Particles In Optical Tweezers Research Articles

Effects of detection-beam focal offset on back-focal-plane displacement detection

High-resolution displacement detection can be achieved by analyzing the scattered light of the trapping beams from the particle in optical tweezers. In some applications where trapping and detecting beams must be separated, a detecting beam can be introduced for independent displacement measurement. However, the detecting beam focus possibly deviates from the center of the particle, which will affect the performance of displacement detection. Here, we detect the displacement of the particle by utilizing the forward scattered light of the detection beam from the particle. The effects of the lateral and axial offsets between the detection beam focus and the particle center on displacement detection are analyzed by the simulation and experiment. These results show that the lateral offsets will decrease the detection sensitivity and linear range. Moreover, it aggravates the crosstalk between the x-direction signal and the y-direction signal of the quadrant photodiode. Besides, the axial offsets also affect the detection sensitivity. More interestingly, an optimal axial offset can improve the sensitivity of displacement detection substantially. In addition, the influence of system parameters, such as particle radius a, numerical aperture of the condenser NAc, and numerical aperture of the objective NAo, on the optimal axial offset is also discussed. This work not only provides ideas for improving the performance of precision measurement by the method of forward scattered light detection but also expands the application of this method in fundamental physics.

Brownian Motion in Optical Tweezers, a Comparison between MD Simulations and Experimental Data in the Ballistic Regime.

The four most popular water models in molecular dynamics were studied in large-scale simulations of Brownian motion of colloidal particles in optical tweezers and then compared with experimental measurements in the same time scale. We present the most direct comparison of colloidal polystyrene particle diffusion in molecular dynamics simulations and experimental data on the same time scales in the ballistic regime. The four most popular water models, all of which take into account electrostatic interactions, are tested and compared based on yielded results and resources required. Three different conditions were simulated: a freely moving particle and one in a potential force field with two different strengths based on 1 pN/nm and 10 pN/nm. In all cases, the diameter of the colloidal particle was 50 nm. The acquired data were compared with experimental measurements performed using optical tweezers with position capture rates as high as 125 MHz. The experiments were performed in pure water on polystyrene particles with a 1 μm diameter in special microchannel cells.

Spin–orbit interaction in non-paraxial Gaussian beams and the spin-only measurement of optical torque

A circularly polarized focussed Gaussian beam carries total angular momentum of per photon about the beam axis, but less than spin per photon, due to the focussing of the beam. The remainder of the angular momentum is carried as orbital angular momentum. When such beams are used to rotate microscopic birefringent particles in optical tweezers, the change in angular momentum can be optically measured. However, this measurement is made using the collimated transmitted beam, rather than the focussed beam. Therefore, the conversion of spin to orbital angular momentum by focussing or collimating the beam is expected to affect the measurement. We show that for the typical cases where rotating optical tweezers are used for such measurements, the error due to spin–orbit conversion is unimportant, but there exist cases where a spin-only torque measurement would be completely erroneous.

FDTD simulation of optical force under non-ideal conditions

In this paper, the optical forces of particles in optical tweezers under non-ideal conditions are investigated. The calculation of optical forces are carried out by combining three dimensional finite-difference time-domain (FDTD) method and Maxwell stress Tensor (MST). Numerical results show the changes of trapping stiffness and equilibrium position induced by several common seen non-ideal conditions in experiment. This study is expected to estimate the error of optical force in real situation and that is of great use to further optimize the performance of optical tweezers.

Dynamic Analysis and Simulation of an Optically Levitated Rotating Ellipsoid Rotor in Liquid Medium

Optical trap, a circularly polarized laser beam can levitate and control the rotation of microspheres in liquid medium with high stiffness. Trapping force performs as confinement while the trapped particle can be analog to a liquid floated gyroscope with three degree-of-freedom. In this work, we analyzed the feasibility of applying optically levitated rotor in the system. We presented the dynamic analysis and simulation of an ellipsoid micron particle. The precession motion and nutation motion of a rotating ellipsoid probe particle in optical tweezers were performed. We also analyzed the attitude changes of an optically levitated ellipsoid when there was variation of the external torque caused by deviation of the incident light that was provided. Furthermore, the trail path of the rotational axis vertex and the stabilization process of a particle of different ellipticities were simulated. We compared the movement tendencies of particles of different shapes and analyzed the selection criteria of ellipsoid rotor. These analytical formulae and simulation results are applicable to the analysis of the rotational motion of particles in optical tweezers, especially to the future research of the gyroscope effect.

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 kBT 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.

