Non-conservative optical forces

Electrodynamic Interference and Induced Polarization in Nanoparticle-Based Optical Matter Arrays

Optical matter (OM) arrays are self-organizing, ordered arrangements of nanometer- to micrometer-size particles, where interparticle forces are mediated by incident and scattered coherent light. The structures that form and their dynamics depend on the properties (e.g., material, size) of the constituent particles, as well as the incident and scattered light. While significant progress has been made toward understanding how the OM arrays are affected by the phase, polarization, and intensity profile of the incident light, the polarization induced in the particles and the light scattered by OM arrays have received less attention. In this paper, we establish the roles of electrodynamic interference, many-body coupling, and induced-polarization concomitant with the coherent light scattered by OM arrays. Experiments and simulations together demonstrate that the spatial profile and directionality of coherent light scattered by OM arrays in the far field are primarily influenced by interference, while electrodynamic coupling (interactions) and the associated polarization induced in the nanoparticle constituents have a quantitative wavelength-dependent effect on the total amount of light scattered by the arrays. Furthermore, the electrodynamic coupling in silver nanoparticle OM arrays is significantly enhanced by constructive interference and increases superextensively with the number of particles in the array. Particle size, and hence polarizability, also has a significant effect on the strength of the coupling. Finally, we simulate larger hexagonal OM arrays of Ag nanoparticles to demonstrate that the electrodynamic coupling and scattering enhancement observed in small OM arrays develop into surface lattice resonances observed in the infinite array limit. Our work provides insights for designing OM arrays to tune many-body forces and the coherent light that they scatter.

Helicity and Polarization Gradient Optical Trapping in Evanescent Fields

Optical traps using nonconservative forces instead of conservative intensity-gradient forces expand the trap parameter space. Existing traps with nonconservative helicity-dependent forces are limited to chiral particles and fields with helicity gradients. We relax these constraints by proposing helicity and polarization gradient optical trapping of achiral particles in evanescent fields. We further propose an optical switching system in which a microsphere is trapped and optically manipulated around a microfiber using polarization gradients. Our Letter deepens the understanding of light-matter interactions in polarization gradient fields and expands the range of compatible particles and stable trapping fields.

Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum

We explore, experimentally and theoretically, the emergence of coherent coupled oscillations and synchronization between a pair of non-Hermitian, stochastic, opto-mechanical oscillators, levitated in vacuum. Each oscillator consists of a polystyrene microsphere trapped in a circularly polarized, counter-propagating Gaussian laser beam. Non-conservative, azimuthal forces, deriving from inhomogeneous optical spin, push the micro-particles out of thermodynamic equilibrium. For modest optical powers each particle shows a tendency towards orbital circulation. Initially, their stochastic motion is weakly correlated. As the power is increased, the tendency towards orbital circulation strengthens and the motion of the particles becomes highly correlated. Eventually, centripetal forces overcome optical gradient forces and the oscillators undergo a collective Hopf bifurcation. For laser powers exceeding this threshold, a pair of limit cycles appear, which synchronize due to weak optical and hydrodynamic interactions. In principle, arrays of such Non-Hermitian elements can be arranged, paving the way for opto-mechanical topological materials or, possibly, classical time crystals. In addition, the preparation of synchronized states in levitated optomechanics could lead to new and robust sensors or alternative routes to the entanglement of macroscopic objects.

Tunable optical traps over nonreciprocal surfaces

We propose engineering optical traps over plasmonic surfaces and precisely controlling the trap position with an external bias by inducing in-plane nonreciprocity on the surface. The platform employs an incident Gaussian beam to polarize targeted nanoparticles, and exploits the interplay between nonreciprocal and spin-orbit lateral recoil forces to construct stable optical traps and manipulate their position within the surface. To model this process, we develop a theoretical framework based on the Lorentz force combined with nonreciprocal Green's functions and apply it to calculate the trapping potential. Rooted on this formalism, we explore the exciting possibilities offered by graphene to engineer stable optical traps using low-power laser beams in the mid-IR and to manipulate the trap position in a continuous manner by applying a longitudinal drift bias. Nonreciprocal metasurfaces may open new possibilities to trap, assemble and manipulate nanoparticles and overcome many challenges faced by conventional optical tweezers while dealing with nanoscale objects.

