Introduction

Solitons, or solitary waves, are ubiquitous in nature. They are self-sustained, localized wave entities that can propagate in nonlinear media while maintaining their shape and velocity constant after pairwise collisions1. The full significance of the solitary wave, termed “soliton” by Zabusky and Kruskal in 1965, was established through numerical analysis of the Korteweg-de Vries (KdV) equation2. These soliton phenomena have been extensively studied across various branches of physics, including nonlinear photonics3,4, magnetic materials5,6, Bose–Einstein condensates7, and cosmology8. However, creating stable solitons with high-dimensional geometries in experiments is rare in comparison to the majority of theoretical research, primarily due to the susceptibility of even fundamental structures to strong instabilities and nonsingular perturbations within uniform media9,10. Among diverse media, liquid crystals (LCs) have served as an ideal arena for investigating solitons, thanks to the ease of controlling and the directness of observing LC structure in virtue of the anisotropic feature of the LC phase, which is originated from the long-range ordered molecular director n0, where n0 is a headless unit vector representing the average orientation of the local LC molecules.

Various solitonic structures have been observed in LCs, including both topologically protected static solitons11,12,13,14 and non-topologically protected dynamic solitons15,16. Notably, electrically driven three-dimensional (3D) dynamic solitons, known as “directrons”, which represent local director oscillations with the frequency of the applied electric field, have recently gained considerable attention17,18,19,20,21,22,23,24,25,26. From a fundamental perspective, directrons can serve as promising alternatives to conventional macroscopic systems, such as animal herds, for understanding the underlying universal principles of collective motions24. Beyond their fundamental significance, directrons are prototypical miniaturized micromachines capable of performing tasks such as micro-cargo transport and data processing schemes from an applied perspective18,20,27. The capability of steering directrons to facilitate desired motion is crucial for the abovementioned application. To fully harness the potential of directron micromanipulation, many efforts have been invested, including electric field-assisted steering19, photoalignment layers22,26, and surface chemistry23,25. These strategies have proven to be highly effective in the overall maneuvering of directrons. However, the reliance on a global electric field for generating and manipulating existing studies hampers the development of a parallel platform capable of multitasking, thus limiting the practical application of directrons in more complex scenarios. Strategic confinement acts as a means of localization effectively limiting range of object motions have been proven in many branches of physics28,29,30, especially for soliton research31. Intuitively, constructing the microstructure of a patterned electrode can provide a confined ___domain to guide and control the directrons. However, the static geometry of lithography-based patterned electrodes inevitably constrains the real-time and continuous tunability in directron dynamics. This typical limitation highlights the need for versatile applications where a reconfigurable confined ___domain, combined with structural flexibility and enhanced functionality, is highly demanded.

Light emerges as a powerful tool for real-time and programmable motion control, offering unparalleled temporal and spatial resolution at the microscale and nanoscale32. Various mechanisms for light-controlled micromanipulation have been explored, including optical gradient forces33, photochemical reactions34, optothermal forces35,36, and optoelectronic manipulation37,38. Among these, the optoelectronic manipulation is a state-of-art technique that synergistically combines light stimuli with electric fields by exploiting the photoconductive effect of semiconductor materials. This method allows for direct control over the behavior of micro-objects by optically inducing changes in electric fields. In addition, the flexibility of light-actuated electric fields is achieved through the modulation of light intensity and the customization of projected patterns. In the past decades, optically addressed liquid crystal light valves (LCLVs) based on the photoconductive effect have garnered significant attention due to their potential applications as elementary pixels for information storage39. These applications contribute to the development of parallel processing systems capable of simultaneously responding to multiple spatially distributed continuous inputs. In LCLVs, control functions are directly mediated by light during the writing process. Consequently, several optical functions of LCLVs with high parallelism have been demonstrated, including nonlinear wave mixing40 and digital holography41,42. Drawing from recent progress, we propose that the photoconductive effect can also facilitate the reconfiguration of directron dynamics in nematic liquid crystals. By adjusting patterns in real-time, the photoconductive effect not only supports traditional optical functions but also enhances the capability of LCLVs to dynamically manipulate directrons, thereby expanding their potential applications in advanced optical systems.

