Fourier Acoustical Tweezers: Synthesizing Arbitrary Radiation Force Using Nonmonochromatic Waves on Discrete-Frequency Basis

Existing acoustical tweezers (ATs) modulate source geometries to achieve monochromatic focusing, the wide frequency space allowed by sources is neglected. Here an analogous approach is proposed to synthesize AT fields in temporal frequency instead of wave vector. The base element is a standing wave, its counterpart in beam ATs is the field of a pitch. After field periodization, radiation-force theory is extended to nonmonochromatic waves having arbitrary in-period force based on discrete-frequency Fourier analysis. Fourier acoustical tweezers (FATs) achieve a minimal spacing of $\lambda /4$ for independent trapping. System complexity is reduced to two sources per dimension.

Figure 1

Working mechanism of 1D FATs. FFT of a target ARF profile gives the amplitudes and phases of monochromatic components, which within a limited band help to synthesize the driving voltage for two opposing sources. An ARF pattern as required is generated in the tweezing area. The prototype is a SAW-driven microfluidic channel.

Figure 2

Synthesized single trap in 1D tweezing. (a) Comparison between the measured ARF, represented by the velocity of $5-\mu \mathrm{m}$-radius particles, and the expected ARF as functions of $x$. (b) Snapshots of particle trapping. Scale bars, $100\mu \mathrm{m}$.

Figure 3

Arbitrary 1D trapping. Particles of $a=2.5\mu \mathrm{m}$ are captured by a single trap at $x=$ (a) $300\mu \mathrm{m}$, and (b) $-500\mu \mathrm{m}$, and by (c) two traps at $x=0$ and $600\mu \mathrm{m}$, and (e) three traps at $x=-500$, $0$, and $700\mu \mathrm{m}$. Each image is followed by a vertically averaged grayscale. Scale bars, $100\mu \mathrm{m}$.

Figure 4

1D (experiment) and 2D (simulation) tweezing. (a) In 1D experiments, three particle lines are initially trapped at $x=-180,0$, and $180\mu \mathrm{m}$, the middle one is then moved to $x=50\mu \mathrm{m}$. Scale bars, $100\mu \mathrm{m}$. In 2D simulations, (b) a single 2D trap is generated at $\left(x,y\right)=\left(500,500\right)\mu \mathrm{m}$, and (c) three traps at ($-500$, $-700$), (0, 0) and $\left(300,500\right)\mu \mathrm{m}$: black, 0; white, 1. Scale bars, $500\mu \mathrm{m}$. (d) Three particles are independently manipulated to follow trajectories “$N$,” “$J$,” and “$U$.” Scale bar, $100\mu \mathrm{m}$.

Figure 5

Spacing limit for two traps. (a) Two traps merge as their separated distance is $d<\lambda /2$. (b) 1D potential profiles as functions of $d$: black, 0; white, 1. (c) Three profiles extracted from (b), corresponding to $d=62$, 64, and $66\mu \mathrm{m}$. (d) 1D trapping, where only $d=66\mu \mathrm{m}$ (approximately $\lambda /4$) allows two independent particle lines to be trapped. Scale bars, $100\mu \mathrm{m}$.