Driven optical matter: Dynamics of electrodynamically coupled nanoparticles in an optical ring vortex

Power dissipation and entropy production rate of high-dimensional optical matter systems

Entropy production is an essential aspect of creating and maintaining nonequilibrium systems. Despite their ubiquity, calculation of entropy production rates is challenging for high-dimensional systems, so it has only been reported for simple (i.e., l-particle) systems. Moreover, there is a dearth of nontrivial experimental systems where precise measurements of entropy production rate and characterization of the nonequilibrium steady state (NESS) are simultaneously possible. We report an approach to calculate the entropy production rate of overdamped, nonconservative, N-body systems and demonstrate this on a six-particle triangle optical matter (OM) system as a nontrivial example. OM systems consist of (nano-)particles organized into ordered arrays that are bound by electrodynamic interactions associated with the scattering and interference of light, and the associated induced-polarizations in and among the particles in coherent optical beams. The flux of laser light in OM systems in a solution environment necessitates that they dissipate energy, produce entropy, and relax to a NESS. The NESS may have several ordered particle configurations (i.e., isomers) that can interchange by barrier crossing processes. Understanding the power dissipation and entropy production rate of a NESS in an OM system along different (collective) modes of motion can advance understanding of the relative stability of the NESSs as well as inform design and control of OM structures. Therefore, we compute the components of the entropy production rate and power dissipation along the collective coordinates of the 6 Ag nanoparticle triangle OM system from OM NESS trajectory data and verify the Seifert relation [U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)10.1088/0034-4885/75/12/126001] for these complex systems with a nuanced interpretation.

Creating stable trapping force and switchable optical torque with tunable phase of light

Light-induced rotation of microscopic objects is of general interest as the objects may serve as micromotors. Such rotation can be driven by the angular momentum of light or recoil forces arising from special light-matter interactions. However, in the absence of intensity gradient, simultaneously controlling the position and switching the rotation direction is challenging. Here, we report stable optical trapping and switchable optical rotation of nanoparticle (NP)-assembled micromotors with programmed phase of light. We imprint customized phase gradients into a circularly polarized flat-top (i.e., no intensity gradient) laser beam to trap and assemble metal NPs into reconfigurable clusters. Modulating the phase gradients allows direction-switchable and magnitude-tunable optical torque in the same cluster under fixed laser wavelength and handedness. This work provides a valuable method to achieve reversible optical torque in micro/nanomotors, and new insights for optical trapping and manipulation using the phase gradient of a spatially extended light field.

Radiation forces on a Mie particle in the evanescent field of a resonance waveguide structure

Evanescent waves of a guided mode carry both momentum and energy, which enables them to move small objects located on a waveguide surface. This optical force can be used for optical near-field manipulation, arrangement, and acceleration of particles. In this paper, using arbitrary beam theory, the optical force on a dielectric particle in the evanescent wave of a resonance waveguiding structure is investigated. Using Maxwell's equations and applying the boundary conditions, all the field components and a generalized dispersion relation are obtained. An expression for the evanescent field is derived in terms of the spherical wave functions. Cartesian components of the radiation force are analytically formulated and numerically evaluated by ignoring the multiple scattering that occurs between the sphere and plane surface of the structure. Our numerical data show that both the horizontal and vertical force components and the forward particle velocity are enhanced significantly in the proposed resonance structure compared to those reported for three-layer conventional waveguides. Exerting stronger force on macro- and nanoparticles can be very useful to perform advanced experiments in solutions with high viscosity and experiments on biological cells. In addition, this resonance planar structure can be mounted on an inverted optical microscope stage for imaging the motion of nanoparticles especially when the particle collides and interacts with objects.

Opto-Thermocapillary Nanomotors on Solid Substrates

Motors that can convert different forms of energy into mechanical work are of profound importance to the development of human societies. The evolution of micromotors has stimulated many advances in drug delivery and microrobotics for futuristic applications in biomedical engineering and nanotechnology. However, further miniaturization of motors toward the nanoscale is still challenging because of the strong Brownian motion of nanomotors in liquid environments. Here, we develop light-driven opto-thermocapillary nanomotors (OTNM) operated on solid substrates where the interference of Brownian motion is effectively suppressed. Specifically, by optically controlling particle-substrate interactions and thermocapillary actuation, we demonstrate the robust orbital rotation of 80 nm gold nanoparticles around a laser beam on a solid substrate. With on-chip operation capability in an ambient environment, our OTNM can serve as light-driven engines to power functional devices at the nanoscale.

