High trapping forces for high-refractive index particles trapped in dynamic arrays of counterpropagating optical tweezers

We demonstrate the simultaneous trapping of multiple high-refractive index (n > 2) particles in a dynamic array of counterpropagating optical tweezers in which the destabilizing scattering forces are canceled. These particles cannot be trapped in single-beam optical tweezers. The combined use of two opposing high-numerical aperture objectives and micrometer-sized high-index titania particles yields an at least threefold increase in both axial and radial trap stiffness compared to silica particles under the same conditions. The stiffness in the radial direction is obtained from measured power spectra; calculations are given for both the radial and the axial force components, taking spherical aberrations into account. A pair of acousto-optic deflectors allows for fast, computer-controlled manipulation of the individual trapping positions in a plane, while the method used to create the patterns ensures the possibility of arbitrarily chosen configurations. The manipulation of high-index particles finds its application in, e.g., creating defects in colloidal photonic crystals and in exerting high forces with low laser power in, for example, biophysical experiments.     

Sorting of micron-sized particles using holographic optical Raman tweezers in aqueous medium

We have constructed a holographic optical tweezers system combined with Raman spectroscopy to sort trapped particles. Our software automatically moves the trapped objects to the measurement positions to obtain individual Raman signals from multiple trapped particles. We performed the sorting by comparing their spectra with the previously measured training dataset using the correlation coefficients. We used yeast cells and polystyrene beads as test particles. This study aims to show that biological particles can be separated using single cell analysis with combined holographic optical tweezers and Raman spectroscopy system.     

Measuring microscopic viscosity with optical tweezers as a confocal probe

We demonstrate, what is to the best our knowledge, a new method for studying the motion of a particle trapped by optical tweezers; in this method the trapping beam itself is used as a confocal probe. By studying the response of the particle to periodic motion of the tweezers, we obtain information about the medium viscosity, particle properties, and trap stiffness. We develop the mathematical model, demonstrate experimentally its validity for our system, and discuss advantages of using this method as a new form of scanning photonic force microscopy for applications in which a high spatial and temporal resolution of the medium viscosity is desired.     

Optical manipulation in combination with multiphoton microscopy for single-cell studies

We demonstrate how optical tweezers can be incorporated into a multiphoton microscope to achieve three-dimensional imaging of trapped cells. The optical tweezers, formed by a cw 1064 nm Nd:YVO4 laser, were used to trap live yeast cells in suspension while the 4',6-diamidino-2-phenylindole-stained nucleus was imaged in three dimensions by use of a pulsed femtosecond laser. The trapped cell was moved in the axial direction by changing the position of an external lens, which was used to control the divergence of the trapping laser beam. This gives us a simple method to use optical tweezers in the laser scanning of confocal and multiphoton microscopes. It is further shown that the same femtosecond laser as used for the multiphoton imaging could also be used as laser scissors, allowing us to drill holes in the membrane of trapped spermatozoa.     

Optical trapping of fluorescent beads

Optical tweezers have been successfully used to trap a variety of particles and biological specimens for numerous applications. Particles which are reflective as well as absorbing could be trapped using beams such as optical vortex. Here we give the details of our efforts to trap fluorescent microparticles. We have set up an optical trap for these fluorescent microparticles using holographic optical tweezers; we observe that it is not possible to trap fluorescent microparticles with a Gaussian laser beam or a hollow beam. However, as the fluorescence of these particles gets degraded they could be trapped in custom-made holographic tweezers. Moreover, when a fluorescent particle is brought in the trap containing stably trapped non-fluorescent particle, the stably trapped non-fluorescent particle also escapes from the trap.     

Using polarization-shaped optical vortex traps for single-cell nanosurgery

Single-cell nanosurgery and the ability to manipulate nanometer-sized subcellular structures with optical tweezers has widespread applications in biology but so far has been limited by difficulties in maintaining the functionality of the transported subcellular organelles. This difficulty arises because of the propensity of optical tweezers to photodamage the trapped object. To address this issue, this paper describes the use of a polarization-shaped optical vortex trap, which exerts less photodamage on the trapped particle than conventional optical tweezers, for carrying out single-cell nanosurgical procedures. This method is also anticipated to find broad use in the trapping of any nanoparticles that are adversely affected by high-intensity laser light.     

The transverse trapping force of an optical trap: Factors affecting its measurement

Abstract

We report new observations that question the validity of using the escape method to deduce optical trapping forces in optical tweezers. The results were obtained by measuring the minimum beam power required to trap a particle subject to fluid flow, created by movement of the sample stage. The power was found to increase by approximately 50% over the range of amplitudes of movement used. This suggests that the measured trapping force is not solely dependent upon the velocity of the fluid past the trapped particle, as commonly assumed. These effects were observed at all fluid velocities and accelerations employed. We consider various causes for the observed effects but an explanation remains an outstanding challenge.     

Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film

Optical tweezers have found many applications in biology, but for reasonable intensities, conventional traps are limited to particles >100 nm in size. We use a double-nanohole in a gold film to experimentally trap individual nanospheres, including 20 nm polystyrene spheres and 12 nm silica spheres, at a well-defined trapping point. We present statistical studies on the trapping time, showing an exponential dependence on the optical power. Trapping experiments are repeated for different particles and several nanoholes with different gap dimensions. Unusually, smaller particles can be more easily trapped than larger ones with the double-nanohole. The 12 nm silica sphere has a size and a refractive index comparable to the smallest virus particles and has a spherical shape which is the worst case scenario for trapping.     

Calibration of sound forces in acoustic traps

A two-dimensional or transverse acoustic trapping and its capability to noninvasively manipulate micrometersized particles with focused sound beams were experimentally demonstrated in our previous work. To apply this technique, as in optical tweezers, for studying mechanical properties of and interactions among biological particles such as cells, the trapping forces must be calibrated against known forces, i.e., viscous drag forces exerted by fluid flows. The trapping forces and the trap stiffness were measured under various conditions and the results were reported in this paper. In the current experimental arrangement, because the trapped particles were positioned against an acoustically transparent mylar membrane, the ultrasound beam intensity distribution near the membrane must be carefully considered. The total intensity field (the sum of incident and scattering intensity fields) around the droplet was thus computed by finite element analysis (FEA) with the membrane included, and it was then used in the ray acoustics model to calculate the trapping forces. The membrane effect on trapping forces was discussed by comparing effective beam widths with and without the membrane. The FEA results found that the broader beam width, caused by the scattered beams from the neighboring membrane and the droplet, resulted in the lower intensity, or smaller force, on the droplet. The experimental results showed that the measured forces were as high as 64 nN. The trap stiffness, approximated as a linear spring, was estimated by linear regressions and found to be 1.3 to 4.4 nN/μm, which was on a larger scale than that of optical trapping estimated for red blood cells, a few tenths of piconewtons/nanometer. The experimental and theoretical results were in good agreement.     

Nonlinear optical processes in optically trapped InP nanowires

We report on the observation of nonlinear optical excitation and related photoluminescence from single InP semiconductor nanowires held in suspension using a gradient force optical tweezers. Photoexcitation of free carriers is achieved through absorption of infrared (1.17 eV) photons from the trapping source via a combination of two- and three-photon processes. This was confirmed by power-dependent photoluminescence measurements. Marked differences in spectral features are noted between nonlinear optical excitation and direct excitation and are related to band-filling effects. Direct observation of second harmonic generation in trapped InP nanowires confirms the presence of nonlinear optical processes.     

Defining the trapping limits of holographical optical tweezers

Abstract

We report on the limitations of using a spatial light modulator (SLM) within optical tweezers to produce both lateral and axial displacements. We find that lateral displacements of optical traps are limited by the optical efficiency of the SLM, whereas the axial displacements are limited by the abberations of the objective lens. In addition, we show the SLM can be used for correcting abberations arising from trapping deep within the sample. The maximum possible lateral and axial displacements were 50 μm and 40 μm, respectively.     

Force mapping of an optical trap using an acousto-optical deflector in a time-sharing regime

We suggest and study experimentally a time-sharing protocol for acousto-optical deflectors (AODs) that permits one to map the radial optical trapping force of optical tweezers without using a controllable flux control or an additional beam. Variations of the trapping potential due to modifications of the optical system are easily detected in terms of the force map. The protocol can be used in optical tweezers that already include an AOD without adding new elements in the existing optical system.     

Efficient optical trapping and visualization of silver nanoparticles

We performed efficient optical trapping combined with sensitive optical detection of individual silver nanoparticles. The particles ranging in size from 20 to 275 nm in diameter were trapped in three dimensions using low laser power by minimizing spherical aberrations at the focus. The optical forces were quantified, and we found that the larger the particle, the stronger the optical force. The particles were imaged by an additional strongly scattered laser.     

Optical tweezers and optical spanners with Laguerre–Gaussian modes

Abstract

We numerically model the axial trapping forces within optical tweezers arising from Laguerre–Gaussian laser modes. For an 8 μm diameter sphere suspended in water, the higher-order modes produce an axial trapping force several times larger than that of the fundamental. Partial absorption results in a transfer of the orbital angular momentum from the Laguerre–Gaussian mode to the trapped particle. This results in the rotation of the particle by what may be called an optical spanner (wrench). For an absorption coefficient of α = 5700 m^?1 and a laser power of 10 mW, we find that an 8 μm diameter sphere would acquire an angular acceleration of 10 × 10⁴ rad s^?2 and a limiting angular velocity of 0.2 rad s^?1.     

