Integrated Hybrid Tweezer for Particle Trapping with Combined Optical and Acoustic Forces

Featured Application

The proposed integrated hybrid tweezer can capture micron-sized particles and control their movements. It can be used as the fixed center for yeasts and other small biological objects in chip laboratories within the fields of biology and medicine, including applications in drinking water technology and drug delivery.

Abstract

We propose an on-chip integrated hybrid tweezer that can simultaneously apply optical and acoustic forces on particles to control their motions. Multiple potential wells can be formed to trap particles, and the acoustic force generated by an interdigital transducer can balance the optical force induced by an optical waveguide. For example, by driving the waveguide with an optical power of 100 mW and the interdigital transducer with a voltage of 1.466 V, the particle with a refractive index of 1.4 and a diameter of 5 μm (similar to yeast cells) can be stably trapped on the waveguide surface, and its trapping position is controllable by changing the optical power or voltage.

1. Introduction

Tweezers are tools that manipulate the positions and movements of very small objects. For particles with sizes in the micrometers and nanometers, there are many types of tweezers, such as optical tweezers (can be used in molecular sensing, precision molecular manipulation, and cell assembly [1,2]), acoustic tweezers (can be used in particle separation, material manufacture, cell transportation, sorting, and enrichment [3]), magnetic tweezers (can be used in parallel single-molecule fluorescence detection measurements and cell transport [4,5]), dielectrophoretic tweezers (can be used in medical diagnostics, material characterization, drug discovery, cell therapeutics, and particle filtration [6]), and plasmonic tweezers (can be used in biomanipulation, spectrographic sensing and imaging, and particle transport and sorting [7]), etc. Various methods based on optics [8,9,10,11,12,13,14,15,16,17,18,19], acoustics [20,21,22,23,24], magnetism [4,5,25], dielectrophoresis [6], and plasma [7,26] for the remote driving of particles, have been developed. In 1986, Ashkin proved that particles could be trapped by the gradient force generated by a light beam [27]. Optical tweezers are mainly divided into two categories, namely free-space optical tweezers [8,9,10] and near-field optical tweezers [11,12,13,14,15,16,17,18,19]. Free-space optical tweezers mainly include tweezers based on lens group [9], optical fiber tweezers [8], and optical tweezers based on metasurfaces [10]. In order to achieve complex optical manipulation, in 2017, Zhang et al. proposed optical fiber tweezers that can trap multiple particles [8]. In 2018, Bhebhe et al. implemented a vector beam holographic optical trap array based on holographic optical trap technology [9]. Due to the limited beam control ability of optical fibers, optical tweezers based on metasurfaces were proposed, and in 2020, Chantakit et al. achieved polarization-sensitive particle manipulation using metasurfaces [10]. Kawata and Sugiura were the first to realize the manipulation of polystyrene microspheres on optical waveguides [28]. Thereafter, many near-field optical tweezers have been reported [11,12,13,14,15,16,17,18,19]. Near-field optical tweezers mainly include optical tweezers based on waveguides and optical tweezers based on resonant cavities. In 2018, Ahmad et al. manipulated biological cells using optical waveguides [11], and Baudoin et al. proposed a V-groove waveguide as an appropriate platform for nanoparticle trapping and transporting [12]. In these works, particles are pushed by optical scattering forces and moved forward with traveling optical waves along waveguides. In some other cases [13,29], the positions of traps can also be effectively controlled by changing the wavelength or forming standing waves in waveguides. Resonant cavities can enhance optical fields. In 2020, Ho et al. achieved the stability enhancement of resonance for particle capture based on a self-locked scheme [14]. In 2022, Ye et al. achieved sufficient optical force for base-pair resolution measurements of multiple molecules by forming standing waves in microrings [15]. In 2022, Shi et al. utilized photonic crystal cavities to manipulate viruses with large trapping areas [16]. To ease the observation of particles in some studies, photonic crystal cavities [30,31] were used to establish a strong local light field to trap the particles at fixed positions.

