Optical manipulation techniques, particularly optical tweezers as introduced by Ashkin et al. [1,2], have found fertile ground in the fields of biological research [3–6], chemistry [7,8], and micro- and nanoscale materials assembly [9,10]. Conventional optical tweezers have been primarily concentrated on transparent dielectric particles (e.g., polymer microspheres [11] or biological cells [12]) by leveraging gradient forces induced by refractive index mismatches in the medium, however, with little consideration given to non-transparent particles. A concept distinct from transparent particles is that of absorbing particles, such as carbon particles and metal nanoparticles, which exhibit strong light absorption properties and thus possess unique applications [13]. For instance, the high temperatures generated by absorbing particles under laser irradiation can be utilized to destroy cancer cells [14], act as a catalyst for chemical reactions [15], or they can serve as crucial photothermal conversion materials in solar steam power generation [16]. Therefore, an effective photonic tool for manipulating absorbing particles can be extremely beneficial in the fields of biomedical engineering and materials science.

Different from transparent particles with inherent light-seeking behavior (conservation of momentum) [17], absorbing particles are subject to photophoretic and thermophoretic forces and tend to move away from regions of high light intensity [18–20], leading to challenges for particle manipulation. A typical approach to easing such problem is to design an optical bottle (OB) structure, formed by a low- or zero-intensity region surrounded by high-intensity regions in three-dimensional space [21–29], which can be used to wrap absorbing particles entirely.

Since the pioneering works of Grier’s team, dynamic holographic optical tweezers have revolutionized particle manipulation, with functional enrichment of holographic manipulation emerging as a developing trend in the field [30–33]. In liquid media, a variety of optical tweezers have been proposed for the manipulation of transparent particles, such as particle rotation [34], cleaning [35], and transport along predefined trajectories [36–38]. For absorbing particles, the Δα-type photophoretic force can transport the particles through power adjustment [39]. Recently, the difference-of-Gaussians traps described by Abacousnac et al. can flexibly transport absorbing particles along arbitrary paths [40]. As for gaseous environments, particles are sensitive to external perturbations, making manipulation more complicated. Holographic optical trapping has been used for light-seeking aerosols [41], and a method for the coalescence of these particles has been proposed [42]. However, challenges arise when attempting to flexibly manipulate absorbing particles. Specifically, due to their dark-seeking properties, manipulating absorbing particles typically requires constructing bottle-like beams. Thus, further dynamic manipulation over absorbing particles through OBs is of significance. Although some methods have been proposed to switch OB “on/off” via a polarization state or oblique circular aperture [43,44], and dynamically move OB by adjusting the objective lens position or holograms displayed on a spatial light modulator (SLM) [23,45,46], these approaches rely on mechanical control or collective manipulation of trapped particles subject to a single OB. When multiple OBs are used for simultaneous trapping, it remains challenging to selectively manipulate a specific one. Moreover, different from Ref. [42], simply bringing the two OBs close is not sufficient for merging two parts of absorbing particles, because there will always be a high-intensity optical barrier persisting between the two bottles. Therefore, flexibly employing targeted manipulation of individual OBs in multi-bottle configurations and merging two OBs into a single entity would significantly enrich dynamic manipulation capabilities and expand potential applications, such as precise manipulation of multi-particle systems and construction of micro-scale chemical reactors.

In this work, we propose a dynamic manipulation method for absorbing particles based on the SLM. By employing multiple acceleration trajectories phase and vortex phase modulation, we generate OBs with distinct characteristics, which are encoded as holograms. This dynamic holographic approach enables selective switching and moving of OBs, as well as merging of two OBs. These functionalities corresponding to the release, transport, and merging of absorbing particles have been experimentally demonstrated. We also illustrate that the distance and velocity of particle transport can be flexibly controlled. The experimental results are consistent with the expectations.

