Holographic optical trapping of microrods and nanowires

Scannable Dual-Focus Metalens with Hybrid Phase

Metalenses with two foci in the longitudinal or transverse direction, called bifocal or dual-focus metalenses, are promising building blocks in tomography techniques, data storage, and optical tweezers. For practical applications, relative movement between the beam and specimen is required, and beam scanning is highly desirable for high-speed operation without vibration. However, dual-focus metalenses employ a hyperbolic phase that experiences off-axis aberrations, which is not suitable for beam scanning. Here, we demonstrated a scannable dual-focus metalens by employing a new phase called "hybrid phase". The hybrid phase consists of a hyperbolic phase inside and a quadratic phase outside to reduce off-axis aberrations while maintaining a high numerical aperture. We show that the two foci of the scannable dual-focus metalens move together without severe distortion for incident angles of up to 2.5°. Our design easily extends to the case of multifocusing, which is essential for various applications ranging from imaging to manipulation.

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.

Dynamics of angular momentum-torque conversion in silicon waveguides

We present a refined theoretical analysis on the relationship between the optical total angular momenta (TAM) and the optical torque (OT) in a birefringent silicon waveguide. By using the vector angular spectrum method, we demonstrate the dynamic evolutions of the OT, TAM, spin angular momentum (SAM), and orbital angular momentum (OAM). The SAM and OAM coexist and evolve simultaneously in the propagation. The ratio between the OAM and TAM is related to the incident wavelength and the size of waveguide. Moreover, we design a three-layer waveguide structure to convert the light chirality and generate high torque. The performance of such torque-generator is analyzed numerically in detail.

Giant and tunable optical torque for micro-motors by increased force arm and resonantly enhanced force

Micro-motors driven by light field have attracted much attentions for their potential applications. In order to drive the rotation of a micro-motor, structured optical beams with orbital angular momentum, spin angular momentum, anisotropic medium, and/or inhomogeneous intensity distribution should be used. Even though, it is still challenge to increase the optical torques (OT) in a flexible and controllable way in case of moderate incident power. In this paper, a new scheme achieving giant optical torque is proposed by increasing both the force arm and the force amplitude with the assistance of a ring resonator. In this case, the optical torque doesn’t act on the target directly by the incident beam, but is transmitted to it by rotating the ring resonator connected with it. Using the finite-difference in time-domain method, we calculate the optical torque and find that both the direction and the amplitude of the torque can be tuned flexibly by modifying the frequency, or the relative phases of the sources. More importantly, the optical torque obtained here by linearly polarized beams can be 3 orders larger than those obtained using the structured beams. This opt-mechanical-resonator based optical torque engineering system may find potential applications in optical driven micro-machines.

Extending calibration-free force measurements to optically-trapped rod-shaped samples

Optical trapping has become an optimal choice for biological research at the microscale due to its non-invasive performance and accessibility for quantitative studies, especially on the forces involved in biological processes. However, reliable force measurements depend on the calibration of the optical traps, which is different for each experiment and hence requires high control of the local variables, especially of the trapped object geometry. Many biological samples have an elongated, rod-like shape, such as chromosomes, intracellular organelles (e.g., peroxisomes), membrane tubules, certain microalgae, and a wide variety of bacteria and parasites. This type of samples often requires several optical traps to stabilize and orient them in the correct spatial direction, making it more difficult to determine the total force applied. Here, we manipulate glass microcylinders with holographic optical tweezers and show the accurate measurement of drag forces by calibration-free direct detection of beam momentum. The agreement between our results and slender-body hydrodynamic theoretical calculations indicates potential for this force-sensing method in studying protracted, rod-shaped specimens.

