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

Modelling red blood cell optical trapping by machine learning improved geometrical optics calculations

Optically trapping red blood cells allows for the exploration of their biophysical properties, which are affected in many diseases. However, because of their nonspherical shape, the numerical calculation of the optical forces is slow, limiting the range of situations that can be explored. Here we train a neural network that improves both the accuracy and the speed of the calculation and we employ it to simulate the motion of a red blood cell under different beam configurations. We found that by fixing two beams and controlling the position of a third, it is possible to control the tilting of the cell. We anticipate this work to be a promising approach to study the trapping of complex shaped and inhomogeneous biological materials, where the possible photodamage imposes restrictions in the beam power.

Generation of partial roll rotation in a hexagonal NaYF4 particle by switching between different optical trapping configurations

Typically a rigid body can have three degrees of rotational freedom. Among these, there can be two types of out-of-plane rotational modes, called the pitch and the roll. The pitch motion is typically to turn the particle along an axis orthogonal to the axis of symmetry. However, rotation about the axis of symmetry (called the roll motion) has so far not been shown in optical tweezers. It is here that we use a hexagonal shaped particle (NaYF₄) which prefers to align side on with the optical tweezers [Rodriguez-Sevilla et al., Nano Letters 16, 8005 (2016)]. In this work, we find that the stable configuration of the hexagonal particle changes while using one beam and two beams, so that when one of the tweezers beams is switched on and off, the particle tends to switch between the different configurations. Thus we get a controlled roll motion. This is the first time that controlled partial roll motions have been generated in optical tweezers.

Simulation and Experiment of the Trapping Trajectory for Janus Particles in Linearly Polarized Optical Traps

The highly focused laser beam is capable of confining micro-sized particle in its focus. This is widely known as optical trapping. The Janus particle is composed of two hemispheres with different refractive indexes. In a linearly polarized optical trap, the Janus particle tends to align itself to an orientation where the interface of the two hemispheres is parallel to the laser propagation as well as the polarization direction. This enables a controllable approach that rotates the trapped particle with fine accuracy and could be used in partial measurement. However, due to the complexity of the interaction of the optical field and refractive index distribution, the trapping trajectory of the Janus particle in the linearly polarized optical trap is still uncovered. In this paper, we focus on the dynamic trapping process and the steady position and orientation of the Janus particle in the optical trap from both simulation and experimental aspects. The trapping process recorded by a high speed camera coincides with the simulation result calculated using the T-matrix model, which not only reveals the trapping trajectory, but also provides a practical simulation solution for more complicated structures and trapping motions.

Brownian dynamics simulations of sphere clusters in optical tweezers

Computationally modeling the behavior of wavelength-sized non-spherical particles in optical tweezers can give insight into the existence and stability of trapping equilibria as well as the optical manipulation of such particles more broadly. Here, we report Brownian dynamics simulations of non-spherical particles that account for detailed optical, hydrodynamic, and thermal interactions. We use a T-matrix formalism to calculate the optical forces and torques exerted by focused laser beams on clusters of wavelength-sized spheres, and we incorporate detailed diffusion tensors that capture the anisotropic Brownian motion of the clusters. For two-sphere clusters whose size is comparable to or larger than the wavelength, we observe photokinetic effects in elliptically-polarized beams. We also demonstrate that multiple trapping equilibria exist for a highly asymmetric chiral cluster of seven spheres. Our simulations may lead to practical suggestions for optical trapping and manipulation as well as a deeper understanding of the underlying physics.

Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects

Since the invention of optical tweezers, optical manipulation has advanced significantly in scientific areas such as atomic physics, optics and biological science. Especially in the past decade, numerous optical beams and nanoscale devices have been proposed to mechanically act on nanoparticles in increasingly precise, stable and flexible ways. Both the linear and angular momenta of light can be exploited to produce optical tractor beams, tweezers and optical torque from the microscale to the nanoscale. Research on optical forces helps to reveal the nature of light-matter interactions and to resolve the fundamental aspects, which require an appropriate description of momenta and the forces on objects in matter. In this review, starting from basic theories and computational approaches, we highlight the latest optical trapping configurations and their applications in bioscience, as well as recent advances down to the nanoscale. Finally, we discuss the future prospects of nanomanipulation, which has considerable potential applications in a variety of scientific fields and everyday life.