The use of acoustic methods to capture particles has been extensively studied as well. Since Lord Rayleigh analyzed the acoustic force, controlling particle movement with an acoustic wave has been widely studied for objects with sizes ranging from nanometers to millimeters [3]. For acoustic tweezers, some studies on integrated acoustic tweezers used the acoustic radiation force [21] and streaming-induced drag force [22] to manipulate particles based on conventional interdigital transducers. Meanwhile, in 2019, Baudoin et al. designed acoustic tweezers based on flat holographic transducers to selectively trap and move one particle independently [23]. In 2020, Kang et al. designed acoustic tweezers based on circular, slanted-finger piezoelectric interdigital transducers to enable the dynamic and reconfigurable manipulation of micro-objects using multi-tone excitation signals [24]. Due to the high accuracy and selectivity of optical tweezers and the large-scale trapping ability of acoustic tweezers, it is meaningful to combine them to meet the requirement of accuracy and efficiency in the field of cell capture for biomedicine. Recently, some studies have tried to combine optical and acoustic tweezers for particle sorting [32] and trapping [33,34,35]. However, integrating both optical and acoustic tweezers on a chip remains unexplored. The state of the art of optical and acoustic tweezers are listed in

Table 1. The state of the art of optical and acoustic tweezers and the proposed tweezer.

Type of Tweezer	Tweezer Composition	Captured Particle	Type of Force	Feature	Reference
Free-space optical tweezer	The optical fiber	Yeast cells	Optical force	Multiple yeast cells 3D stable trapping	[8]
	The holographic lens group	2 μm diameter silica beads	Optical force	The 3D shape control of the optical forces	[9]
	The metasurface	Polystyrene particles with a diameter of 4.5 μm	Optical force	Polarization-sensitive 2D manipulation	[10]
Near-field optical tweezer	The strip and rib waveguides	Red blood cells	Optical force	Developing a methodology for quantitatively studying red blood cells	[11]
	The V-groove waveguide	Polystyrene nanoparticles	Optical force	The much higher capability to trap nanoparticles	[12]
	The one-dimensional (1D) photonic crystal waveguide	The polystyrene particle with a refractive index of 1.56 and a radius of 150 nm	Optical force	Efficient optical trapping and transportation in a peristaltic way	[13]
	The microring resonator	Polystyrene beads of sizes up to 3 µm	Optical force	The trapping capability maintaining based on the self-locked scheme	[14]
	The resonator and nanophotonic standing-wave array	380 nm polystyrene beads	Optical force	Significant force enhancement and base-pair resolution measurements of multiple molecules	[15]
	The photonic crystal cavity	Viruses with diameters ranging from 20 to 100 nm and RI of 1.4 (virus) and 1.58 (polystyrene nanoparticle)	Optical force	Single or massive virus transporting, positioning, patterning, sorting, and concentrating	[16]
Acoustic tweezer	The piezoelectric transducer	The 10 μm polystyrene bead	Acoustic force	Dynamic wavefields reshaping and dynamic and reconfigurable particle/cell manipulation	[21]
	The piezoelectric transducer	The zebrafish larvae and oil droplets	Acoustic force	The digital actuation of small objects on the surface of water	[22]
	The flat holographic transducer	Polystyrene particles with a radius of 75 ± 2 μm	Acoustic force	Selectively trapping and moving for one particle independently	[23]
	The circular, slanted-finger piezoelectric transducer	10.2 μm yellow-green polystyrene microspheres and K562 cells	Acoustic force	Dynamic and reconfigurable manipulations of microparticles and cells	[24]
Hybrid tweezer	The holographic lens group (free-space) and piezoelectric transducer	Polystyrene and silica spheres	Optical and acoustic forces	Optical sorting and acoustic trapping	[32]
	The holographic lens group (free-space) and piezoelectric transducer	Micro-organisms	Optical and acoustic forces	Controlled reorientation and controlled continuous rotation of specimens	[33]
	The rectangle waveguide (near-field integrated) and piezoelectric transducer	The particle with a refractive index of 1.4 and a diameter of 5 μm (similar to yeast cells)	Optical and acoustic forces	Particle capturing, controlled reorientation, and the separation of particles with significantly different refractive indices	This work

.