Heat-Mediated Optical Manipulation

Progress in optical manipulation has stimulated remarkable advances in a wide range of fields, including materials science, robotics, medical engineering, and nanotechnology. This Review focuses on an emerging class of optical manipulation techniques, termed heat-mediated optical manipulation. In comparison to conventional optical tweezers that rely on a tightly focused laser beam to trap objects, heat-mediated optical manipulation techniques exploit tailorable optothermo-matter interactions and rich mass transport dynamics to enable versatile control of matter of various compositions, shapes, and sizes. In addition to conventional tweezing, more distinct manipulation modes, including optothermal pulling, nudging, rotating, swimming, oscillating, and walking, have been demonstrated to enhance the functionalities using simple and low-power optics. We start with an introduction to basic physics involved in heat-mediated optical manipulation, highlighting major working mechanisms underpinning a variety of manipulation techniques. Next, we categorize the heat-mediated optical manipulation techniques based on different working mechanisms and discuss working modes, capabilities, and applications for each technique. We conclude this Review with our outlook on current challenges and future opportunities in this rapidly evolving field of heat-mediated optical manipulation.

Optical manipulation of a dielectric particle along polygonal closed-loop geometries within a single water droplet

We report a new method to optically manipulate a single dielectric particle along closed-loop polygonal trajectories by crossing a suite of all-fiber Bessel-like beams within a single water droplet. Exploiting optical radiation pressure, this method demonstrates the circulation of a single polystyrene bead in both a triangular and a rectangle geometry enabling the trapped particle to undergo multiple circulations successfully. The crossing of the Bessel-like beams creates polygonal corners where the trapped particles successfully make abrupt turns with acute angles, which is a novel capability in microfluidics. This offers an optofluidic paradigm for particle transport overcoming turbulences in conventional microfluidic chips.

Data-driven reaction coordinate discovery in overdamped and non-conservative systems: application to optical matter structural isomerization

Optical matter (OM) systems consist of (nano-)particle constituents in solution that can self-organize into ordered arrays that are bound by electrodynamic interactions. They also manifest non-conservative forces, and the motions of the nano-particles are overdamped; i.e., they exhibit diffusive trajectories. We propose a data-driven approach based on principal components analysis (PCA) to determine the collective modes of non-conservative overdamped systems, such as OM structures, and harmonic linear discriminant analysis (HLDA) of time trajectories to estimate the reaction coordinate for structural transitions. We demonstrate the approach via electrodynamics-Langevin dynamics simulations of six electrodynamically-bound nanoparticles in an incident laser beam. The reaction coordinate we discover is in excellent accord with a rigorous committor analysis, and the identified mechanism for structural isomerization is in very good agreement with the experimental observations. The PCA-HLDA approach to data-driven discovery of reaction coordinates can aid in understanding and eventually controlling non-conservative and overdamped systems including optical and active matter systems.

Non-equilibrium properties of an active nanoparticle in a harmonic potential

Active particles break out of thermodynamic equilibrium thanks to their directed motion, which leads to complex and interesting behaviors in the presence of confining potentials. When dealing with active nanoparticles, however, the overwhelming presence of rotational diffusion hinders directed motion, leading to an increase of their effective temperature, but otherwise masking the effects of self-propulsion. Here, we demonstrate an experimental system where an active nanoparticle immersed in a critical solution and held in an optical harmonic potential features far-from-equilibrium behavior beyond an increase of its effective temperature. When increasing the laser power, we observe a cross-over from a Boltzmann distribution to a non-equilibrium state, where the particle performs fast orbital rotations about the beam axis. These findings are rationalized by solving the Fokker-Planck equation for the particle's position and orientation in terms of a moment expansion. The proposed self-propulsion mechanism results from the particle's non-sphericity and the lower critical point of the solution.

