhibits promising application potentials in particle manipulations. However, the harmonic impact on the mechanical, thermal and cavitation effects cannot be ignored when the peak pressure exceeds MPa level. Few studies on the calculation, analysis and application of nonlinear FAVs have been reported so far. Here, by introducing helical phases to the focused sectorial transducer array, an improved 3-D solution of nonlinear acoustic fields is developed to calculate harmonic-FAVs using the Gauss-Seidel iterative algorithm and the fourth-order Runge-Kutta method. Source pressure dependences of harmonic pressure, vortex-radius and topological property of harmonic-FAVs are numerically and experimentally studied for FAVs with topological charges (TCs) of 0 and 1. Harmonic-FAVs with the harmonic-TC of the product of the fundamental-TC and harmonic-order can be generated along the beam axis with the center a little longer than that of the fundamental. As source pressure increases, the harmonic pressure gain of the higher-order harmonic-FAV increases accordingly with a decreasing fundamental one. The almost identical vortex-radius of harmonic-FAVs is independent of the harmonic-order, which can be applied to accomplish the large-OAM-based object manipulation in the same focal volume. The unique harmonic characteristics of nonlinear fields lay solid foundations for further studies on the mechanical and thermal effects, and may pave a new avenue of the particle manipulation assisted high-intensity focused-ultrasound therapy based on FAV tweezers in biomedical applications.