In this work, we propose an integrated hybrid tweezer that is capable of particle capturing, controlled reorientation, the separation of particles with significantly different refractive indices, and reducing the volume and cost to a certain extent. This integrated hybrid tweezer is capable of trapping particles of 5 µm in diameter. The acoustic and optical forces generated by an interdigital transducer (IDT) and the evanescent optical field can be balanced to trap the particle. Trapping the particles with different refractive indices (n = 1.4, 1.5, and 1.6) and controlling their positions can be achieved by adjusting the optical power in the waveguide or the voltage applied to the IDT.

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~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 × 10⁻¹⁷ s²/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.

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.

The optical force ${\mathit{F}}_{\mathit{o}}$ can be calculated by integrating the time-independent Maxwell stress tensor over the surface of particles [42]:

$${\mathit{F}}_{\mathit{o}}=\underset{S}{{\displaystyle \oint }}(\overleftrightarrow{⟨{\mathit{T}}_{\mathit{M}}⟩}•\mathit{n})dS,$$

(1)

$$\overleftrightarrow{⟨{\mathit{T}}_{\mathit{M}}⟩}=\mathit{D}{\mathit{E}}^{*}+\mathit{H}{\mathit{B}}^{*}-\frac{1}{2}\left(\mathit{D}·{\mathit{E}}^{*}+\mathit{H}·{\mathit{B}}^{*}\right)\mathit{I},$$

(2)

where $\overleftrightarrow{{\mathit{T}}_{\mathit{M}}}$ is the Maxwell stress tensor, $\mathit{n}$ is the normal vector, $S$ is the surface of the particle, $\mathit{E}$ is the electric field, $\mathit{D}$ is the electric displacement, $\mathit{H}$ is the magnetic field, and $\mathit{B}$ is the magnetic flux field, and $\mathit{I}$ is an isotropy tensor.

The total acoustic force ${\mathit{F}}_{\mathit{a}}$ exerted on particles can be divided into two parts. One is the acoustic radiation force, and the other is the Stokes drag force caused by the acoustic streaming.

Due to the relatively small viscosity of water, the viscous and thermal boundary layer thicknesses are smaller than 10% of the size of the particle, which is within the validity range of the ideal fluid assumption [43]. Therefore, the acoustic radiation force ${\mathit{F}}_{\mathit{a}\mathit{r}}$ can be calculated by integrating the Brillouin stress tensor on the surface of the particles [44]:

$${\mathit{F}}_{\mathit{a}\mathit{r}}=-\underset{S}{{\displaystyle \oint }}(\overleftrightarrow{{\mathit{T}}_{\mathit{B}}}•\mathit{n})dS,$$

(3)

$$T_{Bij}={\rho }_0{v}_{1i}{v}_{1j}+\frac{1}{2}\left[\frac{1}{{\rho }_0}{\left(\frac{p_1}{c_0}\right)}^2-{\rho }_0{v}_{1k}{v}_{1k}\right]{\delta }_{ij},$$

(4)

where $\overleftrightarrow{{\mathit{T}}_{\mathit{B}}}$ is the Brillouin stress tensor, ${\rho }_0$ is the density of water, $v_{1i}$ is the i-th direction component of the first-order velocity, $p_1$ is the first-order pressure, $c_0$ is the speed of sound in water, and ${\delta }_{ij}$ is the Kronecker delta.

The Stokes drag force ${\mathit{F}}_{\mathit{a}\mathit{s}}$ exerted on particles can be calculated by the time-averaged second-order velocity. In the case of a particle near the surface, the Stokes drag force can be expressed as [45,46]:

$${\mathit{F}}_{\mathit{a}\mathit{s}}=\frac{6\pi \mu R\cdot \left({\mathit{v}}_{\mathbf{2}}-{\mathit{v}}_{\mathit{p}}\right)}{\left[1-\frac{9}{16}\left(\frac{R}{h}\right)+\frac{1}{8}{\left(\frac{R}{h}\right)}^3-\frac{45}{256}{\left(\frac{R}{h}\right)}^4-\frac{1}{16}{\left(\frac{R}{h}\right)}^5\right]},$$

(5)

where $\mu$ is the viscosity of water, $R$ is the radius of particle, ${\mathit{v}}_{\mathbf{2}}$ is the second-order velocity of water, ${\mathit{v}}_{\mathit{p}}$ is the velocity of the particle, and $h$ is the distance between the center of the particle and the surface. From Equation (5), it can be seen that if the velocity of the particle is different from the time-averaged second-order velocity of water, the particle will be subjected to the Stokes drag force.

