“Optical tweezers” [1], introduced by Ashkin in 1986, are important tools that use tightly focused laser beams to exert or measure forces/torques on particles in three dimensions. Since then, numerous advancements in this technology have promoted optical tweezers as powerful tools in biology [2], physics [3,4], and other microscale research [5]. With the development of beam shaping techniques, a variety of structured beams have been studied, such as optical vortices [6], perfect optical vortices (POVs) [7], Bessel beams [8], and line patterns [9]. With these beams, versatile manipulations of micro/nano-objects can be achieved. Commonly, the most used objects for optical tweezers are high-refractive-index particles, whose refractive index is greater than that of the surrounding medium. Low-refractive-index (LRI) particles, such as vesicles [10], droplets [11], and bubbles [12,13], have not attained sufficient study yet. Additionally, LRI particles play significant roles in physics, biomedicine, and biotechnology. For instance, droplets and vesicles have been applied as self-contained and flexible microreactors in drug delivery [14,15] and have been used to fabricate biopolymer structures in artificial cell synthesis [16–18]. Various LRI subcellular organelles have been observed recently in cell functions [19] and structures [20]. Given the significance of LRI particles, the versatile manipulation of such particles will provide a better understanding of the particles’ interactions in cell biology, biomedicine, biopharmaceuticals, etc.

Unlike high-refractive-index particles, LRI particles tend to be repelled away from the bright spot [21], making stable trapping and controllable manipulation of LRI particles a big challenge. The straight strategy to confine LRI particles is to create a low-intensity dark region surrounded by a high-intensity barrier [21–24]. Yet, more precise, controllable, and versatile manipulation of LRI particles remains an ongoing challenge. POVs provide a viable solution for LRI particle manipulation because of their ring-like intensity profiles independent of topological charge [24–26]. However, in the particle manipulation, the rotation of LRI particles using POVs was limited by the fixed ring trajectory. Inspired by the recently demonstrated “double-ring POVs” with dark ring profiles [27] and generalized perfect optical vortices with arbitrary trajectories [28–30], dark traps with arbitrary profiles will facilitate versatile manipulations of LRI particles.

In this paper, we construct customized dark traps to manipulate LRI particles multifunctionally. The customized dark traps are created by assembling multiple structured beams generated with the free lens modulation (FLM) method [31]. Using this method, we produced various types of dark traps and achieved versatile manipulation of LRI particles, including velocity-controlled rotation along arbitrary trajectories, parallel dynamic manipulation, and sorting of LRI particles by size. The multifunction of the customized dark traps enables us to perform desired operations on LRI particles in biotechnology, such as selecting specific components for observation or subsequent targeted treatments in cell separation, facilitating fusion or assembly of LRI vesicles to perform cell-mimetic functions, and precisely controlling the specific interaction among different components in drug delivery. With the high flexibility and high light field quality, we envisage that the customized dark traps could significantly expand the application potential of LRI particles, facilitating their enhanced contributions to biology, medicine, physics, and other fields.

The idea of generating customized dark traps is based on the FLM method, which functions as an “optical pen” [31] to shape arbitrary beam patterns with controllable orbital angular momentum. The transmission function of the digital lens designed by the FLM method can be written as tl=P(r,φ)e−ik(r−ρ0(φ))2/2f(φ)eilφ,(1)where (r, φ) are the polar coordinates, P(r,φ) represents the aperture function, k=2π/λ refers to the illumination wave number, ρ0(φ) and f(φ) represent the shape and focal length of the designed digital lens, and l represents the topological charge. The diffracted light field at the focal plane of the digital lens, according to the Fresnel diffraction theorem, satisfies E(r,φ|c(φ))=Aeikziλzeiπρ2/λzF[e−ik(r−ρ0(φ))2/2f(φ)eiπr2/λzeilφ],(2)where F[⋅] represents the Fourier transform and c(φ)=(ρ0(φ),φ,f(φ)) is the 3D curve parameterized by the azimuthal angle φ. Our previous study [31] has demonstrated the FLM method’s capability to generate high-perfection and high-efficiency generalized POVs. Furthermore, we assembled multiple generalized POVs to generate multifunctional complex light fields. The assembled light field is written as E(r,φ|c(θ))=a1E(r,φ|c1(θ))+a2E(r,φ|c2(θ))+⋯+anE(r,φ|cn(θ)),(3)where a1,a2,…,andan represent the amplitude weights of different components, and E(r,φ|c1(θ)),E(r,φ|c2(θ)),…,andE(r,φ|cn(θ)) represent the freely modulated light fields. Figure 1(a) shows the schematic illustration of generating customized dark traps using the FLM method.

Our experimental setup is a homemade holographic optical tweezers (HOTs) setup, as shown in Fig. 1(b). The linearly polarized near-infrared laser beam (λ=1064nm, Connet Laser Technology, Shanghai, China) was expanded and collimated by a telescope system. A pure phase spatial light modulator (Pluto-NIR-II, HOLOEYE Photonics, Berlin) was used to modulate light fields. The resulting light field was reflected to a relay system consisting of lens 1 and a high NA oil-immersion objective (100×/NA=1.4, Oil, Nikon, Japan) by a specially designed triangle reflector. The end-to-end efficiency of the setup was 15%.