Computation of radiation pressure force exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beams using MLFMA

Due to special characteristics of nondiffraction and self reconstruction, the Bessel beams have attracted wide attention in optical trapping and appear to be a dramatic alternative to Gaussian beams. We present in this paper an efficient approach based on the surface integral equations (SIE) to compute the radiation pressure force (RPF) exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beam (HOBVB). The incident beam is described by vector expressions perfectly satisfy Maxwell's equations. The problem is formulated with the combined tangential formulation (CTF) and solved iteratively with the aid of the multilevel fast multipole algorithm (MLFMA). Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle and analytical expression for electromagnetic fields of incident beam in near region are used. The numerical predictions are compared with the results of the rigorous method for spherical particle to validate the accuracy of the approach. Some numerical results on relative large particles of complex shape, such as biconcave cell-like particles with different geometry parameters are given, showing powerful capability of our approach. These results are expected to provide useful insights into the RPF exerted on complex shaped particles by HOBVB.

Optical disassembly of cellular clusters by tunable 'tug-of-war' tweezers

Bacterial biofilms underlie many persistent infections, posing major hurdles in antibiotic treatment. Here we design and demonstrate 'tug-of-war' optical tweezers that can facilitate the assessment of cell-cell adhesion-a key contributing factor to biofilm development, thanks to the combined actions of optical scattering and gradient forces. With a customized optical landscape distinct from that of conventional tweezers, not only can such 'tug-of-war' tweezers stably trap and stretch a rod-shaped bacterium in the observing plane, but, more importantly, they can also impose a tunable lateral force that pulls apart cellular clusters without any tethering or mechanical movement. As a proof of principle, we examined a Sinorhizobium meliloti strain that forms robust biofilms and found that the strength of intercellular adhesion depends on the growth medium. This technique may herald new photonic tools for optical manipulation and biofilm study, as well as other biological applications.

Transformation and patterning of supermicelles using dynamic holographic assembly

Although the solution self-assembly of block copolymers has enabled the fabrication of a broad range of complex, functional nanostructures, their precise manipulation and patterning remain a key challenge. Here we demonstrate that spherical and linear supermicelles, supramolecular structures held together by non-covalent solvophobic and coordination interactions and formed by the hierarchical self-assembly of block copolymer micelle and block comicelle precursors, can be manipulated, transformed and patterned with mediation by dynamic holographic assembly (optical tweezers). This allows the creation of new and stable soft-matter superstructures far from equilibrium. For example, individual spherical supermicelles can be optically held in close proximity and photocrosslinked through controlled coronal chemistry to generate linear oligomeric arrays. The use of optical tweezers also enables the directed deposition and immobilization of supermicelles on surfaces, allowing the precise creation of arrays of soft-matter nano-objects with potentially diverse functionality and a range of applications.

Block copolymers can form micelles and assemblies of micelles (supermicelles) when placed in suitable solvents. Here, the authors use optical tweezers to control the arrangement and deposition of supermicelles into higher-order patterned nanostructures.

Computational study of radiation torque on arbitrary shaped particles with MLFMA

The surface integral equation (SIE) method is used for the computational study of radiation torque on arbitrarily shaped homogeneous particles. The Multilevel Fast Multipole Algorithm (MLFMA) is employed to reduce memory requirements and improve the capability of SIE. The resultant matrix equations are solved iteratively to obtain equivalent electric and magnetic currents. Then, radiation torque is computed using the vector flux of the pseudotensor over a spherical surface tightly enclosing the particle. We use, therefore, the analytical electromagnetic field expression for incident waves in the near region, instead of the far-field approximation. This avoids the error which may be caused when describing the incident beam. The numerical results of three kinds of non-spherical particles are presented to illustrate the validity and capability of the developed method. It is shown that our method can be applied to predict, in the rigorous sense, the torque from a beam of any shape on a particle of complex configuration with a size parameter as large as 650. The radiation torques on large ellipsoids are exemplified to show the performance of the method and to study the influence that different aspect ratios have on the results. Then, the code is used for the calculation of radiation torque on objects of complex shape including a biconcave cell-like particle and a motor with a non-smooth surface.

