Brownian particle in an optical potential of the washboard type

The Rise of the OM-LoC: Opto-Microfluidic Enabled Lab-on-Chip

The integration of optical circuits with microfluidic lab-on-chip (LoC) devices has resulted in a new era of potential in terms of both sample manipulation and detection at the micro-scale. On-chip optical components increase both control and analytical capabilities while reducing reliance on expensive laboratory photonic equipment that has limited microfluidic development. Notably, in-situ LoC devices for bio-chemical applications such as diagnostics and environmental monitoring could provide great value as low-cost, portable and highly sensitive systems. Multiple challenges remain however due to the complexity involved with combining photonics with micro-fabricated systems. Here, we aim to highlight the progress that optical on-chip systems have made in recent years regarding the main LoC applications: (1) sample manipulation and (2) detection. At the same time, we aim to address the constraints that limit industrial scaling of this technology. Through evaluating various fabrication methods, material choices and novel approaches of optic and fluidic integration, we aim to illustrate how optic-enabled LoC approaches are providing new possibilities for both sample analysis and manipulation.

Fokker-Planck analysis of optical near-field traps

The motion of a nanoparticle in the vicinity of a near-field optical trap is modeled using the Fokker-Planck equation. A plasmonic C-shaped engraving on a gold film is considered as the optical trap. The time evolution of the position probability density of the nanoparticle is calculated to analyze the trapping dynamics. A spatially varying diffusion tensor is used in the formulation to take into account the hydrodynamic interactions. The steady-state position distribution obtained from the Fokker-Planck equation is compared with experimental results and found to be in good agreement. Computational cost of the proposed method is compared with the conventionally used Langevin equation based approach. The proposed method is found to be computationally efficient (requiring 35 times less computation time) and scalable to more complex lab-on-a-chip systems.

Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement

Particle trapping and binding in optical potential wells provide a versatile platform for various biomedical applications. However, implementation systems to study multi-particle contact interactions in an optical lattice remain rare. By configuring an optofluidic lattice, we demonstrate the precise control of particle interactions and functions such as controlling aggregation and multi-hopping. The mean residence time of a single particle is found considerably reduced from 7 s, as predicted by Kramer’s theory, to 0.6 s, owing to the mechanical interactions among aggregated particles. The optofluidic lattice also enables single-bacteria-level screening of biological binding agents such as antibodies through particle-enabled bacteria hopping. The binding efficiency of antibodies could be determined directly, selectively, quantitatively and efficiently. This work enriches the fundamental mechanisms of particle kinetics and offers new possibilities for probing and utilising unprecedented biomolecule interactions at single-bacteria level.

Optical trapping is a versatile tool for biomedical applications. Here, the authors use an optofluidic lattice to achieve controllable multi-particle hopping and demonstrate single-bacteria-level screening and measurement of binding efficiency of biological binding agents through particle-enabled bacteria hopping.

Continuous-feed optical sorting of aerosol particles

We consider the problem of sorting, by size, spherical particles of order 100 nm radius. The scheme we analyze consists of a heterogeneous stream of spherical particles flowing at an oblique angle across an optical Gaussian mode standing wave. Sorting is achieved by the combined spatial and size dependencies of the optical force. Particles of all sizes enter the flow at a point, but exit at different locations depending on size. Exiting particles may be detected optically or separated for further processing. The scheme has the advantages of accommodating a high throughput, producing a continuous stream of continuously dispersed particles, and exhibiting excellent size resolution. We performed detailed Monte Carlo simulations of particle trajectories through the optical field under the influence of convective air flow. We also developed a method for deriving effective velocities and diffusion constants from the Fokker-Planck equation that can generate equivalent results much more quickly. With an optical wavelength of 1064 nm, polystyrene particles with radii in the neighborhood of 275 nm, for which the optical force vanishes, may be sorted with a resolution below 1 nm.