Tailored optical propulsion forces for controlled transport of resonant gold nanoparticles and associated thermal convective fluid flows

Noble metal nanoparticles illuminated at their plasmonic resonance wavelength turn into heat nanosources. This phenomenon has prompted the development of numerous applications in science and technology. Simultaneous optical manipulation of such resonant nanoparticles could certainly extend the functionality and potential applications of optothermal tools. In this article, we experimentally demonstrate optical transport of single and multiple resonant nanoparticles (colloidal gold spheres of radius 200 nm) directed by tailored transverse phase-gradient forces propelling them around a 2D optical trap. We show how the phase-gradient force can be designed to efficiently change the speed of the nanoparticles. We have found that multiple hot nanoparticles assemble in the form of a quasi-stable group whose motion around the laser trap is also controlled by such optical propulsion forces. This assembly experiences a significant increase in the local temperature, which creates an optothermal convective fluid flow dragging tracer particles into the assembly. Thus, the created assembly is a moving heat source controlled by the propulsion force, enabling indirect control of fluid flows as a micro-optofluidic tool. The existence of these flows, probably caused by the temperature-induced Marangoni effect at the liquid water/superheated water interface, is confirmed by tracking free tracer particles migrating towards the assembly. We propose a straightforward method to control the assembly size, and therefore its temperature, by using a nonuniform optical propelling force that induces the splitting or merging of the group of nanoparticles. We envision further development of microscale optofluidic tools based on these achievements.

Rapidly and accurately shaping the intensity and phase of light for optical nano-manipulation

Holographic optical tweezers can be applied to manipulate microscopic particles in various optical patterns, which classical optical tweezers cannot do. This ability relies on accurate computer-generated holography (CGH), yet most CGH techniques can only shape the intensity profiles while the phase distributions remain poor. Here, we introduce a new method for fast generation of holograms that allows for accurately shaping both the intensity and phase distributions of light. The method uses a discrete inverse Fourier transform formula to directly calculate a hologram in one step, in which a random phase factor is introduced into the formula to enable complete control of intensity and phase. Various optical patterns can be created, as demonstrated by the experimentally measured intensity and phase profiles projected from the holograms. The high-quality shaping of intensity and phase of light provides new opportunities for optical trapping and manipulation, such as controllable transportation of nanoparticles in optical trap networks with variable phase profiles.

Synergy of Intensity, Phase, and Polarization Enables Versatile Optical Nanomanipulation

Micromanipulation by optical tweezers mainly relies on the trapping force derived from the intensity gradient of light. Here we show that the synergy of intensity, phase, and polarization in structured light allows versatile optical manipulation of nanostructures. When a metal nanoparticle is confined by a linearly polarized laser field, the sign of optical force depends on the particle shape and the laser intensity, phase, and polarization profiles. By tuning these parameters in optical line traps, optical trapping, transporting, and sorting of silver nanostructures have been demonstrated. These findings inspired us to control the motion of nanostructures with designed intensity, phase, and polarization of light using holographic optical tweezers with advanced beam shaping techniques. This work provides a new perspective on active colloidal nanomanipulation in fully controlled optical landscapes, which largely expands the existing optical manipulation toolbox.

Effect of hydrodynamic inter-particle interaction on the orbital motion of dielectric nanoparticles driven by an optical vortex

We experimentally and theoretically characterize dielectric nano- and microparticle orbital motion induced by an optical vortex of the Laguerre-Gaussian beam. The key to stable orbiting of dielectric nanoparticles is hydrodynamic inter-particle interaction and microscale confinement of slit-like fluidic channels. As the number of particles in the orbit increases, the hydrodynamic inter-particle interaction accelerates orbital motion to overcome the inherent thermal fluctuation. The microscale confinement in the beam propagation direction helps to increase the number of trapped particles by reducing their probability of escape from the optical trap. The diameter of the orbit increases as the azimuthal mode of the optical vortex increases, but the orbital speed is shown to be insensitive to the azimuthal mode, provided that the number density of the particles in the orbit is same. We use experiments, simulation, and theory to quantify and compare the contributions of thermal fluctuation such as diffusion coefficients, optical forces, and hydrodynamic inter-particle interaction, and show that the hydrodynamic effect is significant for circumferential motion. The optical vortex beam with hydrodynamic inter-particle interaction and microscale confinement will contribute to biosciences and nanotechnology by aiding in developing new methods of manipulating dielectric and nanoscale biological samples in optical trapping communities.

Generation of coupled orbital angular momentum modes from an optical vortex parametric laser source

We report on the generation of flower (wheel) modes, which manifest coupled orbital angular momentum (OAM) modes, from a vortex pumped optical parametric oscillator simply by employing a pump source with a short temporal coherence time. This vortex oscillator was also developed to generate a further higher-order vortex signal output with ℓs=2-4 by replacement of the pump source with a longer coherence time. The signal and idler outputs were tuned within wavelength ranges of 745-955 nm and 1200-1855 nm, respectively. The maximum signal output energy of 1.2 mJ was measured with an optical efficiency of 15.6%.