After calculating optical and acoustic forces, the trajectory of particles in water can be expressed through the motion equation of particles.

$$m\mathit{a}={\mathit{F}}_{\mathit{g}}+{\mathit{F}}_{\mathit{b}}+{\mathit{F}}_{\mathit{o}}+{\mathit{F}}_{\mathit{a}\mathit{r}}+{\mathit{F}}_{\mathit{a}\mathit{s}}+{\mathit{F}}_{\mathit{s}},$$

(6)

where $m$ is the mass of the particle, $\mathit{a}$ is the acceleration of the particle, ${\mathit{F}}_{\mathit{g}}$ is the gravity of the particle, ${\mathit{F}}_{\mathit{b}}$ is the buoyancy of the particle in water, and ${\mathit{F}}_{\mathit{s}}$ is the supporting force. In Equation (6), ${\mathit{F}}_{\mathit{g}}$, ${\mathit{F}}_{\mathit{b}}$, and ${\mathit{F}}_{\mathit{s}}$ are in x-direction. ${\mathit{F}}_{\mathit{o}}$, ${\mathit{F}}_{\mathit{a}\mathit{r}}$, and ${\mathit{F}}_{\mathit{a}\mathit{s}}$ have components in y-direction. To trap particles, the y-component of acoustic radiation force $F_{ary}$, Stokes drag force $F_{asy}$, and optical force $F_{oy}$ are required to be balanced. Meanwhile, the resultant force of ${\mathit{F}}_{\mathit{g}}$, ${\mathit{F}}_{\mathit{b}}$, the x-component of acoustic radiation force $F_{arx}$, Stokes drag force $F_{asx}$, and optical force $F_{ox}$, are required to be downward.

All mathematical symbols used in the equations and their notation are listed in

Table 2. All mathematical symbols used in equations and their notation.

Symbol	Notation
${\mathit{F}}_{\mathit{o}}$	The optical force
${\mathit{F}}_{\mathit{a}}$	The total acoustic force
${\mathit{F}}_{\mathit{a}\mathit{r}}$	The acoustic radiation force
${\mathit{F}}_{\mathit{a}\mathit{s}}$	The Stokes drag force
${\mathit{F}}_{\mathit{g}}$	The gravity of the particle
${\mathit{F}}_{\mathit{b}}$	The buoyancy of the particle
${\mathit{F}}_{\mathit{s}}$	The supporting force
$\overleftrightarrow{{\mathit{T}}_{\mathit{M}}}$	The Maxwell stress tensor
$\mathit{n}$	The normal vector
$S$	The surface of the particle
$\mathit{E}$	The electric field
$\mathit{D}$	The electric displacement
$\mathit{H}$	The magnetic field
$\mathit{B}$	The magnetic flux field
$\mathit{I}$	The isotropy tensor
$\overleftrightarrow{{\mathit{T}}_{\mathit{B}}}$	The Brillouin stress tensor
${\rho }_0$	The density of water
$v_{1i}$	The i-th direction component of the first-order velocity
$p_1$	The first-order pressure
$c_0$	The speed of sound in water
${\delta }_{ij}$	The Kronecker delta
$\mu$	The viscosity of water
$R$	The radius of particle
${\mathit{v}}_{\mathbf{2}}$	The second-order velocity of water
${\mathit{v}}_{\mathit{p}}$	The velocity of the particle
$h$	The distance between the center of the particle and the surface
$m$	The mass of the particle
$\mathit{a}$	The acceleration of the particle

.