In this work, we present an optoelectronic approach that facilitates on-demand micromanipulation of directrons, enabling reconfigurable dynamics throughout their full lifecycle (i.e., generation, propagation, annihilation) within the light-actuated domains formed by various virtual patterned electrodes, as opposed to conventional global electric field control. This method allows for precise control over the direction velocity, direction, and trajectory, which can be further expanded for extensive and parallel manipulation. Furthermore, we demonstrate that dynamic light patterns can enable migrating directron flocks to an arbitrary spatial ___domain. We believe that this optoelectronic steering strategy offers extra flexibility, making it particularly well-suited for the manipulation of individual and multiple directrons in potential applications.

Results

Concept and theory

As depicted in Fig. 1a, our technique is grounded in a straightforward physical principle: the photoconductive substrate is typically insulating; however, upon exposure to a light pattern, it becomes conductive in real-time. A light-activated virtual electrode forms in the illuminated region due to an increase in electrical conductivity, which in turn induces an electric field in the LC layer. This electric field can elicit a distinctive structural response in the nematic LCs, manifesting as dynamic directrons. By adopting a multi-strategy digital projection approach, the characteristics of the non-uniform electric field, such as its amplitude and patterning, can be modulated. This concept can be harnessed for directron micromanipulation by utilizing light-activated virtual electrodes to generate controllable and dynamically steerable directrons with precise programming (as shown in Fig. 1b).

Fig. 1: Essential concept and reconfigurable behaviors.
figure 1

a Schematic of the photoconductive cell for directron manipulation via multi-strategy digital light projection. b The schematic illustrates the manipulation of directrons through predesigned light patterns to exhibit various dynamic behaviors. Beginning from the top and proceeding clockwise along the periphery: dynamic directrons emerge from predetermined sites (in-situ generation). Their speed is then varied (velocity modulation), and their direction of propagation is altered (direction control). At the bottom, the directrons navigate along a predefined path (trajectory tracking). The final two images depict directrons converging as the projected pattern contracts and diverging as it expands.

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The design of the photoconductive cell and optical setup is shown in Supplementary Fig. 1. The cell is similar to that reported previously43, with a thin LC layer sandwiched between a glass plate and a photoconductor plate, both equipped with transparent electrodes. These electrodes are composed of an indium tin oxide (ITO) layer strategically positioned on the inner surface of glass plate to act as the upper substrate. On the opposite side, forming the lower substrate, is a <100> orientation cut bismuth silicon oxide (Bi12SiO20, BSO) crystal, also coated with an ITO layer at outer surface. This specific electrode configuration enables the serial application of driving voltage across the photoconductive BSO and the LC layer. Notably, this particular structure of the cell is broadly similar to that utilized in BSO LCLVs44, which are recognized for their capability in generating localized structures and facilitating pattern formation.

Considering the absorption spectrum of BSO crystal implemented in the photoconductive cell (Supplementary Fig. 2a), in which the absorption wavelengths are less than 500 nm approximately, we employed a digital micromirror device (DMD) system, equipped with 405 nm light-emitting diode (LED) operating in gray-scale mode for exposure and photo-addressing in multiple domains. Each individual pixel of the projected area is addressed with a matrix of applied voltages, modulated by altering the gray value, which ranges from 0 to 255. This system enables the generation of programmable light patterns, which are projected onto the photoconductive cell through a \(\times\)5 objective lens. We employed LEDs with wavelengths of 532 nm and 635 nm as the observation light source to uniformly illuminate the entire cell. These wavelengths are minimally absorbed by BSO, thus preventing unexpected photoelectric effects (Supplementary Fig. 2b).

To precisely produce predictable voltages within the nematic LC layer, the photoconductive cell modeled with an electrical equivalent circuit is shown in Supplementary Fig. 3a. This model was used to simulate the electrical response of BSO when exposed to uniform illumination and subjected to an applied AC electric field44. The voltage drop ULC across the LC layer can be approximated as

$${U}_{{\mbox{LC}}}\propto \left({\sigma }_{0}+\beta \phi \right){U}_{{\mbox{AC}}}$$
(1)