Optically driven oscillations of ellipsoidal particles. Part II: ray-optics calculations

We report numerical calculations on the mechanical effects of light on micrometer-sized dielectric ellipsoids immersed in water. We used a simple two-dimensional ray-optics model to compute the radiation pressure forces and torques exerted on the object as a function of position and orientation within the laser beam. Integration of the equations of motion, written in the Stokes limit, yields the particle dynamics that we investigated for different aspect ratios k. Whether the beam is collimated or focused, the results show that above a critical aspect ratio k(C), the ellipsoids cannot be stably trapped on the beam axis; the particle never comes to rest and rather oscillates permanently in a back-and-forth motion involving both translation and rotation in the vicinity of the beam. Such oscillations are a direct evidence of the non-conservative character of optical forces. Conversely, stable trapping can be achieved for k < k(C) with the particle standing idle in a vertical position. These predictions are in very good qualitative agreement with experimental observations. The physical origin of the instability may be understood from the force and torque fields whose structures greatly depend on the ellipsoid aspect ratio and beam diameter. The oscillations arise from a non-linear coupling of the forces and torques and the torque amplitude was identified as the bifurcation control parameter. Interestingly, simulations predict that sustained oscillations can be suppressed through the use of two coaxial counterpropagating beams, which may be of interest whenever a static equilibrium is required as in basic force and torque measurements or technological applications.

Optically driven oscillations of ellipsoidal particles. Part I: experimental observations

We report experimental observations of the mechanical effects of light on ellipsoidal micrometre-sized dielectric particles, in water as the continuous medium. The particles, made of polystyrene, have shapes varying between near disk-like (aspect ratio k = 0.2) to very elongated needle-like (k = 8). Rather than the very tightly focused beam geometry of optical tweezers, we use a moderately focused laser beam to manipulate particles individually by optical levitation. The geometry allows us varying the longitudinal position of the particle, and to capture images perpendicular to the beam axis. Experiments show that moderate-k particles are radially trapped with their long axis lying parallel to the beam. Conversely, elongated (k > 3) or flattened (k < 0.3) ellipsoids never come to rest, and permanently "dance" around the beam, through coupled translation-rotation motions. The oscillations are shown to occur in general, be the particle in bulk water or close to a solid boundary, and may be periodic or irregular. We provide evidence for two bifurcations between static and oscillating states, at k ≈ 0.33 and k ≈ 3 for oblate and prolate ellipsoids, respectively. Based on a recently developed 2-dimensional ray-optics simulation (Mihiretie et al., EPL 100, 48005 (2012)), we propose a simple model that allows understanding the physical origin of the oscillations.

An optically actuated surface scanning probe

We demonstrate the use of an extended, optically trapped probe that is capable of imaging surface topography with nanometre precision, whilst applying ultra-low, femto-Newton sized forces. This degree of precision and sensitivity is acquired through three distinct strategies. First, the probe itself is shaped in such a way as to soften the trap along the sensing axis and stiffen it in transverse directions. Next, these characteristics are enhanced by selectively position clamping independent motions of the probe. Finally, force clamping is used to refine the surface contact response. Detailed analyses are presented for each of these mechanisms. To test our sensor, we scan it laterally over a calibration sample consisting of a series of graduated steps, and demonstrate a height resolution of ∼ 11 nm. Using equipartition theory, we estimate that an average force of only ∼ 140 fN is exerted on the sample during the scan, making this technique ideal for the investigation of delicate biological samples.

Equilibrium orientations and positions of non-spherical particles in optical traps

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

Stability analysis and thermal motion of optically trapped nanowires

We investigate the stability and thermal motion of optically trapped nanowires, with aspect ratios in the range 10-100. A simple analytical model is used to determine qualitative features of the system, assuming that the nanowire is weakly scattering and the incident beam is paraxial. As expected, the model predicts that the nanowire will align with the beam axis. In this configuration the translational stiffness coefficients of the trap approach their limiting values for long nanowires like O(L(-3)), where L is the nanowire length, the limit for the stiffness parallel to the beam axis being zero. The rotational stiffness coefficients vary more slowly, according to O(L(-1)). Also, it is predicted that defocusing decreases the translational stiffness perpendicular to the beam, while increasing rotational stiffness. These findings are reinforced by comparison with rigorous electromagnetic calculations which additionally reveal the effects of radiation pressure and finite scattering. A strong polarization effect is observed in the numerical simulations and coupled translational and rotational motions arise which influence the trap stability. The use of nanowire traps for force sensing is discusse.