Controlling chaos-assisted directed transport via quantum resonance

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Angular scattering of light by a homogeneous spherical particle in a zeroth-order Bessel beam and its relationship to plane wave scattering

The angular scattering of light from a homogeneous spherical particle in a zeroth-order Bessel beam is calculated using a generalized Lorenz-Mie theory. We investigate the dependence of the angular scattering on the semi-apex angle of the Bessel beam and discuss the major features of the resulting scattering plots. We also compare Bessel beam scattering to plane wave scattering and provide criterion for when the difference between the two cases can be considered negligible. Finally, we discuss a method for characterizing spherical particles using angular light scattering. This work is useful to researchers who are interested in characterizing particles trapped in optical beams using angular dependent light scattering measurements.

Diffusion and mobility of anisotropic particles in tilted periodic structures

We numerically investigated the transport of anisotropic particles in tilted periodic structures. The diffusion and mobility of the particles demonstrate distinct behaviors dependence on the shape of the particles. In two-dimensional (2D) periodic potentials, we find that the mobility is influenced a little by the anisotropy of the particle, while the diffusion increases monotonically with the increasing of the particle anisotropy for large enough biased force. However, due to the sensitivity of the channels for the particle anisotropy, the transport in smooth channels is obviously different from that in energy potentials. The mobility decreases monotonically with the increasing of the particle anisotropy, while the diffusion can be a non-monotonic function of the particle anisotropy with a peak under appropriate biased force.

Transport and trapping in two-dimensional nanoscale plasmonic optical lattice

We report the transport and trapping behavior of 100 and 500 nm diameter nanospheres in a plasmon-enhanced two-dimensional optical lattice. An optical potential is created by a two-dimensional square lattice of gold nanostructures, illuminated by a Gaussian beam to excite plasmon resonance. The nanoparticles can be guided, trapped, and arranged using this optical potential. Stacking of 500 nm nanospheres into a predominantly hexagonal closed pack crystalline structure under such a potential is also reported.

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping

Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.

SYNCHRONIZATION AND TRANSPORT IN AN OSCILLATING PERIODIC POTENTIAL

We study the motion of overdamped Brownian particles in a periodic potential with a temporally oscillating amplitude. First we investigate diffusive motion in the untitled potential. Furthermore, if a constant force is applied, the oscillating potential induces a synchronized motion. The deterministic dynamics becomes in resonance with the potential oscillations. This dynamics gives rise to a transport with extremely low dispersion. We distinguish slow and fast oscillatory driving and give analytical expressions for the mean velocity and effective diffusion.

Shear-flow-enhanced barrier crossing

We consider a single Brownian particle confined in a double well potential (DWP) and investigate its response to a linear shear flow by means of the probability density and current determined via numerical solution of the Fokker-Planck equation. Besides a shear-dependent distortion of the probability distribution, we find that the associated current crossing the potential barrier exhibits a convex dependency on the shear rate when the DWP's minima are far apart. With decreasing distance this functional dependency changes from a convex to concave characteristics accompanied with an increase of the probability current crossing the DWP's barrier. Through the difference map of the particle density distribution it is possible to extract the shear-flow-induced contribution to the particle density driving the barrier-crossing current. This may open the possibility to design specific flow profiles to optimize flow-induced activated transport of nanoparticles.

Quasideterministic transport of Brownian particles in an oscillating periodic potential

We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the diffusion coefficient. Furthermore we analyze the effect of the oscillating potential on the transport if additionally a constant force is applied. We show the existence of synchronization regimes at which the deterministic dynamics is in resonance with the potential oscillations, giving rise to transport with extremely low dispersion. We distinguish slow and fast oscillatory driving and give analytical expressions for the mean velocity and effective diffusion.