As a typical type of customized dark traps, the annular dark traps are generated by combining two concentric POVs. By doing so, a dark intensity gap exists between the two POVs, where the LRI particles can be confined. Meanwhile, the particles will be transported along the beam trajectory driven by the azimuthal force arising from the orbital angular momentum. The annular dark traps have tunable gap widths between the two rings, exhibiting greater flexibility than the previously reported ones [27]. We theoretically and experimentally investigated the annular dark traps by changing the gap width between the two rings and the amplitude weight [Figs. 1(c)–1(f)]. To be consistent with the experiments, for simulation we set the light wavelength to 1064 nm, the topological charge to l=10, the input Gaussian waist to w0=2.6mm, and the focal length of the digital lens to f0=200mm. The size of the simulated annular dark traps in the focal plane of the digital lens is 100 times that in the focal plane of the objective (100×). The gap width dgap of the two rings can be controlled by changing the radius ratio σ, defined as σ=(ρ2−ρ1)/ρ1=dgap/ρ1,(4)where ρ1 and ρ2 denote the radius of the inner and outer rings, respectively. Setting ρ1=1.7mm, we obtained simulated and experimentally measured dgap of 81.2 μm and 0.75 μm for σ=0.05, and 1.67 mm and 16.15 μm for σ=1, respectively [Fig. 1(c)]. As shown in Fig. 1(e), the experimental gap width changes linearly with the radius ratio. Notice that while changing the gap width, the intensity difference between the two rings gets pronounced. The difference will influence the uniformity of the light fields and the trapping performance. This problem can be overcome by changing the amplitude weight ratio ε of the two rings, i.e., ε=a2/a1.(5)We performed a comparative analysis by varying ε from 1 to 2 while setting σ=1 [Figs. 1(d) and 1(f)]. Results show that the maximal intensity of the outer ring changes from 28% to 315% of the maximal intensity of the inner one by setting ε from 1 to 2 without degrading the beam quality. Therefore, the gap width and intensity of the customized dark traps can be freely controlled, which provides remarkable flexibility and controllability in manipulating LRI particles.

We now demonstrate versatile manipulations of LRI particles, including quantitative rotation along arbitrary trajectories, multi-particle dynamic manipulation, and sorting by size utilizing diverse customized dark traps.

Liang et al. first utilized POVs to manipulate LRI particles by introducing “an extra point trap at the center of the vortex” [24] to improve the rotation performance. However, the trajectories are limited to the ring profiles. In contrast, the customized dark traps with a tunable gap width and ring size can drive particles along adjustable trajectories.

Setting the gap width to dgap=7μm for the particle with rp=5.3μm, we then experimentally explored the particle dynamics by only changing the topological charge (see Visualization 2). Figure 3(d) presents the rotation rate against the topological charge. The linear fitting shows that the rotation rate grows linearly with 22<l<42 [align with Fig. 2(d)]. The rotation speed decreases significantly for l<22. In this case, the azimuthal force arising from the phase gradient is so small that the disturbance of the surrounding medium and the friction would have a significant influence on the rotation. For large topological charges (i.e., l≥42), the rotation speed changes slightly because of the degradation of the generated light fields caused by the pixelated structure of the spatial light modulator for large topological charge [31].

The customized dark traps with arbitrary trajectories can be created by the elaborate design of the digital lens, providing more functions besides manipulating LRI particles along circular trajectories. For example, we designed polygonal trajectories for the dark traps, which satisfy the following expression: ρn(φ)=1−1pcos(qφ),(6)where p controls the smoothness of the polygon, and q controls the shape of the curve. Based on Eq. (6), we produced four types of dark traps: oval (p=5, q=2), triangular (p=10, q=3), square (p=15, q=4), and pentagonal (p=20, q=5). The free lens models, light field models, phase maps (l=10), and intensity patterns of the four types of dark traps are shown in Fig. 3(e). To obtain uniform intensities between the inner and outer rings, we set ε=1.05. The customized dark traps confined the LRI particles in the gap between the two profiles at the equilibrium positions and drove them along the shaped orbits with the force along the trajectory (see Visualization 3). Figure 3(f) shows the screenshots of the captured particles and time-lapse images of the manipulation results with l=28 and dgap=5.9μm. The average rotation rates of the particle in the oval, triangular, square, and pentagonal trajectories are 0.16 Hz, 0.18 Hz, 0.20 Hz, and 0.17 Hz (Table 3), respectively.Table 3.