Unconventional structure-assisted optical manipulation of high-index nanowires in liquid crystals

Stable optical trapping and manipulation of high-index particles in low-index host media is often impossible due to the dominance of scattering forces over gradient forces. Here we explore optical manipulation in liquid crystalline structured hosts and show that robust optical manipulation of high-index particles, such as GaN nanowires, is enabled by laser-induced distortions in long-range molecular alignment, via coupling of translational and rotational motions due to helicoidal molecular arrangement, or due to elastic repulsive interactions with confining substrates. Anisotropy of the viscoelastic liquid crystal medium and particle shape give rise to a number of robust unconventional trapping capabilities, which we use to characterize defect structures and study rheological properties of various thermotropic liquid crystals.

Automatic transportation of biological cells with a robot-tweezer manipulation system

The positioning of biological cells has become increasingly important in biomedical research such as drug discovery, cell-to-cell interaction, and tissue engineering. Significant demand for both accuracy and productivity in cell manipulation highlights the need for automated cell transportation with integrated robotics and micro/nano-manipulation technologies. Optical tweezers, which use highly focused low-power laser beams to trap and manipulate particles at the micro/nanoscale, can be treated as special robot ‘end-effectors’ to manipulate biological objects in a noninvasive way. In this paper, we propose to use a robot-tweezer manipulation system for automatic transportation of biological cells. A dynamics equation of the cell in an optical trap is analyzed. Closed-loop controllers are designed for positioning single cells as well as multiple cells. A synchronization control technology is utilized for multicell transportation with maintained cell pattern. Experiments are performed on transporting live cells to demonstrate the effectiveness of the proposed approach.

Application of the discrete dipole approximation to optical trapping calculations of inhomogeneous and anisotropic particles

The accuracy of the discrete dipole approximation (DDA) for computing forces and torques in optical trapping experiments is discussed in the context of dielectric spheres and a range of low symmetry particles, including particles with geometric anisotropy (spheroids), optical anisotropy (birefringent spheres) and structural inhomogeneity (core-shell spheres). DDA calculations are compared with the results of exact T-matrix theory. In each case excellent agreement is found between the two methods for predictions of optical forces, torques, trap stiffnesses and trapping positions. Since the DDA lends itself to calculations on particles of arbitrary shape, the study is augmented by considering more general systems which have received recent experimental interest. In particular, optical forces and torques on low symmetry letter-shaped colloidal particles, birefringent quartz cylinders and biphasic Janus particles are computed and the trapping behaviour of the particles is discussed. Very good agreement is found with the available experimental data. The efficiency of the DDA algorithm and methods of accelerating the calculations are also discussed.

Automated Transportation of Single Cells Using Robot-Tweezer Manipulation System

Manipulation of biological cells becomes increasingly important in biomedical engineering to address challenge issues in cell—cell interaction, drug discovery, and tissue engineering. Significant demand for both accuracy and productivity in cell manipulation highlights the need for automated cell transportation with integrated robotics and micro/nano manipulation technologies. Optical tweezers, which use highly focused low-power laser beams to trap and manipulate particles at micro/nanoscale, have emerged as an essential tool for manipulating single cells. In this article, we propose to use a robot-tweezer manipulation system to solve the problem of automatic transportation of biological cells, where optical tweezers function as special robot end effectors. Dynamics equation of the cell in optical tweezers is analyzed. A closed-loop controller is designed for transporting and positioning cells. Experiments are performed on live cells to demonstrate the effectiveness of the proposed approach in effective cell positioning.