where \({\sigma }_{0}\) is the dark conductivity of the BSO crystal, \(\beta\) is the absorption coefficient at a specific wavelength, and \(\phi\) is the uniform optical intensity (detailed description in Supplementary Note 1). We calculated the voltage ratio on the LC layer as a function of the driving voltage frequency under uniform illumination at varying intensities, as shown in Supplementary Fig. 3b. The voltage across the LC layer is proportional to the intensity of the illuminated light (Supplementary Fig. 4), indicating that the voltage amplitude within the virtual electrode can be modulated by varying the gray value of the light pattern projected onto the cell. Furthermore, it is important to note that the frequency of the applied electric field at different gray values plays a crucial role in determining the voltage ratio. At a low gray value (<100), the voltage ratio is ∼8% and shows a slight decrease within the 15–30 Hz frequency range, where directrons generate. In contrast, at a high gray value mode (≥ 100), the voltage ratio can reach up to 56% over the same frequency range. These findings suggest that light patterns with higher gray values is suitable for the micromanipulation of directrons within the frequency range where directrons can stably exist. Guided by the theoretical electric model, we deliberately employed patterns with gray values of 100 or higher in subsequent experiments.

Localized generation of directrons

We initially demonstrated the underlying phenomenon of photoconductive technology in generating directrons and confining them within locally created virtual electrodes through illuminated light patterns. The critical voltage, Ud, is applied across the photoconductive cell, where Ud represents the threshold voltage for directron formation. As shown in Fig. 2a, no directron formation is observed under applied voltage Ud without light. Nonetheless, when a square light pattern is projected onto the photoconductive layer, it induces an increase in voltage within the LC layer. This leads to the nucleation of directrons, which gradually evolves into dynamic propagation, parallel to n0, as clearly illustrated in Fig. 2b and Supplementary Movie 1. Typically, directrons collide with the boundaries of the virtual electrode, resulting in a reflection in the opposite direction or a rebound at an angle due to a sudden voltage drop. Such behavior is analogous to dynamic directrons near the solid ITO electrode edge18. Therefore, the motion of directrons can be confined to pre-designed areas using light-activated virtual electrodes. Moreover, diverse intriguing patterning consisting of numerous dynamic directrons can be accomplished by reconfigurable light-actuated patterning. As depicted in Fig. 2c, the propagating range of directrons was restricted within structural patterns, including alphabets ‘X’, ‘M’, and ‘U’, and the Chinese characters ‘厦’, ‘门’, ‘大’, ‘学’ (‘Xiamen university’ in Chinese), serving as a proof-of-concept.

Fig. 2: Localized generation of directrons.
figure 2

Crossed polarized optical microscopy (POM) images of the sample with the projected light (a) off and (b) on at U = 15.2 V and f = 30 Hz. Scale bars, 200 µm. c The movement of directrons is confined by various light-actuated patterns, including the alphabets ‘X’, ‘M’, ‘U’, and the Chinese characters ‘厦‘, ‘门‘, ‘大‘, ‘学‘ (Xiamen University). Scale bar, 200 µm. n0 denotes the alignment direction, and E indicates the electric field perpendicular to the xy plane. Simulated electric potential distribution for the LC layer on the (d) xz cut plane and (e) xy cut plane (z = 5 μm) of a square pattern driven at U = 16 V. (f) Plot of the simulated electric potential along a cross-sectional line at z = 5 μm, as indicated by the dashed line in (d).

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To contextualize the experimental results further, 3D numerical simulations of electric potential within an illuminated square light pattern were conducted using COMSOL Multiphysics. In this model, a square light pattern, identical to the experimental setup, was continuously projected to generate a stable electric field (Fig. 2d, e and Supplementary Fig. 5a, b). We assumed the illuminated region and non-illuminated region of photoconductive layer as a conductor and an insulator, respectively, due to the photoconductivity of BSO crystal is larger than the dark conductivity for more than three orders of magnitude (detailed model description in Supplementary Note 2). As shown in Fig. 2e, since most directrons move through the middle plane of the cell18, a two-dimensional (2D) xy plane slice at z = 5 μm was examined. The simulated results not only show a uniform electric potential distribution across the plane, ensuring the generation of directrons within this area, but also reveal a localized electric field that rapidly diminishes from the edge of the light pattern (Fig. 2f and Supplementary Fig. 5c). This diminishment creates a boundary at the edge of the virtual electrode, effectively restricting the propagation of directrons, and aligns with experimental observation.