Optically modulated electrokinetic manipulation and concentration of colloidal particles near an electrode surface

We study a recently demonstrated AC electrokinetic technique for manipulation and concentration of colloidal particles on an electrode surface. The technique uses indium tin oxide (ITO)-based parallel-plate electrodes on which highly localized infrared (1064 nm) laser illumination is shone. We show that the highly localized laser illumination leads to a highly nonuniform heating of the electrode substrate, which in turn drives an electrothermal microvortex resulting in a rapid transport of particles toward the illuminated site. Hundreds of polystyrene particles, with diameters ranging from 2.0 to 0.1 microm, suspended in a low conductivity solution (2.0 mS/m) could be aggregated at selected locations on the electrode by activating the laser illumination at suitable AC frequencies. Subsequent deactivation of the laser illumination causes the particles to scatter, and we explore this dynamical behavior for 1.0 microm particles using Delaunay tessellations and high-speed videography. We establish that drag from the electrothermal microvortex acts against a repulsive force, which decreases with increasing AC frequency, to create stable particle clusters. Moreover, experimentally we show that this particle capturing technique can be characterized by a critical frequency: a frequency at which the captured colloidal particle cluster becomes unstable and particles are carried away into the bulk by the electrothermal microvortex. This critical frequency increases with decreasing particle diameter for similar particles. For 0.1 microm particles, comparison of aggregation at different AC frequencies is achieved by the comparison of fluorescent intensity profiles of the aggregations.

Gouy phase shift in nondiffracting Bessel beams

The results of a theoretical and experimental investigation of the Gouy effect in Bessel beams are presented. We point out that the peculiar feature of the Bessel beams of being nondiffracting is related to the accumulation of an extra axial phase shift (i.e., the Gouy phase shift) linearly dependent on the propagation distance. The constant spatial rate of variation of the Gouy phase shift is independent of the order of the Bessel beam, while it is a growing function of the transverse component of the angular spectrum wave-vectors, originated by the transverse confinement of the beam. A free-space Mach-Zehnder interferometer has been set-up for measuring the transverse intensity distribution of the interference between holographically-produced finite-aperture Bessel beams of order from zero up to three and a reference Gaussian beam, at a wavelength of 633 nm. The interference patterns have been registered for different propagation distances and show a spatial periodicity, in agreement with the expected period due to the linear increase of the Gouy phase shift of the realized Bessel beams.

Giant enhanced diffusion of gold nanoparticles in optical vortex fields

We study the diffusion of a metal nanoparticle in the nonconservative force field of an optical vortex lattice. Radiation pressure in the vortex array is shown to induce a giant enhancement over the free thermal diffusion. Langevin dynamics simulations show that the diffusion coefficient of (50 nm radius) gold particles at room temperature is enhanced by 2 orders of magnitude at power densities of the order or smaller than those used to trap nanoparticles with optical tweezers.

Phase-locking of magnetic vortices mediated by antivortices

Synchronized spin-valve oscillators may lead to nanosized microwave generators that do not require discrete elements such as capacitors or inductors. Uniformly magnetized oscillators have been synchronized, but offer low power. Gyrating magnetic vortices offer greater power, but vortex synchronization has yet to be demonstrated. Here we find that vortices can interact with each other through the mediation of antivortices, leading to synchronization when they are closely spaced. The synchronization does not require a magnetic field, making the system attractive for electronic device integration. Also, because each vortex is a topological soliton, this work presents a model experimental system for the study of interacting solitons.

Directed transport of an inertial particle in a washboard potential induced by delayed feedback

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist; for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noiseless case.

Current control in a tilted washboard potential via time-delayed feedback

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

Force mapping of an extended light pattern in an inclined plane: deterministic regime

We present a full quantitative mapping of the non-linear optical trapping force associated to an extended interference pattern of fringes as a function of the position. To map this force, we studied the dynamics of microscopic spherical beads of different sizes (8, 10 and 14.5 microns in diameter) moving through the light pattern. For this range of particle sizes, the system is overdamped due to the viscous drag and the effect of thermal noise is negligible. The novel experimental approach consists in tilting the sample cell a small angle with respect to the horizontal, thus we have a deterministic particle in an inclined plane. The combined action of the optical force and gravity gives rise to a washboard potential. We compared our experimental results with a ray optics model and found a good quantitative agreement. For each size of the microsphere we studied different spatial periods of the interference fringes.