The experiment setup for generating versatile OBs is shown in Fig. 1(a) [47]. A solid-state laser emits a linearly polarized beam at 532 nm and with a power ranging from 1 mW to 6 W, continuously adjusted through a Glan-Taylor prism (GLP10 from LBTEK), and the size can be controlled by an eightfold beam expander (BE). The SLM (Santec SLM-200, 1920×1080 pixels) is a programmable device that allows reconfigurable Holograms I–IV to encode and modify the information of the designed pattern [30,48]. Subsequently, the 4f spatial filtering system consisting of lenses L1 (f1=300mm) and L2 (f2=150mm) is employed to eliminate the diffraction order fringes other than the +1st order. The generated designed beams can be passed through a beam reduction system composed of lenses L3 (f3=150mm) and L4 (f4=50mm) to match the size for particle manipulation in a cuvette (10mm×10mm×50mm), in which the mesocarbon microbeads (MCMBs) with diameters of about 20 μm are chosen as the sample of absorbing particles. As seen in the left inset of Fig. 1(a), when the particles are trapped in the bottle-like structure, the observation of them is achieved through scattered light. In the imaging system, not only do we capture the manipulated particles by a camera above the cuvette, but also the microscopic motion image of the trapped particles is collected by the microscope objective (10×, NA=0.25) and a lens (f5=50mm), and subsequently projected onto a CMOS camera (MindVision MV-XG170GM-T) for detection.

Absorbing particles are trapped in OB through momentum transfer with gas molecules on the hot side of the particles, which pushes them into the low-intensity bottle region. Particles can remain trapped as long as the structure of OB remains unchanged, which links particle dynamics to the configuration of OB. The schematic diagrams of versatile manipulation of MCMBs are shown in Figs. 1(b1) and 1(b2), demonstrating the two main manipulation capabilities we propose: selective switching and selective moving. As revealed in Fig. 1(b1), we generate a two-OB beam using Hologram I initially, trapping two clusters of absorbing particles at separate locations. By switching to Hologram II, which selectively switches off the second OB while maintaining the first one, a new single-OB configuration is constructed. The first OB retains its original stable trapping capability, whereas switching off the second OB causes the previously trapped particles in this region to escape the influence of the beam, thereby achieving selective switching functionality. To be specific, it is possible to selectively choose which OB to open and which to close within a two-OB configuration. This allows us to release a portion of particles as needed while retaining the other portion. Additionally, despite the availability of many methods for transporting absorbing particles [49–53], selective transport of multi-part particles remains challenging. To adapt to more application scenarios, we propose a scheme where one of the two OBs can be selectively moved while the other remains unchanged. As Fig. 1(b2) depicts, firstly, two portions of absorbing particles are trapped at distinct regions by a two-OB beam using Hologram III. By dynamically adjusting to the Hologram IV, the second OB is selectively moved forward while the first remains stationary. As a result, the movement of the second OB transports the trapped particles in this region along with it, leaving the other portion of particles undisturbed. This enables precise transportation of the targeted particle cluster to designated positions. Such selective manipulation overcomes the limitations of mechanical control or collective manipulation, meeting a broader range of application requirements.

To achieve versatile particle manipulation, we need to generate the corresponding highly flexible and controllable bottle-like beams. First, we generate OBs by applying vortex phase and multiple acceleration trajectories phase modulation on circular Airy-like beams in the cylindrical coordinate system. The acceleration trajectory is of the form c(z)=azn, whose shape is controlled by the coefficients a (scaling factor) and n (n can be chosen as an even number). Here, we set n=2, and get the form of parabolic trajectory. The corresponding phase ϕ(r) at the plane z=0 can be written as [54] ϕ(r)=−43a12kr32,(1)where k is the wave number, and r=x2+y2 acts as the radial distance. In a rotationally symmetric coordinate system, the propagation of the optical field in each transverse direction exhibits an accelerated trajectory, which results in the auto-focusing behavior of the beam. Thus, superimposing designed multiple acceleration trajectories with different shapes gives the beam multiple foci, and then can form multiple OBs under the influence of vortex phase. The initial electric field of OBs can be described as E(r,θ,0)=U0Olp(r)ψ(r)Vl(r),(2)where U0 is the normalized constant amplitude of the initial optical field, Olp(r) is the electric field of the p-th order circular Olver beams (COBs), which are typical circular Airy-like beams [55,56], and Vl(r) represents the optical vortex defined by Vl(r)=rexp[il·arctan(yx)], with l denoting the topological charge. Notably, when l=0, we can get multi-focus beams, and conversely, when l≥1, the vortex phase builds a hollow region inside the beam, allowing us to get optical bottle-like beams. Here, we set p=2 and l=1. The ψ(r) term represents the superposition of wavefronts corresponding to m parabolic trajectories [57], expressed as ψ(r)=∑j=1mAj(r)exp[iϕj(r)]qj(r), where Aj(r) is the amplitude of the j-th wavefront of parabolic trajectories to adjust the intensity distribution of trajectories. The truncation function qj(r) can be indicated as qj(r)={1,0≤r≤Rj,0,other, where Rj is the radius of the j-th aperture. The value of Rj controls the energy distribution of the beam, which affects the focusing position and intensity of the beam [58,59]. For the detailed derivations, please see Appendix A.