Synergistic action in colloidal heat engines coupled by non-conservative flows

Colloidal heat engines are model systems to analyze mechanisms of transduction of heat to work at the mesoscale. While engines developed hitherto were realized using conservative potentials and operated in isolation, biological micromotors - their real counterparts - seldom perform under such simplifications. Here, we examine thermodynamics beyond such idealizations by constructing a pair of engines from two colloidal microspheres in optical traps at close separation. We demonstrate that at such proximity, non-conservative scattering forces that were hitherto neglected affect the particle motion. Hydrodynamics generated while dissipating these are hindered by the microsphere in the adjacent trap and energy that was otherwise rejected into the medium gets reused. Thus, despite being in contact with the same reservoir, the particles are driven out of equilibrium and can exchange energy, allowing cooperative behavior. Leveraging this in a manner analogous to microswimmers and active Brownian particles that utilize such flows to enhance propulsion, we construct two colloidal engines in close proximity. To estimate thermodynamic quantities, we develop a minimal model that is appropriate in the asymptotic limit and is similar to active Brownian particles. While complete theoretical frameworks to understand such scenarios remain to be developed, results based on our model demonstrate the intuitive idea that a pair of Stirling engines at close proximity outperform those that are well separated. Although these results explore the simplest case of two Stirling engines, the concepts unraveled could aid in designing larger collections akin to biological systems.

Recent Progress on Optical Micro/Nanomanipulations: Structured Forces, Structured Particles, and Synergetic Applications

Optical manipulation has achieved great success in the fields of biology, micro/nano robotics and physical sciences in the past few decades. To date, the optical manipulation is still witnessing substantial progress powered by the growing accessibility of the complex light field, advanced nanofabrication and developed understandings of light-matter interactions. In this perspective, we highlight recent advancements of optical micro/nanomanipulations in cutting-edge applications, which can be fostered by structured optical forces enabled with diverse auxiliary multiphysical field/forces and structured particles. We conclude with our vision of ongoing and futuristic directions, including heat-avoided and heat-utilized manipulation, nonlinearity-mediated trapping and manipulation, metasurface/two-dimensional material based optical manipulation, as well as interface-based optical manipulation.

Electromagnetic forces in nanoparticles made of multilayer hyperbolic metamaterials

We theoretically study the electromagnetic forces (optical gradient force, optical torque and vacuum friction) acting on a spherical anisotropic nanoparticle, which can be characterized by multilayer hyperbolic metamaterials (mHMMs). We find three important results about these forces: (i) Firstly, we theoretically demonstrate that the optical gradient force produced on a mHMMs nanoparticle can be flexibly tuned, from pushing the particle to pulling it, just via changing incident angle of illuminating plane light wave. (ii) Secondly, we find the optical torque acting on the mHMMs nanoparticle (its filling factor is around 0.3) can be tuned between positive and negative via changing the incident angle of circularly polarized plane light. Therefore, the rotating mHMMs nanoparticle with designed filling factor can be accelerated or decelerated by the optical torque. (iii) Finally, due to the large fluctuations of dipole polarizability of mHMMs nanoparticle with appropriate filling factor, we propose a new method to obtain the large enhancement of vacuum friction torque by designing the filling factor of the rotating mHMMs nanoparticle.

Enhanced transverse optical gradient force on Rayleigh particles in two plane waves

Based on the full wave simulation and the Maxwell stress tensor theory, we demonstrate an enhanced transverse optical gradient force acting on Rayleigh particles immersed in a simple optical field formed by two linearly polarized plane waves. The optical gradient force acting on a conventional dielectric particle can be enhanced by two orders of magnitude via coating an extremely thin silver shell, whose thickness is only about one-tenth of the dielectric core. The analytical results based on the multipole expansion theory reveal that the enhanced optical gradient force comes mostly from the interaction between the incident field and the electric quadrupole excited in the core-shell particle. It is worth noting that the force expression within the dipole approximation commonly used for Rayleigh particles is invalid in our situation, even the particle is within the Rayleigh regime. In addition, both the optical potential energy and the optical trapping stiffness for the core-shell particle exhibit a great enhancement by two orders of magnitude stronger than a conventional dielectric particle and thus is favorable to a stable optical trapping. These results may extend the application range of optical tweezers and enrich optical manipulation techniques.

Optical Trapping Separation of Chiral Nanoparticles by Subwavelength Slot Waveguides

Enantiomer separation opens great opportunities to develop the technologies of pharmaceutics, chemicals, and biomedicine, but faces daunting challenges. Here, we discover a considerable chiral-dependent trapping force to separate nanometer-scale enantiomers in a new silicon-based waveguide platform. The electromagnetic chirality gradient of strongly confined evanescent fields can be largely enhanced by the counterpropagating slot waveguides so that the resulting chiral gradient forces can shift the trapping equilibrium positions of dielectric gradient forces. Especially, there exists a transitional width for the slot waveguides to exchange the trapping equilibrium positions between two opposite enantiomers. Our thoroughly numerical investigations demonstrate that the chiral-separable slot waveguides here can offer high efficiency and feasibility of separating chiral nanoparticles, and may pave a route toward new on-chip chiral optical tweezers or optofluidic transport systems for large-scale chiral separation.