Light at work: the use of optical forces for particle manipulation, sorting, and analysis

We review the combinations of optical micro-manipulation with other techniques and their classical and emerging applications to non-contact optical separation and sorting of micro- and nanoparticle suspensions, compositional and structural analysis of specimens, and quantification of force interactions at the microscopic scale. The review aims at inspiring researchers, especially those working outside the optical micro-manipulation field, to find new and interesting applications of these methods.

Phase synchronization in tilted inertial ratchets as chaotic rotators

The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of the external periodic forcing; this oscillator then acquires an intrinsic frequency that can be locked with the frequency of the external driving. We introduced an instantaneous linear phase, using a set of discrete time markers, and the associated average frequency, and show that this frequency can be synchronized with the frequency of the driving. We calculate Arnold tongues in a two-dimensional parameter space and discuss their implications for the chaotic transport in ratchets. We show that the local maxima in the current correspond to the borders of these Arnold tongues; in this way we established a link between optimal transport in ratchets and phase synchronization.

Transverse particle dynamics in a Bessel beam

Spatially periodic optical fields can be used to sort dielectric microscopic particles as a function of size, shape or refractive index. In this paper we elucidate through both theory and experiment the behavior of silica microspheres moving under the influence of the periodic optical field provided by a Bessel beam. We compare two different computational models, one based on Mie scattering, the other on geometrical ray optics and find good qualitative agreement, with both models predicting the existence of distinct size-dependent phases of particle behavior. We verify these predictions by providing experimental observations of the individual behavioral phases.

Characterizing potentials by a generalized Boltzmann factor

Based on the concept of a nonequilibrium steady state, we present a method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system, we explore potential landscapes with barriers up to several hundred k_BT. As an illustration, we use this approach to measure the effective diffusion coefficient of a colloidal particle moving in a tilted potential.

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

Cellular and Colloidal Separation Using Optical Forces

The separation or sorting of cellular and colloidal particles is currently a central topics of research. In this chapter, we give an overview of the range of optical methods for cell sorting. We begin with an overview of fluorescence and magnetically activated cell sorting. We progress to describing methods at the microfluidic scale level particularly those exploiting optical forces. We distinguish between what we term passive and active schemes for sorting. Optical forces pertinent to the sorting schemes are described, notably the gradient force and the optical radiation pressure (or scattering force). We discuss some of the most recent advances. This includes techniques without fluid flow where we have either stationary or moving light patterns to initiate separation. Further methods have shown how using an externally driven flow either counter-propagating against a light field (optical chromatography) or over a periodic light pattern (an optical potential energy landscape) may result in the selection of particles and cells based on physical attributes such as size and refractive index. We contrast these schemes with the field of dielectrophoresis where electric field gradients may separate cells and also briefly mention the upcoming area of light-induced dielectrophoresis which marries the reconfigurability of optical fields with the power of dielectrophoresis.

Microfluidic sorting in an optical lattice

The response of a microscopic dielectric object to an applied light field can profoundly affect its kinetic motion. A classic example of this is an optical trap, which can hold a particle in a tightly focused light beam. Optical fields can also be used to arrange, guide or deflect particles in appropriate light-field geometries. Here we demonstrate an optical sorter for microscopic particles that exploits the interaction of particles-biological or otherwise-with an extended, interlinked, dynamically reconfigurable, three-dimensional optical lattice. The strength of this interaction with the lattice sites depends on the optical polarizability of the particles, giving tunable selection criteria. We demonstrate both sorting by size (of protein microcapsule drug delivery agents) and sorting by refractive index (of other colloidal particle streams). The sorting efficiency of this method approaches 100%, with values of 96% or more observed even for concentrated solutions with throughputs exceeding those reported for fluorescence-activated cell sorting. This powerful, non-invasive technique is suited to sorting and fractionation within integrated ('lab-on-a-chip') microfluidic systems, and can be applied in colloidal, molecular and biological research.