Tomographic active optical trapping of arbitrarily shaped objects by exploiting 3D refractive index maps

Optical trapping can manipulate the three-dimensional (3D) motion of spherical particles based on the simple prediction of optical forces and the responding motion of samples. However, controlling the 3D behaviour of non-spherical particles with arbitrary orientations is extremely challenging, due to experimental difficulties and extensive computations. Here, we achieve the real-time optical control of arbitrarily shaped particles by combining the wavefront shaping of a trapping beam and measurements of the 3D refractive index distribution of samples. Engineering the 3D light field distribution of a trapping beam based on the measured 3D refractive index map of samples generates a light mould, which can manipulate colloidal and biological samples with arbitrary orientations and/or shapes. The present method provides stable control of the orientation and assembly of arbitrarily shaped particles without knowing a priori information about the sample geometry. The proposed method can be directly applied in biophotonics and soft matter physics.

Controlling the three-dimensional behaviour of arbitrarily shaped and oriented particles with optical tweezers is a challenging task. Here, Kim and Park use tomographic active trapping to manipulate non-spherical particles and particle ensembles as well as biological cells.

Optical Torque Wrench Design and Calibration

Expanding the capabilities of optical traps with angular control of the trapped particle has numerous potential applications in all fields where standard linear optical tweezers are employed. Here we describe in detail the construction, alignment, and calibration of the Optical Torque Wrench, a mode of function that can be added to linear optical tweezers to simultaneously apply and measure both force and torque on birefringent microscopic cylindrical particles. The interaction between the linear polarization of the laser and the birefringent cylinder creates an angular trap for the particle orientation, described by a periodic potential. As a consequence of the experimental control of the tilt of the periodic potential, the dynamical excitability of the system can be observed. Angular optical tweezers remain less widespread than their linear counterpart. We hope this technical guide can foster their development and new applications.

Optical trapping force and torque on spheroidal Rayleigh particles with arbitrary spatial orientations

We investigate the spatial orientation dependence of optical trapping forces and intrinsic torques exerted on spheroidal Rayleigh particles under irradiation of highly focused linearly and circularly polarized beams. It is revealed that the maximal trapping forces and torques strongly depend on the orientation of the spheroid, and the spheroidal particle is driven to be stably trapped at the beam focus with its major axis perpendicular to the optical axis. For a linearly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the polarization direction of the incident beam. Therefore, the spheroid tends to rotate its major axis along with the polarization direction. However, for a circularly polarized trapping beam, the optical torque is always perpendicular to the plane containing the major axis and the optical axis. What is different from the linear polarization case is that the spheroid tends to have the major axis parallel to the projection of the major axis in the transverse plane. The optical torque in the circular polarization case is half of that in the linear polarization case. These optical trapping properties may be exploited in practical optical manipulation, especially for the nonspherical particle's trapping.

Spin-controlled orbital motion in tightly focused high-order Laguerre-Gaussian beams

Spin angular momentum can contribute to both optical force and torque exerted on spheres. Orbit rate of spheres located in tightly focused LG beams with the same azimuthal mode index l is spin-controlled due to spin-orbit coupling. Laguerre-Gaussian beams with high-order azimuthal mode are used here to study the orbit rate of dielectric spheres. Orbit rates of spheres with varying sizes and refravtive indices are investigated as well as optical forces acting on spheres in LG beams with different azimuthal modes. These results would be much helpful to investigation on optical rotation and transfer of spin and orbital angular momentum.

Escape forces and trajectories in optical tweezers and their effect on calibration

Whether or not an external force can make a trapped particle escape from optical tweezers can be used to measure optical forces. Combined with the linear dependence of optical forces on trapping power, a quantitative measurement of the force can be obtained. For this measurement, the particle is at the edge of the trap, away from the region near the equilbrium position where the trap can be described as a linear spring. This method provides the ability to measure higher forces for the same beam power, compared with using the linear region of the trap, with lower risk of optical damage to trapped specimens. Calibration is typically performed by using an increasing fluid flow to exert an increasing force on a trapped particle until it escapes. In this calibration technique, the particle is usually assumed to escape along a straight line in the direction of fluid-flow. Here, we show that the particle instead follows a curved trajectory, which depends on the rate of application of the force (i.e., the acceleration of the fluid flow). In the limit of very low acceleration, the particle follows the surface of zero axial optical force during the escape. The force required to produce escape depends on the trajectory, and hence the acceleration. This can result in variations in the escape force of a factor of two. This can have a major impact on calibration to determine the escape force efficiency. Even when calibration measurements are all performed in the low acceleration regime, variations in the escape force efficiency of 20% or more can still occur. We present computational simulations using generalized Lorenz-Mie theory and experimental measurements to show how the escape force efficiency depends on rate of increase of force and trapping power, and discuss the impact on calibration.