On-demand in-situ generation of directrons

Building on the above work in generating directrons within optically-actuated domains, our research now aims to enhance the precision and control of this process, with a specific focus on achieving the in-situ formation of individual directron. Previous studies have established that individual directron tend to nucleate at defects or irregularities, owing to the distortion in the surrounding director field18. Additionally, local director deformation in LC films induced by the laser-induced electric field has been demonstrated45. It is plausible to hypothesize that the in-situ generation of directrons can be realized through director deformation induced by a light-activated electric field. In contrast to laser actuation, which is constrained by intrinsic intensity distribution and spot size, our system offers customized control over intensity and greater flexibility in spot size by utilizing gray image-driven optical patterns. Thus, this enables us to efficiently create and program array patterns with predetermined sizes. Fig. 3a schematically demonstrates the formation process of directrons in a 2 × 2 dark circle array pattern, representing the non-illuminated areas within a uniform square light pattern (the projected pattern and simulation results are shown in Supplementary Fig. 6a, b, respectively). Each dark circle pattern in the array creates a non-uniform electric field due to the variation in light intensity between the illuminated background and the dark circle regions. This variation leads to the formation of directrons that maintain constant rotation and eventually evolve into dynamic directrons in sequence, as illustrated in Fig. 3b, c and Supplementary Movie 2. This process may be attributed to the elastic deformations of splay and bend46. Notably, when the light illumination process is turned off and then on again, these sites are more likely to begin producing directrons again, indicating this in-situ generation of directrons is reloadable and exhibiting visual consistency before and after light cycling.

Fig. 3: On-demand in-situ generation of directrons.
figure 3

a Schematic illustration of directron generation through the projection of a 2 × 2 circle grid pattern, where dark circles represent the non-illuminated areas contrasting with the illuminated background. b Successive crossed POM images showing the in-situ generation process of directrons. n0 denotes the alignment direction, E indicates the electric field perpendicular to the xy plane, and arrows represent the moving direction of the directrons. Scale bar 100 μm. c Schematic representation of the director field during the generation process in the xy plane. d Simulated electric potential distribution in the LC layer for the dark circle pattern in the xz plane at U = 16 V, with lines representing electric displacement in the x and z dimensions. e Corresponding x and z components of the simulated electric field strength (Ex, red; Ez, black) plotted along a cross-sectional line at z = 5 μm, with positive values in Ex and Ez along the positive axes. f Simulated horizontal component Ex and (g) electric potential in the dark circle pattern along the x axis with various diameters of gaps, plotted along a cross-sectional line at z = 5 μm.

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To understand the role of the non-uniform electric field during the directron generation process, we simulated the xz plane of the electric field across the light-darkness interface (Fig. 3d and Supplementary Fig. 7a, b). The findings indicate that the distorted electric field possesses both a vertical component Ez and a horizontal component Ex within the selected sites, as depicted in Fig. 3e. Its magnitude quickly rises from 0 at the dark circle pattern’s center to 5.5 \(\times\) 105 V/m at its edge. The vertical component Ez causes deformation of the out-of-plane director field. In contrast, the horizontal component Ex, predominantly influences the in-plane director orientation, generating a torque that subsequently reorients the director field. Thus, the distorted director field serves as a ‘seed’, making in-situ nucleation of directrons and evolving into dynamic directrons, as observed in the experiment. Interestingly, we noted that the size of dark circle pattern also affects the effectiveness of directron generation (Supplementary Fig. 8a, b and Supplementary Movie 3). Specifically, the only uniform texture exists in most cases when the diameter of dark patterns is lower than the 24 μm. This phenomenon can be attributed to the reduction in horizontal component Ex as the pattern size diminishes gradually, as illustrated in Fig. 3f. The flexoelectric torque Гfl = Pfl × E, responsible for the directron formation, is linearly proportional to the electric field E, where Pfl is flexopolarization. Although a smaller region leads to a higher electric potential at the center of gap (Fig. 3g), the resulting lower horizontal component Ex is insufficient to support the deformation of the in-plane director, which is crucial for the formation of directrons.