Non-Hermitian physics for optical manipulation uncovers inherent instability of large clusters

Intense light traps and binds small particles, offering unique control to the microscopic world. With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually "melts" the light-bound structures. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. As such, optical forces alone fail to bind a large cluster. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation.

Metamachines of pluripotent colloids

Machines enabled the Industrial Revolution and are central to modern technological progress: A machine's parts transmit forces, motion, and energy to one another in a predetermined manner. Today's engineering frontier, building artificial micromachines that emulate the biological machinery of living organisms, requires faithful assembly and energy consumption at the microscale. Here, we demonstrate the programmable assembly of active particles into autonomous metamachines using optical templates. Metamachines, or machines made of machines, are stable, mobile and autonomous architectures, whose dynamics stems from the geometry. We use the interplay between anisotropic force generation of the active colloids with the control of their orientation by local geometry. This allows autonomous reprogramming of active particles of the metamachines to achieve multiple functions. It permits the modular assembly of metamachines by fusion, reconfiguration of metamachines and, we anticipate, a shift in focus of self-assembly towards active matter and reprogrammable materials.

Quantitative study of conservative gradient force and non-conservative scattering force exerted on a spherical particle in optical tweezers

We rigorously calculate the conservative gradient force (GF) and the non-conservative scattering force (SF) associated with the optical tweezers (the single beam optical trap). A wide range of parameters are considered, with particle size ranging from the Rayleigh to Mie regime (radius ∼3 µm), dielectric constant ranging from metallic (large and negative) to high dielectrics (large and positive), numerical aperture (NA) ranging from 0.5 to 1.33, and different polarizations. The trap depth associated with GF can reach 123 and 168 k_BT per mW for a 0.5 µm-radius polystyrene particle illuminated by a 1064 nm Gaussian beam with NA = 0.9 and 1.3, respectively. This indicates that unless at a low beam power or with a small NA, the Brownian fluctuations do not play a role in the stability. The transverse GF orthogonal to beam propagation always dominates over the transverse SF. While the longitudinal SF can be larger than the longitudinal GF when the scattering is strong, the NA is small, or when absorption is present, optical trapping under these conditions is difficult. Generally speaking, absorption reduces GF and enhances SF, while increasing a dielectric constant enhances GF slightly but boosts SF significantly owing to stronger scattering. These results verify previous experimental observations and explain why optical tweezers are so robust across such a wide range of conditions. Our quantitative calculations will also provide a guide to future studies.

Colloidal density control with Bessel-Gauss beams

Optical manipulation of colloidal systems is of high interest for both fundamental studies and practical applications. It has been shown that optically induced thermophoresis and nonlinear interactions can significantly affect the properties of dense colloidal media. However, macroscopic scale phenomena can also be generated at thermal equilibrium. Here, we demonstrate that steady-state variations of particle density can be created over large, three-dimensional regions by appropriately structured external optical fields. We prove analytically and experimentally that an optical vortex beam can dynamically control the spatial density of microscopic particles along the direction of its propagation. We show that these artificial steady-states can be generated at will and can be maintained indefinitely, which can be beneficial for applications such as path clearing and mass transportation.

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.

Tailoring the gradient and scattering forces for longitudinal sorting of generic-size chiral particles

Based on the concepts of conservative and non-conservative optical forces (COF and NCOF), we analyze the physical mechanism of longitudinal chirality sorting along the direction of light propagation in some simple optical fields. It is demonstrated, both numerically and analytically for particle of arbitrary size, that the sorting relies solely on the NCOF, which switches its direction when particle chirality is reversed. For particles larger than half of the optical wavelength λ, the NCOF far surpasses its counterpart COF, enabling the longitudinal chirality sorting. When the particle is much smaller than λ, however, the COF outweighs the NCOF, destroying the sorting mechanism. A scenario is thus proposed that totally eliminates the COF while leaving the sorting NCOF unchanged, extending the applicability of longitudinal chirality sorting to small particles.

Lateral Optical Force due to the Breaking of Electric-Magnetic Symmetry

Lateral optical forces in a direction perpendicular to light propagation have attracted increasing interest in recent years. Up to now, all lateral forces can be attributed to the symmetry breaking in the lateral directions caused by either the morphology of the scatterer geometry or the optical fields impinging on the scatterer. Here we demonstrate, both numerically and analytically, that when an isotropic scatterer breaks the electric-magnetic symmetry, a new type of anomalous lateral force can be induced along the direction of translational invariance where the illumination striking the scatterer has no propagation, field gradient, or spin density vortex (Belinfante's spin momentum). Our analytical results are rigorous for an arbitrary size scatterer, ensuring the universality of our conclusion. Furthermore, the electric-magnetic symmetry-breaking-induced lateral force is comparable in magnitude to other components of the optical force and reversible in direction for different polarizations of the illuminating light, rendering it capable of practical optical manipulation as well as enriching the understanding of light-matter interaction.