Laser additive nano-manufacturing under ambient conditions

Additive manufacturing at the macroscale has become a hot topic of research in recent years. It has been used by engineers for rapid prototyping and low-volume production. The development of such technologies at the nanoscale, or additive nanomanufacturing, will provide a future path for new nanotechnology applications. In this review article, we introduce several available toolboxes that can be potentially used for additive nanomanufacturing. We especially focus on laser-based additive nanomanufacturing under ambient conditions.

Controlling the Dynamics and Optical Binding of Nanoparticle Homodimers with Transverse Phase Gradients

While transverse phase gradients enable studies of driven nonequilibrium phenomena in optical trapping, the behavior of electrodynamically interacting particles in a transverse phase gradient has not been explored in detail. In this Letter we study electrodynamically interacting pairs of identical nanoparticles (homodimers) in transverse phase gradients. We establish that the net driving force on homodimers is modulated by a separation-dependent interference effect for small phase gradients. By contrast, large phase gradients break the symmetry of the interaction between particles and profoundly change the electrodynamic interparticle energy landscape. Our findings are particularly important for understanding multiparticle dynamics during the self-assembly and rearrangement of optical matter.

Dissipative Self-Assembly of Anisotropic Nanoparticle Chains with Combined Electrodynamic and Electrostatic Interactions

Dissipative self-assembly of colloidal nanoparticles offers the prospect of creating reconfigurable artificial materials and systems, yet the phenomenon only occurs far from thermodynamic equilibrium. Therefore, it is usually difficult to predict and control. Here, a dissipative colloidal solution system, where anisotropic chains with different interparticle separations in two perpendicular directions transiently arise among largely disordered silver nanoparticles illuminated by a laser beam, is reported. The optical field creates a nonequilibrium dissipative state, where a disorder-to-order transition occurs driven by anisotropic electrodynamic interactions coupled with electrostatic interactions. Investigation of the temporal dynamics and spatial arrangements of the nanoparticle system shows that the optical binding strength and entropy of the system are two crucial parameters for the formation of the anisotropic chains and responsible for adaptive behaviors, such as self-replication of dimer units. Formation of anisotropic nanoparticle chains is also observed among colloidal nanoparticles made from other metal (e.g., Au), polymer (e.g., polystyrene), ceramic (e.g., CeO₂ ), and hybrid materials (e.g., SiO₂ @Au core-shell), suggesting that light-driven self-organization will provide a wide range of opportunities to discover new dissipative structures under thermal fluctuations and build novel anisotropic materials with nanoscale order.

Change in collective motion of colloidal particles driven by an optical vortex with driving force and spatial confinement

We studied the change in collective behavior of optically driven colloidal particles on a circular path. The particles are simultaneously driven by the orbital angular momentum of an optical vortex beam generated by holographic optical tweezers. The driving force is controlled by the topological charge l of the vortex. By varying the driving force and spatial confinement, four characteristic collective motions were observed. The collective behavior results from the interplay between the optical interaction, hydrodynamic interaction and spatial confinement. Varying the topological charge of an optical vortex not only induces changes in driving force but also alters the stability of three-dimensional optical trapping. The switch between dynamic clustering and stable clustering was observed in this manner. Decreasing the cell thickness diminishes the velocity of the respective particles and increases the spatial confinement. A jamming-like characteristic collective motion appears when the thickness is small and the topological charge is large. In this regime, a ring of equally-spaced doublets was spontaneously formed in systems composed of an even number of particles.

Direct Visualization of Barrier Crossing Dynamics in a Driven Optical Matter System

A major impediment to a more complete understanding of barrier crossing and other single-molecule processes is the inability to directly visualize the trajectories and dynamics of atoms and molecules in reactions. Rather, the kinetics are inferred from ensemble measurements or the position of a transducer ( e. g., an AFM cantilever) as a surrogate variable. Direct visualization is highly desirable. Here, we achieve the direct measurement of barrier crossing trajectories by using optical microscopy to observe position and orientation changes of pairs of Ag nanoparticles, i. e. passing events, in an optical ring trap. A two-step mechanism similar to a bimolecular exchange reaction or the Michaelis-Menten scheme is revealed by analysis that combines detailed knowledge of each trajectory, a statistically significant number of repetitions of the passing events, and the driving force dependence of the process. We find that while the total event rate increases with driving force, this increase is due to an increase in the rate of encounters. There is no drive force dependence on the rate of barrier crossing because the key motion for the process involves a random (thermal) radial fluctuation of one particle allowing the other to pass. This simple experiment can readily be extended to study more complex barrier crossing processes by replacing the spherical metal nanoparticles with anisotropic ones or by creating more intricate optical trapping potentials.