Controlled modulation of laser beam and dynamic patterning of colloidal particles using optical tweezers

We present controlled generation of complex-structured beam profiles using diffractive optical element and demonstrate multiple dynamic trapping of colloidal particles. The phase element is programmed to generate various tailored optical fields having structures, similar to that of number three, spiral, and circle but in a tractable manner. Thus, the generated spatially tailored optical fields are confined to focal volume in optical tweezers. This enabled real-time trapping of multiple microscopic objects whereby its transverse organization was controlled in a dynamic manner from one structure to another with the help of spatial light modulator. Such a controlled beam shaping finds potential applications in biophotonics, super resolution imaging, and measurement of biophysical parameters, cell sorting, and micro-manipulation of colloidal particles.     

Laser tweezers for atomic solitons

We describe controllable and precise laser tweezers for Bose–Einstein condensates of ultracold atomic gases. In our configuration, a laser beam is used to locally modify the sign of the scattering length in the vicinity of a trapped BEC. The induced attractive interactions between atoms allow us to extract and transport a controllable number of atoms. We analyze, through numerical simulations, the number of emitted atoms as a function of the width and intensity of the outcoupling beam. We also study different configurations of our system, as the use of moving beams. The main advantage of using the control laser beam to modify the nonlinear interactions in comparison to the usual way of inducing optical forces, i.e. through linear trapping potentials, is to improve the controllability of the outcoupled solitary wave-packet, which opens new possibilities for engineering macroscopic quantum states.     

Microfluidic sorting with a moving array of optical traps

Optical sorting was demonstrated by selective trapping of a set of microspheres (having specific size or composition) from a flowing mixture and guiding these in the desired direction by a moving array of optical traps. The approach exploits the fact that whereas the fluid drag force varies linearly with particle size, the optical gradient force has a more complex dependence on the particle size and also on its optical properties. Therefore, the ratio of these two forces is unique for different types of flowing particles. Selective trapping of a particular type of particles can thus be achieved by ensuring that the ratio between fluid drag and optical gradient force on these is below unity whereas for others it exceeds unity. Thereafter, the trapped particles can be sorted using a motion of the trapping sites towards the output. Because in this method the trapping force seen by the selected fraction of particles can be suitably higher than the fluid drag force, the particles can be captured and sorted from a fast fluid flow (about 150 μm/s). Therefore, even when using a dilute particle suspension, where the colloidal trafficking issues are naturally minimized, due to high flow rate a good throughput (about 30 particles/s) can be obtained. Experiments were performed to demonstrate sorting between silica spheres of different sizes (2, 3, and 5 μm) and between 3 μm size silica and polystyrene spheres.     

Tweezing of Magnetic and Non‐Magnetic Objects with Magnetic Fields

Although strong magnetic fields cannot be conveniently “focused” like light, modern microfabrication techniques enable preparation of microstructures with which the field gradients – and resulting magnetic forces – can be localized to very small dimensions. This ability provides the foundation for magnetic tweezers which in their classical variant can address magnetic targets. More recently, the so‐called negative magnetophoretic tweezers have also been developed which enable trapping and manipulations of completely nonmagnetic particles provided that they are suspended in a high‐magnetic‐susceptibility liquid. These two modes of magnetic tweezing are complimentary techniques tailorable for different types of applications. This Progress Report provides the theoretical basis for both modalities and illustrates their specific uses ranging from the manipulation of colloids in 2D and 3D, to trapping of living cells, control of cell function, experiments with single molecules, and more.     

Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave

We study the axial force acting on dielectric spherical particles smaller than the trapping wavelength that are placed in the Gaussian standing wave. We derive analytical formulas for immersed particles with relative refractive indices close to unity and compare them with the numerical results obtained by generalized Lorenz-Mie theory (GLMT). We show that the axial optical force depends periodically on the particle size and that the equilibrium position of the particle alternates between the standing-wave antinodes and nodes. For certain particle sizes, gradient forces from the neighboring antinodes cancel each other and disable particle confinement. Using the GLMT we compare maximum axial trapping forces provided by the Gaussian standing-wave trap (SWT) and single-beam trap (SBT) as a function of particle size, refractive index, and beam waist size. We show that the SWT produces axial forces at least ten times stronger and permits particle confinement in a wider range of refractive indices and beam waists compared with those of the SBT.