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.

Engineered micro- and nanoscale diamonds as mobile probes for high-resolution sensing in fluid

The nitrogen-vacancy (NV) center in diamond is an attractive platform for quantum information and sensing applications because of its room temperature operation and optical addressability. A major research effort focuses on improving the quantum coherence of this defect in engineered micro- and nanoscale diamond particles (DPs), which could prove useful for high-resolution sensing in fluidic environments. In this work we fabricate cylindrical diamonds particles with finely tuned and highly reproducible sizes (diameter and height ranging from 100 to 700 and 500 nm to 2 μm, respectively) using high-purity, single-crystal diamond membranes with shallow-doped NV centers. We show that the spin coherence time of the NV centers in these particles exceeds 700 μs, opening the possibility for the creation of ultrahigh sensitivity micro- and nanoscale sensors. Moreover, these particles can be efficiently transferred into a water suspension and delivered to the region to probe. In particular, we introduce a DP suspension inside a microfluidic circuit and control position and orientation of the particles using an optical trapping apparatus. We demonstrate a DC magnetic sensitivity of 9 μT/√Hz in fluid as well as long-term trapping stability (>30 h), which paves the way toward the use of high-sensitivity pulse techniques on contactless probes manipulated within biological settings.

Equilibrium orientations of oblate spheroidal particles in single tightly focused Gaussian beams

Based on a hybrid discrete dipole approximation (DDA) and T-matrix method, a powerful dynamic simulation model is used to find plausible equilibrium orientation landscapes of micro- and nano-spheroids of varying size and aspect ratio. Orientation landscapes of spheroids are described in both linearly and circularly polarized Gaussian beams. It's demonstrated that the equilibrium orientations of the prolate and oblate spheroids have different performances. Effect of beam polarization on orientation landscapes is revealed as well as new orientation of oblate spheroids. The torque efficiencies of spheroids at equilibrium are also studied as functions of tilt angle, from which the orientations of the spheroids can be affirmed. This investigation elucidates a solid background in both the function and properties of micro-and nano-spheroidal particles trapped in optical tweezers.

5D-Tracking of a nanorod in a focused laser beam--a theoretical concept

Back-focal plane (BFP) interferometry is a very fast and precise method to track the 3D position of a sphere within a focused laser beam using a simple quadrant photo diode (QPD). Here we present a concept of how to track and recover the 5D state of a cylindrical nanorod (3D position and 2 tilt angles) in a laser focus by analyzing the interference of unscattered light and light scattered at the cylinder. The analytical theoretical approach is based on Rayleigh-Gans scattering together with a local field approximation for an infinitely thin cylinder. The approximated BFP intensities compare well with those from a more rigorous numerical approach. It turns out that a displacement of the cylinder results in a modulation of the BFP intensity pattern, whereas a tilt of the cylinder results in a shift of this pattern. We therefore propose the concept of a local QPD in the BFP of a detection lens, where the QPD center is shifted by the angular coordinates of the cylinder tilt.

Non-spherical particles for optical trap assisted nanopatterning

Optical trap assisted nanopatterning is a laser direct-write technique that uses an optically trapped microsphere as a near-field objective. The type of feature that one can create with this technique depends on several factors, one of which is the shape of the microbead. In this paper, we examine how the geometry of the bead affects the focus of the light through a combination of experiments and simulations. We realize nanopatterning using non-spherical dielectric particles to shape the light-material interaction. We model the resulting nanoscale features with a finite difference time domain simulation and obtain very good agreement with the experiments. This work opens the way to systematic engineering of the microparticle geometry in order to tailor the near-field focus to specific nanopatterning applications.

Calibration of nonspherical particles in optical tweezers using only position measurement

Nonspherical probe particles are an attractive choice for optically-trapped scanning probe microscopy. We show that it is possible to calibrate a trap with a nonspherical particle using only position measurements, without requiring measurement of orientation, using a pseudopotential based on the position occupation probability. It is not necessary to assume the force is linear with displacement.