Quadrupole absorption rate for atoms in circularly-polarized optical vortices

Twisted light beams, or optical vortices, have been used to drive the circular motion of microscopic particles in optical tweezers and have been shown to generate vortices in quantum gases. Recent studies have established that electric quadrupole interactions can mediate an orbital angular momentum exchange between twisted light and the electronic degrees of freedom of atoms. Here we consider a quadrupole atomic transition mediated by a circularly-polarized optical vortex. We evaluate the transfer rate of the optical angular momentum to a Ca+ ion involving the 42S1∕2→32D5∕2 quadrupole transition and explain how the polarization state and the topological charge of the vortex beam determine the selection rules.

Revolution of a trapped particle in counter-propagating dual-beam optical tweezers under low pressure.

We presented faster and more accurate simulations and experiments describing the revolution of a suspended particle in optical tweezers under a low pressure. Instead of the state-of-the-art offline method of pinhole alignment, we proposed an in situ method of revolution suppression by adjusting the laser beam while observing the power spectral density and time-domain plot of the particle centroid displacement. The experimental results under different air pressures show that our method is more effective at low pressures. We observed that "revolution occurs when radial alignment error is below the threshold" and uncovered the mechanism behind this phenomenon. The rapidly growing Q value of the revolution indicates a high-precision resonance measurement method under lower air pressure compared with random translation measurements.

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.

Robust and high‐speed rotation control in optical tweezers by using polarization synthesis based on heterodyne interference

The rotation control of particles in optical tweezers is often subject to the spin or orbit angular momentum induced optical torque, which is susceptible to the mechanical and morphological properties of individual particle. Here we report on a robust and high-speed rotation control in optical tweezers by using a novel linear polarization synthesis based on optical heterodyne interference between two circularly polarized lights with opposite handedness. The synthesized linear polarization can be rotated in a hopping-free scheme at arbitrary speed determined electronically by the heterodyne frequency between two laser fields. The experimental demonstration of a trapped vaterite particle in water shows that the precisely controlled rotation frequency of 300 Hz can be achieved. The proposed method will find promising applications in optically driven micro-gears, fluidic pumps and rotational micro-rheology.

Calibration of force detection for arbitrarily shaped particles in optical tweezers

Force measurement with an optical trap requires calibration of it. With a suitable detector, such as a position-sensitive detector (PSD), it is possible to calibrate the detector so that the force can be measured for arbitrary particles and arbitrary beams without further calibration; such a calibration can be called an “absolute calibration”. Here, we present a simple method for the absolute calibration of a PSD. Very often, paired position and force measurements are required, and even if synchronous measurements are possible with the position and force detectors used, knowledge of the force–position curve for the particle in the trap can be highly beneficial. Therefore, we experimentally demonstrate methods for determining the force–position curve with and without synchronous force and position measurements, beyond the Hookean (linear) region of the trap. Unlike the absolute calibration of the force and position detectors, the force–position curve depends on the particle and the trapping beam, and needs to be determined in each individual case. We demonstrate the robustness of our absolute calibration by measuring optical forces on microspheres as commonly trapped in optical tweezers, and other particles such a birefringent vaterite microspheres, red blood cells, and a deformable “blob”.

Observation of particle manipulation with axial plane optical microscopy

Optical micromanipulation of particles based on the optical trapping effect induced by the interaction between light and particles has been successfully applied to many interdisciplinary fields including biomedicine and material sciences. When particles are trapped in three dimensions, the conventional wide-field optical microscopy can only monitor the movement of the trapped particles in a certain transverse plane. The ability to observe the particle movement along light trajectories is limited. Recently, a novel method named axial plane optical microscopy(APOM) has been developed to directly image the axial plane that is parallel to the optical axis of an objective lens. The APOM observes the axial plane by converting the axial information of a sample into that of a transverse plane by using a 45°-tilted mirror. In this paper, we propose and demonstrate that the APOM serves as an effective tool for observing the axial movement of particles in optical tweezers. By combining with a conventional wide-field optical microscopy, we show that both transverse and axial information can be acquired simultaneously for the optical micromanipulation. As in our first experimental demonstration, we observe two particles which are trapped and aligned along the optical axis. From the transverse image, only one particle is observable, and it is difficult to obtain the information along the axial direction. However, in the axial plane imaging, the longitudinal dipolar structure formed by the two particles is clearly visible. This clearly demonstrates the APOM imaging capability along the axial axis. The numerically simulations on the trapping focal spot against the position of a collimating lens agree well with our experimental APOM results. Furthermore, we directly observe the dynamic capture process of a single trapped particle in transverse plane by conventional wide-field optical microscopy as well in axial plane by the APOM, and can obtain the 3D information rapidly and simultaneously. We point out that the observable axial dynamic range is about 30 μm. Taking advantages of no requirement of scanning and data reconstruction, the APOM has potential applications in many fields, including optical trapping with novel beams and 3D imaging of thick biological specimens.