Dynamics control of directrons by light

To enhance the operating controllability of directron micromanipulation, the structured light with tailorable optical intensity and arbitrary pattern by means of a DMD allows us to control the dynamic behavior of multiple directrons. Theoretical calculations of the voltage drop in the LC layer, combined with experimental measurements of directron velocity within a uniform square pattern with various gray values, are presented in Supplementary Fig. 9a–c. These results highlight that the velocity of directrons is proportional to the gray value of the projected pattern. Fig. 4a demonstrates the continuous modulation of directron velocity using gray-in-white images. These images feature rectangles filled with uniform gray, embedded within a white background, with an applied voltage of U = 11.4 V and a frequency of f = 15 Hz. The gray values of the rectangle and the background are set to 100 (‘medium gray value’) and 255 (‘maximum gray value’), corresponding to light intensities of 23.5 mW/cm² and 146.1 mW/cm², respectively (Supplementary Fig. 9d). The mean velocity of directrons exhibited fluctuations ranging from 52 μm/s to 68 μm/s within the illuminated pattern, featuring periodic modulation of domains with varying gray values, as shown in Fig. 4b, e and Supplementary Movie 4. In this case, the propagation direction of directrons can be switched when the applied voltage reaches a higher value of U = 12.2 V. Fig. 4c and d illustrate the dynamic transformation of directrons in the white background, transitioning from an orientation parallel to n0 with a lack of fore-aft symmetry to an orientation perpendicular to n0 with a lack of left-right symmetry, resulting in a nearly 90-degree alteration in their propagation direction (Fig. 4f and Supplementary Movie 5). Compared to conventional electric fields applied across the entire cell, light-activated pattern provides a distinct advantage in multidomain scenarios, enabling flexible and effective steering of directrons.

Fig. 4: Dynamics control of directrons by light.
figure 4

a Schematic illustration of velocity modulation of directrons as they propagate across light patterns periodically modified by different gray values (dark blue represents a gray value of 255, light blue represents a gray value of 100). b Time-lapsed velocity graphs of a directron at U = 11.4 V and f = 15 Hz. Scale bar 200 μm. c Schematic illustration and (d) sequential POM images showing directrons transitioning from an orientation parallel to n0, lacking fore-aft symmetry, to an orientation perpendicular to n0, lacking left-right symmetry. The dark blue area has a gray value of 255, corresponding to light intensity of 146.1 mW/cm², while the light blue area has a gray value of 100, corresponding to light intensity of 23.5 mW/cm². n0 denotes the alignment direction, E indicates the electric field perpendicular to the xy plane, and v represents the velocity of the directrons. Arrows represent the moving direction of the directrons. Scale bar 200 μm. e Transitions in directron velocity depicted in (b) for gray values of 255 and 100, with error bars representing the standard deviation. f The variation in the velocity components Vx and Vy of the directrons over time in the first illustration of (d).

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Light-guided trajectory

The discovery that directrons are confined to the edges of a light pattern enables the control over the trajectory of individual or multiple directrons. As schematically demonstrated in Fig. 5a, we designed a light-guided straight channel with a width of 18 μm matching the width of the directrons as a fundamental component to assess its capability in linear transport. Figure 5b presents the displacement of directrons along the x and y axes, demonstrating the perfect alignment between the directron movement and the light-guided channel. We analyzed the recorded video to quantify the precision of manipulation. The difference between the channel direction vector Dc and the directron movement vector Dd was examined, as sketched in Fig. 5a. The accuracy can be characterized by the dot product of unit vectors along Dc and Dd. We defined a manipulation efficiency Q as the average cos θ over a full manipulation trajectory:

$${\mbox{Q}}=\left\langle \cos \theta \right\rangle=\left\langle \frac{{{{{\bf{D}}}}}_{{\mbox{c}}}\cdot {{{{\bf{D}}}}}_{{\mbox{d}}}}{\left|{{{{\bf{D}}}}}_{{\mbox{c}}}\right|\left|{{{{\bf{D}}}}}_{{\mbox{d}}}\right|}\right\rangle=\frac{1}{N}{\sum}_{i=1}^{N}\cos {\theta }_{i}$$
(2)

where \(\theta\) is the angle between Dc and Dd at each time step. For different angles between Dc and n0, the calculated Q ranges from 0.98 to 0.99, indicating highly precise manipulation of the directrons.

Fig. 5: Light-guided trajectory.
figure 5

a Schematic of directron trajectory steered by a straight light-guided channel and (b) displacement of directrons in the x-axis and y-axis. c–f Diverse light-guided trajectories of directrons at U = 16 V and f = 30 Hz, with the color bar representing the velocity of directrons. Scale bars, 200 µm. n0 denotes the alignment direction, and E indicates the electric field perpendicular to the xy plane. g 3D simulation of a photoconductive cell in which a light pattern (purple) is projected onto a BSO surface. h xy plot at z = 5 μm of the simulated electric potential distribution driven by U = 16 V. The axis dimensions in (g) and (h) are in micrometers.

