# Integrated Hybrid Tweezer for Particle Trapping with Combined Optical and Acoustic Forces
## 2 Principle and Model  
Figure 1a shows the proposed integrated hybrid tweezer, which is divided into two parts by the yellow dashed line. Part A is the acoustic waveguide with an overlying silicon cladding layer, while Part B is the trapping region where an acoustic wave propagates in the water. The IDT patterned on an x-cut thin-film lithium niobate (LN) layer generates an acoustic wave at 200 MHz, which propagates in the shear vertical (SV) mode. Half of the acoustic energy transmits along the +y direction firstly and then into the water after leaving Part A, providing an acoustic force to particles along +y direction. The optical wave propagating along the \(-\)y direction induces an optical force along the \(-\)y direction, which can balance the acoustic force. Note that the strong x-component of optical force formed by the evanescent field can make particles stably bound on the top surface of the optical waveguide. Particle trapping and position control can be achieved by adjusting the optical power and voltage. The optical waveguide features a serpentine shape, fully utilizing the aperture size of the IDT to trap multiple particles. Figure 1b shows the \(x\)-\(y\) plane view of the device. Due to its high piezoelectric coefficient, LN is widely used to efficiently generate acoustic waves. To enhance mechanical confinement in the LN layer and prevent acoustic waves from radiating out, we selected silicon nitride and silicon as cladding layers since their speeds of sound are higher than that of LN [36; 37; 38; 39]. Due to its high refractive index (n\(\sim\)3.4), silicon was also used as an optical waveguide core in Part B. The device was completely immersed in water using a millifluidic channel [40] with a 5-mm-thick water layer. Considering the absorption coefficient of water for ultrasonic waves, which was 25.6 \(\times\) 10\({}^{-17}\)\(s^{2}\)/cm [41], a 200-MHz acoustic wave would quickly attenuate when it propagates in the water and almost decay to zero when it transmits through a 5-mm-thick water layer. Therefore, reflections from the boundaries are negligible. We used perfectly matched layers (PML) as the boundary conditions in the model to mimic an open and non-reflecting infinite domain. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Type of Tweezer** & **Tweezer Composition** & **Captured Particle** & **Type of Force** & **Feature** & **Reference** \\ \hline Acoustic tweezer & The piezoelectric transducer & The zebrafish larvae and oil droplets & Acoustic force & Dynamic wavefields reshaping and dynamic and reconfigurable particle/cell manipulation & [21] \\ The flat holographic transducer & The flat holographic transducer & Polystyrene particles with a radius of \(75\pm 2\upmu\)m & Acoustic force & The digital actuation of small objects on the surface of water & [22] \\ The circular, slanted-finger piezoelectric transducer & 10.2 \(\upmu\)m velocity-green microspheres and K562 cells & Acoustic force & Selectively trapping and moving for one particle independently & [23] \\ \hline Hybrid tweezer & The holographic lens group (free-space) and piezoelectric transducer & Polystyrene and silica spheres & Optical and acoustic forces &
\begin{tabular}{c} Optical sorting and acoustic \\ trapping \\ controlled continuous rotation of specimens \\ experiments \\ reorientation, and the separation of particles with significantly different refractive indices \\ \end{tabular} & [32] \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._Initially, particles are released into water and move along the top surface of the optical waveguide by the optical force. After the acoustic wave was excited, the particle feels the optical and acoustic forces, gravity, buoyancy, and supporting force brought by the optical waveguide. We present all kinds of forces applied to the particle, as shown in Figure 1b.