Transfer of optical orbital angular momentum to a bound electron.

Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light–matter interaction and pave the way for its application and observation in other systems.

Transfer of non-Gaussian quantum states of mechanical oscillator to light

Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

Simultaneous detection of rotational and translational motion in optical tweezers by measurement of backscattered intensity.

We describe a simple yet powerful technique of simultaneously measuring both translational and rotational motion of mesoscopic particles in optical tweezers by measuring the backscattered intensity on a quadrant photodiode (QPD). While the measurement of translational motion by taking the difference of the backscattered intensity incident on adjacent quadrants of a QPD is well known, we demonstrate that rotational motion can be measured very precisely by taking the difference between the diagonal quadrants. The latter measurement eliminates the translational component entirely and leads to a detection sensitivity of around 50 mdeg at S/N of 2 for angular motion of a driven microrod. The technique is also able to resolve the translational and rotational Brownian motion components of the microrod in an unperturbed trap and can be very useful in measuring translation-rotation coupling of micro-objects induced by hydrodynamic interactions.

Optical forces on arbitrary shaped particles in optical tweezers

Discrete dipole approximation (DDA) method is an efficient method for computing electromagnetic (EM) field of nanometer/micrometer-sized dielectric particles with arbitrary geometric shape and topology. In this work we employ the DDA method to calculate the optical force of dielectric shaped particles embedded in optical tweezers made from focused Gaussian laser beams. The EM force is calculated based on the self-consistent solution of EM field distribution and discrete dipole moment distribution within the particles. The DDA method agrees well with the Mie theory for spherical dielectric particles and this supports the effectiveness of the DDA method in handling optical forces in optical tweezers. The optical force for shaped particles such as cubes, rectangles, cylinders, and core-shell composite particles shows many interesting features. The force strongly depends on the orientation of the particle with respect to the laser beam propagation and polarization direction and the aspect ratio of the anisotropic particle. For a core-shell composite particle the zero-force balance point shifts from the particle center to its two sides. When an additional particle comes close a trapped particle, the perturbation effect strongly depends on the relative location of the center of the focused laser beam with respect to the two particles. Furthermore, the geometry of shaped particles not only affects the magnitude of the optical force but also influences the optical trap stiffness.

Rotation of birefringent particles in optical tweezers with spherical aberration

Birefringent particles rotate when trapped in elliptically polarized light. When an infinity corrected oil-immersion objective is used for trapping, rotation of birefringent particles in optical tweezers based on an infinity optical microscope is affected by the spherical aberration at the glass-water interface. The maximum rotation rate of birefringent particles occurs close to the coverslip, and the rotation rate decreases dramatically as the trapped depth increases. We experimentally demonstrate that spherical aberration can be compensated by using a finite-distance-corrected objective to trap and rotate the birefringent particles. It is found that the trapped depth corresponding to the maximum rotation rate is 50 microm, and the rotation rates at deep trapped depths are improved.

Constant power optical tweezers with controllable torque

We describe a means for controlling the spin angular-momentum flux of a laser beam at constant power, without introducing any elliptical or linear polarization. This allows a controllable torque, acting to spin the particle uniformly, to be exerted on a birefringent particle in optical tweezers. The constant power means that transverse and axial trapping, and heating due to absorption, are unaffected by changing the torque. The torque can be computer controlled and rapidly changed. In addition, the lateral trapping is kept constant. Very low torques can be obtained such that rotational Brownian motion of birefringent particles can be observed. This has the potential to greatly extend the quantitative applications of the rotation of birefringent objects in optical tweezers.

The effect of Mie resonances on trapping in optical tweezers

We calculate trapping forces, trap stiffness and interference effects for spherical particles in optical tweezers using electromagnetic theory. We show the dependence of these on relative refractive index and particle size. We investigate resonance effects, especially in high refractive index particles where interference effects are expected to be strongest. We also show how these simulations can be used to assist in the optimal design of traps.

Antireflection coating for improved optical trapping

An antireflection coating improves the trapping of high-index particles in optical tweezers by reducing the scattering force. This can allow the strong trapping of high-index particles that cannot normally be trapped, and the use of lower numerical aperture objectives while still obtaining strong trapping. The improvement is not overly sensitive to the refractive index or thickness of the coating.