# Integrated Hybrid Tweezer for Particle Trapping with Combined Optical and Acoustic Forces
## 4 Dynamic Process of Trapping Particles  
The strong x-component of optical force made the resultant force (consisting of the x-component of strong optical force, periodically changing acoustic force, gravity, and buoyancy) consistently downward so that particles could be attracted to the top of the optical waveguide. In the y-direction, the particle could be trapped by balancing the y-component of optical and acoustic forces, which was achieved by adjusting the voltage and optical power. To trap particles at y = 98 \(\upmu\)m with an optical power of 100 mW, the required voltages are presented in Figure 5a for the particles with different refractive indices. As the refractive index of the particle ranged from 1.4 to 1.6, the required voltage changed from 1.466 V to 7.389 V, which was due to a substantial change in the optical force. Figure 4: (**a**) The amplitude of first-order pressures and (**b**) the y-component of time-averaged second-order velocities along the \(y\)-axis at x = 2.5 \(\upmu\)m with different thicknesses of silicon nitride. (**c**) The amplitude of first-order pressures and (**d**) the y-component of time-averaged second-order velocities distribution along the \(y\)-axis at x = 2.5 \(\upmu\)m with different thicknesses of LN. (**e**) The x- and (**f**) y-component of acoustic radiation force, Stokes drag force, and total acoustic force for the particle along the \(y\)-axis on the top surface of the optical waveguide. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{H_{Si}}\) & \(\mathbf{H_{SiN}}\) & \(\mathbf{H_{LN}}\) & \(\mathbf{\lambda}\) & \(\mathbf{L_{Al}}\) & \(\mathbf{P_{Al}}\) & \(\mathbf{D}\) & \(\mathbf{d}\) & \(\mathbf{w_{Si}}\) & \(\mathbf{h_{Si}}\) \\ \hline
15 & 15 & 20 & 20.5 & 5.125 & 20.5 & 272.9 & 20 & 1 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized structural parameters (\(\upmu\)m). The optical force along the waveguide is considered uniform. The y-component of optical and acoustic forces are shown in Figure 5b. This indicates that, to trap the particles with different refractive indices (\(n\) = 1.4, 1.5, and 1.6) at y = 98 \(\upmu\)m with an optical power of 100 mW, voltages of 1.466 V, 4.053 V, and 7.389 V are required for the IDT. Under the same optical power, different refractive indices of particles were subjected to different optical forces. High refractive-index contrast between particles and water results in a strong optical force, and a strong acoustic force is required to balance the optical force to trap particles. Therefore, the device could trap particles with different refractive indices by varying the voltage. Meanwhile, the particle could be trapped in multiple potential wells due to the presence of multiple positions where the y-component of optical force and acoustic force are balanced. In the case of the particle with a refractive index of 1.4, a voltage of 1.466 V and an optical power of 100 mW are utilized. Figure 5c shows the trajectories of particles at various initial positions over time. The initial velocity of the particle was the steady velocity driven by the optical force. Given that the positions where the particle was trapped are y = 88.1, 98.0, and 109.5 \(\upmu\)m, we consider the initial position of the particle from y = 85 \(\upmu\)m to y = 115 \(\upmu\)m. Corresponding to the distinct potential wells, the trapping ranges were y = (85, 91), (92, 104), and (105, 115) \(\upmu\)m. Particles located at y \(<\) 115.5 \(\upmu\)m could be pushed toward the trapping position due to the net force. Figure 5d shows the trajectories of the particles as the optical power or voltage varies. By increasing the optical power from 50 mW to 140 mW with a step of 15 mW, the particle position shifts from y = 99.9 \(\upmu\)m to 96.3 \(\upmu\)m. Similarly, by increasing the voltage from 1.25 V to 2.15 V with a step of 0.15 V, the particle position shifts from y = 96.5 \(\upmu\)m to 100.3 \(\upmu\)m. If the optical power or voltage changes, the particle will be captured again, with good control of trapping positions.