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It’s essential to emphasize that the velocity of directrons depends on the electrode width. Specifically, the velocity increases nearly threefold as the channel width expands from 18 μm to 98 μm. (Supplementary Fig. 10a) However, with further increases in the channel width, the directron velocity tends to remain invariant, due to the diminution of electric edge effects. Furthermore, the mean velocity within the light-guided channel can also be tuned by controlling the angle between the propagation direction and the preset channel. As depicted in Supplementary Fig. 10b, it decreases from 38 μm/s to 20 μm/s as the angle increases from 0° to 90°. Notably, when the direction of directron propagation mismatches the channel direction, the directrons prefer to move along the original propagation direction. This behavior results in collisions with the boundary and moves along the channel boundary, leading to a decrease in the measured velocity of directrons.

Additionally, the geometric design of the light-guided channel facilitates precise manipulation of multiple directrons into more complex trajectories. Fig. 5c–f show that directrons can be guided through channels, exhibiting diverse complex trajectories, including circles, squares, triangles, and even pentagrams (Supplementary Movie 6), a challenging task for directrons driven by electric fields in uniform director fields. We quantitatively analyzed the velocity of directrons in various trajectories using ImageJ. The velocity decreases where there is a mismatch in the orbital directions, which is consistent with previous findings. The simulated electric potential results for the pentagonal illumination pattern suggest that a sufficient electric field can be provided for the propagation of directrons, even in the presence of narrow channel width comparable to the width of directrons and complex guiding patterns. (see Fig. 5g, h)

Directron migration guided by structural light pattern

Although directrons are inanimate, they self-organize into flocks exhibiting density-dependent collective motions like their biological counterparts, as observed by Shen et al.24 Dynamic confinement of directrons by light allows us to explore the other collective motions of directrons, which represents migration in our system. A distinct advantage of structured light generated by DMD lies in its spatial and temporal variability, enabling precise control over the collective behavior of directrons. We leverage this feature to generate dynamic light patterns that not only confine the directrons but also enhance the control over their spatial distribution in a fully reversible and programmable manner. Initially, directrons are randomly distributed in an illuminated circular pattern on a dark background when the voltage drop exceeds a critical value. Fig. 6a–c schematically illustrate and experimentally present how these circularly confined directrons can migrate to an arbitrary spatial ___location when the illuminated region shrinks or expands (Supplementary Movie 7). This behavior mimics phototaxis in biological systems, as directrons always migrate to regions where the electric field exists in order to sustain their motion. Interestingly, the quantity of directron flocks does not change significantly during the shrinking/expanding processes, as shown in Fig. 6d. The migration of directrons leads to its redistribution in space. To further investigate the distribution of directrons, we used the average nearest distance \(\bar{L}\) to quantify the aggregation degree of directrons:

$$\bar{L}=\frac{{\sum }_{i=1}^{N}{l}_{i}}{N}$$
(3)

where \({l}_{i}\) represents the distance between the measured directron and its nearest neighbor directron, and \(N\) represents total quantity of directrons. As shown in Fig. 6e, as the light pattern shrinks, \(\bar{L}\) decreases from 20.4 μm to 16.2 μm, indicating that the distance between the directrons narrows and shows a tendency to gather. Moreover, the transport of directrons can be facilitated by optically linking two spatial domains, as shown in Supplementary Fig. 11 and Supplementary Movie 8. Similar phenomena of microstructure-engaged motion, including translation, have also been observed in other LC systems, such as chromonic nematic47 and semi-free CLC films48.

Fig. 6: Directron migration guided by structural light pattern.
figure 6

a Schematics of time-lapsed convergence and (b) divergence motion of directrons in dynamic light patterns. c Successive crossed POM images showing the real-time migration of directron flocks by varying light patterns. Scale bar, 400 μm. n0 denotes the alignment direction, E indicates the electric field perpendicular to the xy plane, and arrows represent the moving direction of the directrons. d The variation in the quantity of directrons at different applied voltages. e The average nearest distance with changes in the illuminated area. The error bar shows the standard deviation of the measurements.