The above theory reveals that we can customize the bottle-like beams arbitrarily. In order to achieve the effect of dynamic particle manipulation, we designed a number of structured light fields with different propagation characteristics and imported them into the SLM in the form of holograms using a computer for dynamic control, detailed in Appendix B. The four functionalities of particle manipulation are shown in Fig. 2, represented by the side views of numerical simulations of beams, where each slice represents a step in dynamic manipulation.

The switching state “on/off” of the OB is achieved through on-axis destructive interference and constructive interference, respectively. As shown in Fig. 2(a), in the first step, we superimpose two parabolic trajectories with distinct shapes to generate front and rear focal points. The coherent superposition of the wavefronts from these trajectories forms on-axis destructive interference under a specific phase difference, resulting in a low-intensity region. Simultaneously, constructive interference occurs around the center of the beam, forming a high-intensity region that encloses the low-intensity region, i.e., the OB. To close the OB (second step), the position of one focal point is adjusted to alter the phase difference between the two wavefronts. This weakens the intensity of the original bottle body structure and induces on-axis constructive interference, replacing the low-intensity region inside the OB with a high-intensity region that bridges the front and rear focal points. Notably, the front focal point exhibits sharper focusing (smaller focal depth) and higher peak intensity compared to the rear focal point. Therefore, the intensity of the two foci can be balanced by adjusting the amplitudes Aj(r) of the two parabolic trajectory components. Furthermore, the rear focal points, characterized by a larger focal depth due to their longer focal lengths, typically form larger OBs.

Similarly, to generate two OBs, an additional focal point is superimposed, as illustrated in Fig. 2(b). When selectively closing only the second OB while keeping the first one unchanged, we only need to modify the position of the final focal point to induce on-axis constructive interference. To achieve the dynamic manipulation shown in Fig. 2(c), where the second OB is repositioned while the first remains stationary, we adjust the coefficient a of the parabolic trajectories responsible for forming the second OB. Maintaining the shape of OBs may require fine-tuning the number of superimposed trajectories. Additionally, closing an OB can be accomplished not only via on-axis constructive interference but also by simply eliminating the bottle, as demonstrated in Steps 4 and 5 of Fig. 2(c). This process reduces the number of foci by decreasing the number of superimposed parabolic trajectory phases to directly eliminate an OB. In addition, to merge the two OBs into a larger one [Fig. 2(d)], we employ a similar strategy by adjusting the coefficient a of the parabolic trajectory. This adjustment spatially separates the two focal points to a greater distance, thereby expanding the effective region of destructive interference and forming a larger OB. This capability to generate OBs of tunable sizes, numbers, and positions paves the way for multifunctional dynamic particle manipulation.