Dynamics of the Optically Directed Assembly and Disassembly of Gold Nanoplatelet Arrays

The tremendous progress in nanoscience now allows the creation of static nanostructured materials for a broad range of applications. A further goal is to achieve dynamic and reconfigurable nanostructures. One approach involves nanoparticle-based optical matter, but so far, studies have only considered spherical constituents. A nontrivial issue is that nanoparticles with other shapes are expected to have different local electromagnetic field distributions and interactions with neighbors in optical-matter arrays. Therefore, one would expect their dynamics to be different as well. This paper reports the directed assembly of ordered arrays of gold nanoplatelets in optical line traps, demonstrating the reconfigurability of the array by altering the phase gradient via holographic-beam shaping. The weaker gradient forces and resultant slower motion of the nanoplatelets, as compared with plasmonic (Ag and Au) nanospheres, allow the precise study of their assembly and disassembly dynamics. Both temporal and spatial correlations are detected between particles separated by distances of hundreds of nanometers to several microns. Electrodynamics simulations reveal the presence of multipolar plasmon modes that induce short-range (near-field) and longer-range electrodynamic (e.g., optical binding) interactions. These interactions and the interferences between mutipolar plamon modes cause both the strong correlations and the nonuniform dynamics observed. Our study demonstrates new opportunities for the generation of complex addressable optical matter and the creation of novel active optical technology.

Controllable mode transformation in perfect optical vortices

We report a novel method to freely transform the modes of a perfect optical vortex (POV). By adjusting the scaling factor of the Bessel-Gauss beam at the object plane, the POV mode transformation can be easily controlled from circle to ellipse with a high mode purity. Combined with the modulation of the cone angle of an axicon, the ellipse mode can be freely adjusted along the two orthogonal directions. The properties of the "perfect vortex" are experimentally verified. Moreover, fractional elliptic POVs with versatile modes are presented, where the number and position of the gaps are controllable. These findings are significant for applications that require the complex structured optical field of the POV.

Rotation and Negative Torque in Electrodynamically Bound Nanoparticle Dimers

We examine the formation and concomitant rotation of electrodynamically bound dimers (EBD) of 150 nm diameter Ag nanoparticles trapped in circularly polarized focused Gaussian beams. The rotation frequency of an EBD increases linearly with the incident beam power, reaching mean values of ∼4 kHz for relatively low incident powers of 14 mW. Using a coupled-dipole/effective polarizability model, we reveal that retardation of the scattered fields and electrodynamic interactions can lead to a "negative torque" causing rotation of the EBD in the direction opposite to that of the circular polarization. This intriguing opposite-handed rotation due to negative torque is clearly demonstrated using electrodynamics-Langevin dynamics simulations by changing particle separations and thus varying the retardation effects. Finally, negative torque is also demonstrated in experiments from statistical analysis of the EBD trajectories. These results demonstrate novel rotational dynamics of nanoparticles in optical matter using circular polarization and open a new avenue to control orientational dynamics through coupling to interparticle separation.

Accuracy and Mechanistic Details of Optical Printing of Single Au and Ag Nanoparticles

Optical printing is a powerful all-optical method that allows the incorporation of colloidal nanoparticles (NPs) onto substrates with nanometric precision. Here, we present a systematic study of the accuracy of optical printing of Au and Ag NPs, using different laser powers and wavelengths. When using light of wavelength tuned to the localized surface plasmon resonance (LSPR) of the NPs, the accuracy improves as the laser power is reduced, whereas for wavelengths off the LSPR, the accuracy is independent of the laser power. Complementary studies of the printing times of the NPs reveal the roles of Brownian and deterministic motion. Calculated trajectories of the NPs, taking into account the interplay between optical forces, electrostatic forces, and Brownian motion, allowed us to rationalize the experimental results and gain a detailed insight into the mechanism of the printing process. A clear framework is laid out for future optimizations of optical printing and optical manipulation of NPs near substrates.