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Discussion

The unique interplay of anisotropic properties and nonlinear responses to external stimuli enables the formation of various soliton types in LCs1. An archetypal example of solitons in LCs is the so-called nematicons16, which represents self-focused laser beams without diffracting balanced by nonlocal orientation of director field n0. Nematicons can be generated by linearly polarized light at milliwatt power levels and create their own trajectories over millimeter-scale propagation distances49. The trajectory of nematicons may be modified by orientation of their background director field stimulated from electric and optical field15,50,51. Therefore, investigating alternative approaches for controlling solitons in a uniform medium is of considerable interest, especially in light of the pivotal role that the interaction between the propagation medium and the solitons plays in governing their dynamics. Other types of solitons in LCs including topological solitons11,12,13,14,52, discrete solitons53 and electrically driven solitons17,18,19,20,21,22,23,24,25,26. Moreover, different types of solitons can coexist and interact with each other54. Among these, electrically driven solitons, coined as “directrons”, enable controlling their dynamic propagation in uniform background director field. Unfortunately, the requirement for a global electric field to maintain their motion limits the potential for multitasking scenarios. Strategic local confinement serves as a fundamental concept, can offer an alternative control method for the dynamic motion of directrons and further extend to paralleled and independent control for multitasking applications. Intuitively, employing conventional lithography to fabricate the fixed microstructure of electrodes can effectively create a confinement boundary, which in turn guides the motion of directrons. However, the inherent geometry of lithographically patterned electrodes is unbeneficial for directron dynamics, thus highlighting the need for a virtual electrode that combines structural flexibility with enhanced functionality.

In this study, we presented a reconfigurable optoelectronic approach for controlling the entire lifecycle of directrons, encompassing generation, propagation, and annihilation. By harnessing the photoconductive effect, the localized distribution of the electric field can be modulated in response to incident light intensity. Particularly, in contrast to global electric field manipulation, this approach has essentially shrunken the domains of actuation and steering of directrons to the micrometer scale, closely approaching the intrinsic size of directrons (i.e., ∼20 μm). Although the DMD offers pixelated resolution of 2 μm55, it seems difficult to further elevate the resolution with the current cell-type configuration due to lateral charge diffusion in the photoconductor layer and the fringing electric field profile in the LC layer. A thin photoconductor layer might help minimize the lateral charge spread, but fabricating a thin crystalline photoconductor while maintaining the high light sensitivity of BSO crystal may be challenging. Fortunately, this limitation can potentially be surmounted by developing thin photoconductive layers formed by other materials, such as ZnO nanoparticles56, hydrogenated amorphous silicon (a-Si:H) films37, and arsenic trisulfide (a-As2S3) films57. Apart from this, the spatial resolution may be influenced by the elastic response of the NLC58, as the coherence length of director deformations depends on the balance between elastic torque and the applied electric field59. Moreover, we proposed an on-demand in-situ generation method by designing the dark pattern embedded in white background. This localized excitation achieved through optoelectronics presents several advantages over photothermal methods12, including the requirement to reduce light intensity and the capability for high-throughput parallel manipulation. Additionally, the threshold of light intensity \({I}_{{\mbox{th}}}\) for light-induced molecular reorientation is significantly higher. According to Shen et al.60, \({I}_{{\mbox{th}}}\) is determined by the material constant \({P}_{0}\,=\,{K}_{33}{\mbox{c}}\,/\,({n}_{{\mbox{e}}}^{2}-{n}_{{\mbox{o}}}^{2})\). For low birefringence NLCs, the reorientation of director occurs for a pump field of approximately61 ∼100 W/cm2. In our experiment, the maximum optical intensity of 146.1 mW/cm2 is much lower than \({I}_{{\mbox{th}}}\). Thus, the phenomena observed in our experiments cannot be attributed to optical torque, as the light intensity is insufficient to induce the necessary molecular reorientation. The ability of directrons to move along almost arbitrary trajectories opens a broad field of studies for their programmable in-plane dynamics, which may lead to applications in optical information processing and microfluidics62,63. Furthermore, by leveraging light patterns that vary in space and time within a confined environment, we further demonstrated the migration of directron flocks and control their spatial distribution, mimicking phototaxis in biological systems. These confined conditions may provide inhomogeneous density distribution and steric interactions between dynamic elements and geometric boundaries that could potentially induce novel collective motions consisting of numerous directrons, such as spiral vortices64 and oscillating edge flow65, analogous to active matter systems. This could also promote further exploration of biomimetic motions in different LC environments.