To experimentally demonstrate the predicted effects of the versatile OBs, we utilize the experimental setup illustrated in Fig. 1. First, we evaluate the trapping performance of the OB by measuring the vibration and stiffness of the trapped MCMBs. The images of the MCMBs are captured by recording the scattered light from the particles using a CMOS camera (see Visualization 1). We mark the center of the region of intense scattered bright spots with discrete points from each frame, which corresponds approximately to the center of the particle cluster. The points are colored by time. The overlaid image of the marked particle positions from 2000 frames of Visualization 1 is shown in Fig. 3(a), and the white bright spot is the microscopic image of the MCMBs recorded in one frame during its stable trapping period. Due to the elongated body of the OB, the axial displacement of the MCMBs is significantly larger than the lateral displacement. Furthermore, we measure the trapping stiffness of OB through power spectrum density (PSD) analysis (see Appendix C for details). Figures 3(b1) and 3(b2) show the axial and transverse trapping stiffness (κz and κy) of two different sized OBs (OB 1 and OB 2) at various trapped optical powers, where the length of OB 1 is 1.57 times that of OB 2, and the width is 1.30 times. Different from conventional optical tweezers in liquid, we find that the trapping stiffness of the OB does not have a clear correlation with optical power [60]. This is because the OB confines absorbing particles within a three-dimensional dark region, where the particles oscillate without being continuously illuminated by the laser. The results show that OB 1 has a higher axial trapping stiffness κz compared to OB 2, while transverse stiffness κy is not clearly different between the two. Notably, the stiffness κy exceeds κz by two orders of magnitude, which is caused by the elongated shape of the OB and the more intense force-induced vibrations along the axial direction. In addition, the topological charge significantly affects the trapping performance of OB. As the topological charge increases, the dark region along the central axis of the beam expands, leading to a degradation in the closure of the head and bottom of the OB. The MCMBs can be stably trapped when the topological charge l=1, while the particles escape along the axial direction when switching to l=2 (see Visualization 2). The OB structure now transforms into a particle-conveying channel, similar to the phenomenon described in Ref. [53]. Therefore, we set l=1 throughout our work to ensure that the particles are trapped.

Building on these observations, we next explore the dynamic control capabilities of the OB by experimentally demonstrating its “on/off” functionality. Specifically, we investigate the ability of the OB to trap and release particles, as illustrated in Figs. 3(c1) and 3(c2) and Figs. 3(d1) and 3(d2), corresponding to the beams of Figs. 2(a) and 2(b), respectively. Visualization 3 and Visualization 4 illustrate the microscopic and direct observations of the MCMBs when the OB is switched on and off. In Visualization 4, at the 3-s mark, the OB is switched to the off state, and the previously trapped MCMBs (visible as a bright spot) disappear [Figs. 3(c1) and 3(c2)]. Having demonstrated the fundamental “on/off” functionality of a single OB, we further explore the selective control capabilities of multiple OBs. As shown in Visualization 5, in the first step, two separate portions of MCMBs are trapped by two OBs during the first three seconds. At the third second, the system transitions to the second step, where the second OB is turned off, releasing the trapped particles, while the other portion of MCMBs remains continuously trapped [Figs. 3(d1) and 3(d2)].

In order to better utilize the dynamic manipulation capabilities of the SLM, we further explore the advanced manipulation of OBs. Specifically, we experimentally demonstrate the ability to move one OB while keeping the other stationary and then turning off the moving OB, corresponding to Fig. 2(c). Figure 4(a1) presents the photograph of the two portions of MCMBs stably trapped. In the subsequent manipulation, the rear portion of the MCMBs are continuously moved forward and ultimately released [Figs. 4(a2)–4(a5)]. Throughout the entire process, the other portion of the MCMBs remains stably trapped, with its position virtually unchanged (see Visualization 6). This manipulation allows for the selective transport of one portion of particles to a designated position and their subsequent release, while the other portion remains trapped. This advanced functionality significantly enhances the versatility of our system for precise particle manipulation.