3. Optical Force and Acoustic Force

3.1. Optical Force

Light propagates in the fundamental TM mode (TM₀₀) at 1.55 µm, and its evanescent field above the optical waveguide is stronger than that of the fundamental TE mode (TE₀₀), leading to a stronger optical force on the particle. Figure 2a shows the optical field distribution of TM₀₀ with a core size of 1 µm × 220 nm (width × height). Calculation of the light field uses the finite-difference time-domain (FDTD) method. The boundary condition was PML.

Figure 2b,c shows the optical force on a particle for different waveguide widths and heights. The refractive index and radius of the particle are selected to be 1.4 and 2.5 µm, respectively, which are typical for yeast cells [47]. As the size of the optical waveguide gradually decreases, the evanescent field becomes stronger outside the waveguide core, and the particle feels a stronger optical force. However, when the waveguide width was below 1 µm, e.g., around 0.9 µm, the optical force decreased due to the hybridization of the TM₀₀ and the TE₁₀, which resulted in a smaller proportion of the optical field energy above the top surface and a smaller optical force at the same power. Therefore, to guarantee a strong evanescent field and relatively low waveguide loss, the waveguide width and height are selected to be 1 µm and 220 nm, respectively.

Figure 2d,e shows the x- and y-components of optical force along the x-axis at z = 0 µm on the particles with different refractive indices (n = 1.4, 1.5, and 1.6), according to different kinds of cells ranging from 1.4 [47] to 1.54 [48]. Due to the strong x-component of the optical force, the particle was stably trapped on the top surface of the waveguide and pushed along it to the trapping region where the acoustic wave acts against the optical force.

Figure 2f shows the x- and y-components of optical force on a particle on the top surface of the optical waveguide at z = 0 µm, as the refractive index of the particle increases from 1.4 to 1.6, with the index contrast between the particle and water increased and thus a stronger optical force. For the particle with a radius of 2.5 µm and a refractive index from 1.4 to 1.6, the y-component of optical force ranges from 1.37 pN/W to 34.9 pN/W, and meanwhile, the x-component of optical force was large, ensuring the stable trapping of particles on the top surface of the optical waveguide.

3.2. Acoustic Force

To efficiently excite acoustic waves by an IDT, we first evaluate the electromechanical coupling coefficient, which is an indicator of the efficiency with which a piezoelectric material converts electrical energy to mechanical energy. The electromechanical coupling coefficient can be obtained by comparing the acoustic velocity in the presence and absence of a perfect conductor on the piezoelectric material surface [49]. The highest electromechanical coupling coefficient occurs when the propagation direction of an acoustic wave rotates 64° from the y-axis. The thickness of LN was 20 µm, which was optimized and is explained later.

Calculation of the acoustic field uses finite element method (FEM). The boundary condition of the solid and acoustic field was PML to absorb acoustic waves. For the acoustic radiation force, the continuum equation of motion and strain-mechanical displacement relations are used to calculate the vibration displacement of the solid [50]. Simultaneously, based on the structure-acoustic interactive simulation [51], the continuity equation, the Navier–Stokes equation, and the energy equation were used to calculate the first-order pressures and first-order velocity of the acoustic field. For the Stokes drag force, the boundary condition of the solid–liquid interface was the no-slip boundary condition. Due to the equality of inflow rate and outflow rate, the total flow rate was set to 0. The second-order continuity equation and the Navier–Stokes equation were used to calculate the time-averaged second-order velocity of water. The time-averaged second-order velocity was obtained based on the first-order velocity by adding the weak contributions to the computational domain and boundaries [45]. Due to the relatively large aperture of the IDT, the acoustic wave was invariant in the z-direction. Therefore, two-dimensional simulations were performed.

The displacement field is shown in Figure 3a. The enlarged view of the acoustic field is shown in Figure 3b. The red dotted box in Figure 3a highlights the position of the IDT where the acoustic wave was excited. Acoustic wave energy was well confined in the LN layer before leaving Part A. Due to the lack of silicon (the upper cladding layer) in Part B, a part of the acoustic wave propagates into water, as indicated by the black dashed box.