In summary, our method represents a significant advancement in the field of micromanipulation of directron dynamics. We have demonstrated this technique with various controlled behaviors of directrons, covering their entire lifecycle. Our strategy provides a complementary option to conventional electric field-controlled directron regulation and broadens the scope of target objects for optoelectronic manipulation. Furthermore, the concept of optical confinement, supported by digital light projection, holds the potential for extension to various direction-based applications, including emergent behavior, micro-cargo transport, microfluidics, and beyond.

Methods

Materials and photoconductive cell fabrication

We employed a commercial nematic LC, 4’-butyl-4-heptyl-bicyclohexyl-4-carbonitrile (CCN-47), with negative dielectric and conductive anisotropies. The combination of dielectric and conductive anisotropies is selected to preclude the two primary mechanisms of field-induced director reorientation, the dielectric torque and the standard Carr-Helfrich director instability. Its conductivity was modulated by doping with 0.005 wt.% of tetrabutylammonium bromide (TBAB) using dichloromethane as a solvent. The photoconductive cell consists of a LC layer sandwiched between a glass substrate and a photoconductive BSO substrate. The bottom surface of the glass substrate and the top surface of the BSO substrate are coated with ITO film, serving as transparent electrodes with an area of 15 × 20 mm². The azo dye SD1, dissolved in dimethylformamide (DMF) at a concentration of 1 wt.%, was spin-coated onto the ITO electrodes of both substrates as the photoalignment layer. The SD1 molecules tend to induce a planar orientation of the nematic CCN-47 films, with an azimuthal direction perpendicular to the UV light polarization due to the cis-trans isomerization process. The substrates were assembled using double-sided tape, creating a cell gap of ∼10.5 μm, which was measured by the thin film interference method. Subsequently, the photoconductive cell was photo-aligned homogeneously along the x or y axis by linearly polarized light of wavelength λ = 405 nm, resulting in an alignment direction n0 = (1, 0, 0) or n0 = (0, 1, 0). In this case, the nematic LC mixture was injected into the cell in the isotropic phase at 70 °C due to the capillary effect. The anisotropies of dielectric permittivity and conductivity were measured by a dielectric spectrometer (Tonghui, TH2839) with planar and homeotropic alignment at an applied voltage of 0.1 V, which is much lower than the threshold voltage for the electric Freedericksz transition, and at a frequency of 5 kHz. The dielectric constants and conductivities of the LC mixture are ε∥ = 2.954 and ε⊥ = 8.565, σ∥ = 1.785 × 10−9 Ω−1 m−1 and σ⊥ = 5.626 × 10−9 Ω−1 m−1, respectively. The subscripts ∥ and ⊥ indicate directions parallel and perpendicular to the director n0.

Optical setup and characterization

The BSO photoconductor in the device was illuminated using a DMD-based light pattern projector (DLP4500 WXGA, 405 nm LED source) through an optical microscope with a ×5 Mitutoyo objective. The optical power densities of the light patterns, with gray values ranging from 0 to 255, were measured using a power meter (Ophir Nova) connected to a probe (Ophir, PD300-UV). The illumination system consists of two independently controlled LED light sources at 532 nm (green) and 635 nm (red). Samples were observed using an optical microscope with either a ×10 or ×4 Leica objective and lens (JCOPTIX), equipped with a digital camera (Sony, E3ISPM20000KPA).

Generation of directrons

The temperature of the cell is maintained using a hot stage integrated with a controller (Linkam, PE94). The bottom surface of the ITO glass substrate and the top surface of the BSO substrate were connected to a waveform generator (Rigol, DG1022) with a power amplifier (FLC Electronics, A400DI). An AC electric field E = (0, 0, E) (U = 8–25 Vrms, f = 10–30 Hz, square waves) was applied perpendicularly to the xy plane to drive the photoconductive cell.

Correlation data measurement

The videos were recorded using Captura software at a frame rate of 10 fps. The trajectories of the directrons were analyzed using the open-source software ImageJ, employing both the Manual Tracking and TrackMate plugins for manual and automated tracking as needed. The velocity of the directrons was determined by calculating the displacement between consecutive time frames. The intensity of the LED and the transmittance of BSO at different wavelengths were measured by a spectrometer (Ocean Optics USB4000) and an ultraviolet-visible spectrophotometer (SHIMADZU, UV-1900i), respectively.

Numerical Simulations

2D and 3D finite element models were constructed using the electric current module in finite element analysis software (COMSOL Multiphysics version 6.2) to simulate the distribution of electric potential and electric fields. Further details about these COMSOL models are provided in the Supporting Materials.