Three-dimensional to two-dimensional crossover in the hydrodynamic interactions between micron-scale rods

Moving micron-scale objects are strongly coupled to each other by hydrodynamic interactions. The strength of this coupling decays with the inverse particle separation when the two objects are sufficiently far apart. It has been recently demonstrated that the reduced dimensionality of a thin fluid layer gives rise to longer-ranged, logarithmic coupling. Using holographic tweezers we show that microrods display both behaviors interacting like point particles in three dimensions at large distances and like point particles in two dimensions for distances shorter then their length. We derive a simple analytical expression that fits our data remarkably well and further validate it with finite element analysis.

Optical trapping of microrods: variation with size and refractive index

Optical traps can be characterized in terms of two simple parameters: the stiffness, given by the gradient of the force at mechanical equilibrium, and the strength, as expressed by the maximum restoring force available for displacement in a given direction. We present numerical calculations of these quantities for dielectric microrods of varying radius and refractive index held horizontally in pairs of holographically generated Gaussian beams. The resulting variations are seen to be influenced by optical resonances, as well as by the relative sizes of the beam waist and rod diameter. In addition, it is shown that trapping in these systems is sensitive to the polarization state of the incident field; i.e., for certain rods, trapping will occur for beams polarized perpendicular to the long axis of the rod, but not for beams polarized parallel to the long axis. Finally, friction coefficients are evaluated and used to estimate the maximum rates at which the rods may be dragged through the ambient medium.

Mathieu beams as versatile light moulds for 3D micro particle assemblies

We present tailoring of three dimensional light fields which act as light moulds for elaborate particle micro structures of variable shapes. Stereo microscopy is used for visualization of the 3D particle assemblies. The powerful method is demonstrated for the class of propagation invariant beams, where we introduce the use of Mathieu beams as light moulds with non-rotationally-symmetric structure. They offer multifarious field distributions and facilitate the creation of versatile particle structures. This general technique may find its application in micro fluidics, chemistry, biology, and medicine, to create highly efficient mixing tools, for hierarchical supramolecular organization or in 3D tissue engineering.

First-order nonconservative motion of optically trapped nonspherical particles

It is well known that optical force fields are not conservative. This has important consequences for the thermal motion of optically trapped dielectric spheres. In particular, the spheres do not reach thermodynamic equilibrium. Instead, a steady state is achieved in which the stochastic trajectory contains an underlying deterministic bias toward cyclic motion, and the energy of the sphere deviates from that implied by the equipartition theorem. Such effects are second order and only observed at low trap powers when the sphere is able to explore regions of the trap beyond the linear regime. Analogous effects may be expected for particles of less than spherical symmetry. However, in this case the effects are first order and depend on the linear term in the optical force field. As such they are not suppressed by increases in beam power, although the frequency and amplitude of the cyclic motion will be affected by it. In this paper, we present an analysis of the first-order nonconservative behavior of nonspherical particles in optical traps. The analysis is supported by optical force calculations and brownian dynamics simulations of dielectric microrods held vertically in gaussian optical traps.

Orbital motion of optically trapped particles in Laguerre-Gaussian beams

A theoretical examination of off-axial trapping in non-paraxial Laguerre-Gaussian beams is presented for both the Rayleigh and Mie regimes. It is well known that the force acting on a particle may be divided into a term proportional to the intensity gradient and another representing the scattering force. The latter term may be further sub-divided into a dissipative radiation force and a term dependent on the electric field gradient. For Rayleigh particles in Laguerre-Gaussian beams, it is shown that the field gradient term contributes exactly half of the scattering force. This may be compared with a plane wave, in which it makes zero contribution. The off-axis trapping positions for spheres with radii varying from 0.1 to 0.5 mum and a range of refractive indices are calculated numerically in the Mie regime, using a conjugate gradient approach. Azimuthal forces and orbital torques are presented for particles in their trapping positions, for beams with different orbital angular momentum and polarization states. The components of a "spin" torque, acting through the center of the particle, are also computed for absorbing particles in the Mie regime.