Rotation Rate of LRI Particles in Customized Dark Traps

The outstanding flexibility and quality of customized dark traps provide more possibilities for manipulating LRI particles. By elaborately designing the patterns of dark traps, we achieved sorting of hollow glass spheres by size [33]. The dark traps for sorting are shown in Fig. 4(a), which consists of three components: a central POV (structured beam 1, s1: ρ=9.4μm, l=20) and two truncated off-center circular structural beams (structured beam 2, s2: ρ=37.6μm, l=20; structured beam 3, s3: ρ=44.7μm, l=−20). There are several tips for generating off-center and truncated beams. The off-center beams can be generated by changing the origin of the coordinates system [Fig. 4(a), s2], which has higher uniformity compared to the method of adding blazed grating phases. The truncated beams can be achieved by controlling the effective region of the phase map [Fig. 4(a), s3]. Note that azimuthal displacements exist along the orbital angular momentum direction. When precise alignment of different components is required, the effective region should be displaced in the opposite direction by approximately 0.54l deg (according to experimental results). With the repulsive effect of light, the narrow channel consisting of s1 and s2 only allows small particles to enter region z2 and prevents large particles from entering. To ensure large particles get across s2 and enter region z3, we set the amplitude weights a1, a2, and a3 of the three components [Eq. (3)] to 1.2, 1, and 0.9, respectively.

We designed a simple microfluidic chip for sorting LRI particles [Fig. 4(b), see Appendix B for details] based on a microscope slide with a flowrate≥20μms−1. The optical sorting of the hollow glass spheres by size with different gap widths is shown in Figs. 4(c)–4(e) (see Visualization 4). Initially, all the particles are confined at region z1(t1) due to the repulsive force. Setting the smallest gap width of the channel between s1 and s2dgap=8.9μm, the small-sized particles with rp=5.4 and 4.4 μm rotate along z2 (t2 and t3), while the larger-sized particle (rp=6.5μm) gets across s2 due to the more vital repulsive force of s1 and enters z3(t5andt6), as shown in Fig. 4(c). Changing the gap width, we can achieve the sorting of LRI particles by size with various size range. For example, setting dgap=6.6μm, the particle with radius of 3.2 and 3.9 μm rotates along the trajectory of s2 and enters z2, and particles with rp=5.8 and 6.7 μm enter z3 by the action of the microflow [Fig. 4(d)]. Then, setting dgap=4.2μm, we transported the particle with rp=2.2μm rotating into z2, and delivered the particles with rp=3.3μm to z3 [Fig. 4(e)], as shown in Table 4. To our knowledge, this is the first time that optofluidic technology has been applied to sort LRI particles. Since customized dark traps offer remarkable flexibility and modulation efficiency, we anticipate more complicated optical fields will be designed for precise sorting of LRI particles.Table 4.

Radii of Particles Entering Regions s2 and s3 at Different Gap Widths

In addition to particle rotation, dark traps can be used to trap and move LRI particles precisely. In this section, we generated a series of dark trap arrays including 4 and 9 dark traps, 9 intensity-modulated dark traps, 9 triangular dark traps, and hybrid dark traps for parallel trapping and manipulating of multiple LRI particles [Fig. 5(a)].

We take 1×2 dark traps as an example to demonstrate the adjustable intensity array to capture multiple LRI particles [Fig. 5(b)]. At the beginning, the left ring has higher intensity than the right one, and an LRI particle is trapped with the left one. Then, we gradually reduce the intensity of the left ring (L) while increasing that of the right one (R) and confine another LRI particle using the right one, with the first particle being stably held by the left ring throughout the process. With this method, we simultaneously capture four LRI particles with rp=3–3.5μm and move the four particles closer to each other by decreasing the distance of the trap array (see Visualization 5). Due to the boundaries of the light field, the hollow glass spheres would not directly contact each other as the distance decreased. Therefore, we switch the dark trap array to a single POV with ρ=11.48μm to let the four LRI particles aggregate [Fig. 5(c)]. Using dark trap arrays, we have successfully achieved the dynamic manipulation and assembly of LRI particles. We anticipate this method will open avenues for future investigations of vesicles and other LRI particles, providing a powerful tool in artificial cell networks.

In conclusion, the versatile manipulation of LRI particles is derived from customized dark traps, which are high-quality and high-efficiency assembled structured beams with adjustable topological charges, shapes, positions, and intensities. Using the light fields with complex dark regions surrounded by high-intensity barriers, the LRI particles can be confined/driven in arbitrary trajectories. In this paper, we reported the arbitrarily shaped rotation, multiparticle dynamic manipulation, and sorting by size of LRI particles.

The proposed manipulation platform using customized dark traps can be seen as a functional module. When synergistically coworking with diverse technologies, such as microfluidic techniques and vesicle fusion, the module offers a flexible and efficient approach to realizing more advanced functionalities. For example, the versatile manipulation (such as active selecting, transporting, mixing, and sorting) of the artificial cell components (such as droplets and vesicles) will promote the synthesis efficiency and flexibility in biofabrication technology [16]. Incorporating the customized dark traps into fabrication procedures avoids high cost and complex microfluidic chips [34]. Also, the customized dark traps will enable precise control of cell-sized giant vesicles, facilitating complex functionality such as assembling vesicle networks, vesicle fusion, and vesicle communication [35]. Furthermore, the customized dark traps are expected to be applied to drug delivery [36,37] and microscopy combined with super-resolution techniques [38]. We firmly believe that in the future, the reported customized dark traps will promote significant advancement in biotechnology, biomedicine, and other fields.

Acknowledgment. We acknowledge Prof. Shaohui Yan from Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, for his kind help and suggestions.