When the acoustic wave radiates into the water, its wavefront has a slant angle with respect to the waveguide surface. The acoustic waves propagating from the top surface of silicon nitride and the front facet of silicon at the position of y = −d (see Figure 1b) interfere with each other, causing the pressure field disturbance on the top of the silicon optical waveguide. The optical waveguide appears at a distance of 20 µm from the facet of the upper cladding silicon. Since the waveguide height (220 nm) is much smaller than the acoustic wavelength (~7.5 µm), the optical waveguide has negligible effect on the pressure field.

The black dotted box specifies the region where particles are trapped, where the amplitude and direction of the time-averaged second-order velocity were calculated, as shown in Figure 3c. The size and direction of the black arrows are used to indicate the amplitude and direction of the time-averaged second-order velocity.

Optimizing the thickness of each material layer in the device helps achieve the best performance. First, to create an effective acoustic waveguide, the upper silicon cladding was set to be thick enough to confine acoustic waves, e.g., 15 µm, after taking into account the challenges of depositing a thick film.

Second, to determine the thickness of the silicon nitride layer, which acts as both a cladding of the LN acoustic waveguide and controlling of acoustic radiation, we calculated the first-order pressure and the time-averaged second-order velocity to represent the acoustic radiation force and Stokes drag force based on Equations (3) and (5). By fixing the thickness of LN at 20 µm and varying the thickness of silicon nitride, we obtained the amplitude of first-order pressures and the y-component of time-averaged second-order velocities along the y-axis at x = 2.5 µm, as shown in Figure 4a,b. Since the upper silicon cladding ends near Part B, the acoustic wave in the LN waveguide was perturbed and radiated into the water from the top surface of the silicon nitride. As the silicon nitride became thicker, the pressure exhibited a weaker fluctuation, and its maximum amplitude decreased. The local oscillations of the first-order pressure stemmed from the interference between the acoustic waves radiating from the top surface in Part B and the facet at the position of y = −d, as shown in Figure 4a. For thicker silicon nitride, the variation in the y-component of time-averaged second-order velocity is smaller, leading to a more uniform Stokes drag force. The amplitudes of first-order pressure and the y-component of time-averaged second-order velocity become smaller, as shown in Figure 4a,b. Even though the total acoustic force was relatively weaker, it can still be balanced with the optical force by adjusting the optical power or voltage because the total acoustic force on the particle was generally stronger than the optical force. Therefore, a thicker silicon nitride layer is more desirable in terms of acoustic performance. Considering the difficulty of depositing thick silicon nitride, the designed thickness of silicon nitride was 15 µm.

Third, with the 15-µm-thick silicon nitride, the amplitudes of first-order pressure and the y-component of time-averaged second-order velocity become smaller for thicker LN, as shown in Figure 4c,d because more acoustic energy is confined in LN. A thickness of 20 µm is chosen for the relatively uniform distribution of the y-component of time-averaged second-order velocity along the y-axis and the higher first-order pressure.

The acoustic force on the particle is calculated by assuming a particle density of 1110 kg/m³ and a speed of sound of 1600 m/s, with reference to yeast cells [52]. Due to the similar material properties of cells and water, releasing the cells in water has negligible influence on the acoustic field distribution. Figure 4e,f show the acoustic radiation force, the Stokes drag force, and the total acoustic force on the particle along the y-axis with a voltage of 1 V applied to the IDT. Because of the oscillation of the acoustic field above the optical waveguide, the particle feels a periodically changing acoustic radiation force. The Stokes drag force is associated with the time-averaged second-order velocity. The total acoustic force can be obtained by summing the acoustic radiation force and the Stokes drag force.

The thickness of the aluminum electrode and the upper silicon cladding were fixed at 200 nm and 15 µm. After optimization, the thicknesses of the silicon waveguide, silicon nitride, and lithium niobate layers were 220 nm, 15 µm, and 20 µm, respectively, to achieve optimum performance. The thickness of the silicon substrate exceeded one hundred micrometers and had negligible effects on the optimized results. The optimized structural parameters are presented in

Table 3. Optimized structural parameters (µm).

HSi	HSiN	HLN	λ	LAl	pAl	D	d	wSi	hSi
15	15	20	20.5	5.125	20.5	272.9	20	1	0.22

.

