Fig. 1. Principle of wave number–spiral acoustic tweezers.

(A) A schematic of wave number–spiral acoustic tweezers. The acoustic tweezers are composed of M pairs of IDTs, evenly distributed around the coordinate origin O. In each pair, two IDTs [denoted as ${\text{IDT}}_m^L$ and ${\text{IDT}}_m^R$ (m = 1, 2, ⋯, M)] are symmetrically arranged on different sides of the origin O. One multitone signal encoded with phases ${[{\mathrm{\phi }}_m^L]}_M$ and amplitudes ${[A_m^L]}_M$ at frequencies [f_m]_M is the excitation for M IDTs (denoted as ${[{\text{IDT}}_m^L]}_M$) on the left side; another signal with phases ${[{\mathrm{\phi }}_m^R]}_M$ and amplitudes ${[A_m^R]}_M$ at frequencies [f_m]_M is for M IDTs (denoted as ${[{\text{IDT}}_m^R]}_M$) on the right side. (B) The wave numbers k of SAWs generated by IDTs gradually change with respect to direction θ, tracing two central symmetric spirals in the wave number space. (C) The wave frequencies f also gradually change with respect to direction θ, as derived by $f(\mathrm{\theta })=\frac{k(\mathrm{\theta })}{2\mathrm{\pi }\cdot s(\mathrm{\theta })}$, where s(θ) is the slowness of SAWs.