To further investigate the performance of the moving OB system, we track the position of the MCMBs in each frame of Visualization 6, and the resulting trajectory curve and instantaneous velocity curve are shown in Figs. 4(b) and 4(c). Instantaneous velocity is calculated from the displacement between two adjacent frames (green dots). When particles are not stably trapped within the OB, they may exhibit gradual drift and disappear shortly thereafter, which affects our judgment of whether the particle movement is due to the movement of the OB. To rule out this possibility, we deliberately avoid continuous smooth displacement with small step sizes. Instead, we move the MCMBs over significantly larger distances in single steps, followed by a waiting period to confirm that the particles are still stably wrapped in the OB and have not disappeared into the air before proceeding with subsequent operations. Figure 4(b) shows that the displacement-time curve of the MCMBs presents a three-step shape, corresponding to three peaks in the fitted curve of the instantaneous velocity in Fig. 4(c), and the movement of the MCMBs in each step of the manipulation shows acceleration and then deceleration. By setting the final position of the particle movement as the displacement zero point, it can be seen that the MCMBs have moved a distance of about 7.2 mm in total, which can reach about two orders of magnitude of their own particle size. The moving distance between Steps 1 and 2 is longer than those between Steps 2 and 3 and between Steps 3 and 4, resulting in a higher instantaneous velocity of up to 10 mm/s. In contrast, the moving distances between Steps 2 and 3 and between Steps 3 and 4 are approximately equal, leading to similar instantaneous velocity curves. Therefore, we can achieve different moving speeds by setting different moving distances. Furthermore, to explore the minimum spacing between the two OBs, we reduced the beam size by changing the ratio of the beam reduction system (L1–L4), thereby making the two OBs more compact. We use an approximate 10-fold reduction (f1=300mm, f2=150mm, f3=150mm, f4=25.4mm) to perform Step 4 shown in Fig. 2(c), which represents the OB configuration and beam reduction system setting that achieved the minimum spacing in our experiments. The results demonstrate that the minimum spacing between the two OBs is 2.18 mm (see Visualization 7). In the video, the two MCMB clusters first approach each other to the minimum spacing and are then controllably separated, further demonstrating the flexibility of the dynamic manipulation. The selective manipulation can find applications in targeted material or drug delivery [61]. For instance, when localized treatment is required, our optical trapping method provides a physical model for targeted delivery and precision release of specific drugs at the desired site.

Given the dynamic manipulation capabilities of the SLM, we explore the possibility of merging two OBs into one. Generally, when the beam focus is positioned closer to the initial plane, the tighter focusing leads to rapid divergence, making it difficult to form OB structures that require multiple focusing. In order to merge the two parts of the MCMBs, the construction of a larger OB is needed. Therefore, we design the OBs merging process at a longer propagation distance (more loosely focused). As previously discussed, varying the beam reduction ratio directly affects the propagation length scale of the beam, which in turn adjusts the transport distance of the particles. As for merging particles, it is more desirable for the two parts to be closer together. Hence, utilizing a 10-fold beam reduction, we modulate the SLM in accordance with the steps depicted in Fig. 2(d) and successfully achieve the merging of two separate portions of the particle into a single entity (see Visualization 8). Figure 4(d1) shows the two initially trapped portions of MCMBs, separated by 3.5 mm, where the first OB traps two MCMB clusters, while the second one traps a single cluster. In the second step, the two OBs are merged into a larger one, and it can be observed that the two portions of MCMBs move towards each other and converge into a centralized area [Fig. 4(d2)]. Due to the larger size of the OB, the three clusters of MCMBs vibrate within a larger range. Then, in the third and fourth steps, the OB is moved forward, and it can be seen that the merged two portions of MCMBs are transported together, which also confirms the realization of merging the two OBs into one [Figs. 4(d2)–4(d4)]. The capability to merge two distinct particle clusters creates new opportunities for controlled material interactions. When each OB can serve as independent containers for specific chemical reactants or materials, their subsequent merging allows these substances to come into contact within a confined space, demonstrating potential applications in micro-scale chemical reactors and micro-material synthesis.

In summary, our works present an innovative approach to generating versatile OBs by applying vortex phase and multiple acceleration trajectories phase modulation. The core lies in dynamically manipulating the OBs by simply reconfiguring the pre-designed holograms in the SLM, thereby achieving four key functionalities: basic switching of a single OB, and selective switching, moving, and merging of two OBs. In our experiment, these functionalities enable selective release and transport of targeted MCMB clusters, as well as the merging of two separated MCMB groups into a single entity. The results highlight the stability of particle trapping and the effectiveness of dynamic manipulation, with particles exhibiting controlled transport and release under diverse manipulation scenarios. These findings challenge the conventional notion that absorbing particles can only be manipulated collectively, and provide new perspectives on the merging of absorbing particle clusters. The simplicity, flexibility, and selectivity of this approach offer significant advantages over existing techniques, with potential applications in drug delivery, micro-scale chemical reactors, and other techniques. Future work will focus on optimizing the system for higher precision and exploring practical applications for targeted delivery and multi-particle interactions.