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 µm 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.

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 µm 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 µm, we consider the initial position of the particle from y = 85 µm to y = 115 µm. Corresponding to the distinct potential wells, the trapping ranges were y = (85, 91), (92, 104), and (105, 115) µm. Particles located at y < 115.5 µm 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 µm to 96.3 µm. 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 µm to 100.3 µm. If the optical power or voltage changes, the particle will be captured again, with good control of trapping positions. Therefore, the integrated tweezer proposed in this work can achieve particle trapping in multiple potential wells and trapping position control by simply adjusting the optical power or voltage.

5. Discussion

This device is a hybrid integrated optical tweezer with several valuable characteristics, and it possesses a few unique advantages compared to conventional integrated optical tweezers. First, for the optical wave, one can design facet tapers at the input and output ports of optical waveguides to reduce reflection and avoid standing waves [53]. For the acoustic wave, the device was completely immersed in water using a millifluidic channel with a 5-mm-thick water layer. Considering the absorption coefficient of water for ultrasonic waves, which is 25.6 × 10⁻¹⁷ s²/cm [41], a 200-MHz acoustic wave would quickly attenuate when it propagated in the water. Since the acoustic wave was well confined in LN, and the thickness of the silicon substrate exceeded one hundred micrometers, the acoustic wave was very weak on the boundaries of the silicon substrate. Therefore, no standing waves were formed. Due to no formation of standing waves or field enhancement during capturing particles, the light intensity felt by particles was relatively weak, which can mitigate the impact of phototoxicity on cells. Second, it could capture micron-sized particles, such as cells, and control their movements. Continuous particle movement could be achieved by adjusting the optical power or voltage. Third, it could capture particles with different refractive indices, enabling the separation of particles with significantly different refractive indices by simply applying different voltages required for trapping these particles.

Compared with conventional free-space optical tweezers, this device has the potential to reduce the size and cost of the optical system. It also enables the parallel trapping and transporting of multiple particles on a chip without using lenses [54].

For possible applications, the proposed tweezer can be used as the fixed center for yeasts and other small biological objects in chip laboratories within the fields of biology and medicine, including applications in drinking water technology and drug delivery [3,31]. At the same time, the device can separate particles with significantly different refractive indices, which can be used for particle sorting. Additionally, it enables the construction of complete analysis systems by integrating various functional modules on the chip [55].

To avoid adhesion during the strong contact between cells and the surface of the device, it can be achieved by washing cells in isotonic sucrose solution [11] or washing the surface of the device in some specific solutions [56].

Our design is based on mature fabrication processes. First, thin-film lithium niobate with a thickness of 20 µm is commercially available from NANOLN [57], the leading vendor of providing thin-film lithium niobate with a thickness ranging from hundreds of nanometers to tens of microns. Second, IDT made of aluminum can be patterned by magnetron sputtering followed by lift-off [58]. Third, silicon nitride can be deposited by ICPCVD (Oxford PlasmaPro 100), and the upper cladding silicon can be deposited by APCVD [59,60,61,62]. Finally, the silicon waveguide (Part B of the hybrid tweezer in Figure 1) is patterned by dry etching [63]. The millifluidic channel can be fabricated by soft lithography based on Polydimethylsiloxane [40].

6. Conclusions

Here, we propose an integrated hybrid tweezer combining optical and acoustic trapping methods to achieve particle trapping. By optimizing the size of the optical waveguide, the y-component of optical force on the particle with different refractive indices (n = 1.4, 1.5, and 1.6) on the top surface of the optical waveguide ranges from 1.37 pN/W to 34.9 pN/W.

By adjusting the voltage between 1.466 V and 7.389 V, trapping the particle with a refractive index ranging from 1.4 to 1.6 can be accomplished. Considering the case of a voltage of 1.466 V and an optical power of 100 mW, particles are stably trapped on the top surface of the optical waveguide. The y-component of the acoustic force exerted on the particle effectively balances the y-component of optical force generated by the optical waveguide, realizing multiple potential wells. By adjusting the optical power or voltage, trapping positions can be controlled.