Optical Sorting at the Single-Particle Level with Single-Nanometer Precision Using Coordinated Intensity and Phase Gradient Forces

Position-controlled sorting of colloidal nanoparticles (NPs) at the single-particle level is a challenge in nanoscience. Optofluidic potential wells can partially address this challenge, but they have limited flexibility, reconfigurability, and precision. Here we introduce a strategy by feedback-controlled manipulation of NPs using reconfigurable optical traps with designed intensity and phase gradient. Spatiotemporal patterns of these optical traps coordinatively manipulate the NPs based on machine vision of their positions and differentiated scattering intensities. The NPs are always kept inside the optical field during the manipulation and stably trapped once the sorting is accomplished. To substantiate the key advantages of our approach, we present position-controlled optical sorting of single Ag and Au NPs of the same size (150 nm diameter) and ordering of monodisperse Au NPs (80 ± 9 nm diameter) according to their sub-10 nm radius variation, which can hardly be done via other approaches.

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling

We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 10⁸ at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.

Momentum-Topology-Induced Optical Pulling Force

We report an ingenious mechanism to obtain robust optical pulling force by a single plane wave via engineering the topology of light momentum in the background. The underlying physics is found to be the topological transition of the light momentum from a usual convex shape to a starlike concave shape in the carefully designed background, such as a photonic crystal structure. The principle and results reported here shed insightful concepts concerning optical pulling, and pave the way for a new class of advanced optical manipulation technique, with potential applications of drug delivery and cell sorting.

Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities

We examine acoustic radiation force and torque on a small (subwavelength) absorbing isotropic particle immersed in a monochromatic (but generally inhomogeneous) sound-wave field. We show that by introducing the monopole and dipole polarizabilities of the particle, the problem can be treated in a way similar to the well-studied optical forces and torques on dipole Rayleigh particles. We derive simple analytical expressions for the acoustic force (including both the gradient and scattering forces) and torque. Importantly, these expressions reveal intimate relations to the fundamental field properties introduced recently for acoustic fields: the canonical momentum and spin angular momentum densities. We compare our analytical results with previous calculations and exact numerical simulations. We also consider an important example of a particle in an evanescent acoustic wave, which exhibits the mutually orthogonal scattering (radiation-pressure) force, gradient force, and torque from the transverse spin of the field.

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.

Directional scattering and multipolar contributions to optical forces on silicon nanoparticles in focused laser beams

Nanoparticles made of high index dielectric materials have seen a surge of interest and have been proposed for various applications, such as metalenses, light harvesting and directional scattering. With the advent of fabrication techniques enabling colloidal suspensions, the prospects of optical manipulation of such nanoparticles becomes paramount. High index nanoparticles support electric and magnetic multipolar responses in the visible regime and interference between such modes can give rise to highly directional scattering, in particular a cancellation of back-scattered radiation at the first Kerker condition. Here we present a study of the optical forces on silicon nanoparticles in the visible and near infrared calculated using the transfer matrix method. The zero-backscattering Kerker condition is investigated as an avenue to reduce radiation pressure in an optical trap. We find that while asymmetric scattering does reduce the radiation pressure, the main determining factor of trap stability is the increased particle response near the geometric resonances. The trap stability for non-spherical silicon nanoparticles is also investigated and we find that ellipsoidal deformation of spheres enables trapping of slightly larger particles.

3D Optical Vortex Trapping of Plasmonic Nanostructure

3D optical vortex trapping upon a polystyrene nanoparticle (NP) by a 1D gold dimer array is studied theoretically. The optical force field shows that the trapping mode can be contact or non-contact. For the former, the NP is attracted toward a corresponding dimer. For the latter, it is trapped toward a stagnation point of zero force with a 3D spiral trajectory, revealing optical vortex. Additionally the optical torque causes the NP to transversely spin, even though the system is irradiated by a linearly polarized light. The transverse spin-orbit interaction is manifested from the opposite helicities of the spin and spiral orbit. Along with the growth and decline of optical vortices the trapped NP performs a step-like motion, as the array continuously moves. Our results, in agreement with the previous experiment, identify the role of optical vortex in the near-field trapping of plasmonic nanostructure.