Trapping Force Research Articles

Technique for Rapid Mass Determination of Airborne Microparticles Based on Release and Recapture from an Optical Dipole Force Trap

We describe a new method for the rapid determination of the mass of particles confined in a free-space optical dipole-force trap. The technique relies on direct imaging of drop-and-restore experiments without the need for a vacuum environment. In these experiments, the trapping light is rapidly shuttered with an acousto-optic modulator causing the particle to be released from and subsequently recaptured by the trapping force. The trajectories of both the falls and restorations, imaged using a high-speed CMOS sensor, are combined to determine the particle mass. We corroborate these measurements using an analysis of position autocorrelation functions of the trapped particles. We report a statistical uncertainty of less than 2% for masses on the order of $5\times10^{-14}$ kg using a data acquisition time of approximately 90 seconds.

Generalized Lorenz-Mie theory for the reversal of optical force in a nonlinear laser trap

Hybrid nanoparticles have gained intense attention in the field of optical trapping due to their potential wide-ranging applications, for example, in drug delivery. The utility of the optical Kerr effect in modulating trapping force and potential under high-repetition-rate ultrafast pulsed excitation has recently been realized for dielectric and metallic particles ranging from micron to nanometer. However, in the context of hybrid nanoparticles, the mechanism of trapping is yet to be fully explored. Here, we present a comparative study of trapping force and potential on conventional, hybrid, and hollow-core type nanoparticles using generalized Lorenz-Mie theory and dipole approximation incorporating third-order optical nonlinearity. We find an explicit advantage of using pulsed excitation over continous-wave excitation which can have potentially far-reaching practical applications.

Rotation of an elliptical dielectric particle in the focus of a circularly polarized Gaussian beam

A force and a torque exerted on an elliptical dielectric particle in the focus of a spherical circularly polarized laser beam are considered. The numerical simulation is conducted using a diffraction field obtained by an FDTD method, with the force and torque derived using a Maxwell’s stress tensor. It is shown that an optical torque is exerted on the center of an elliptical particle put in the focus of a circularly polarized spherical wave, making it rotate around the optical axis. The rotation occurs when the elliptical microparticle is situated in a transverse plane to the optical axis. When shifting the ellipsoid from the optical axis, an optical trapping force appears that prevents its displacement, meaning that the particle finds itself in an optical trap on the optical axis.

Specular-reflection photonic nanojet: physical basis and optical trapping application

A specular-reflection photonic nanojet (s-PNJ) is a specific type of optical near-field subwavelength spatial localization originated from the constructive interference of direct and backward propagated optical waves focused by a transparent dielectric microparticle located near a flat reflecting mirror. The unique property of s-PNJ is reported for maintaining its spatial localization and high intensity when using microparticles with high refractive index contrast when a regular photonic nanojet is not formed. The physical principles of obtaining subwavelength optical focus in the specular-reflection mode of a PNJ are numerically studied and a comparative analysis of jet parameters obtained by the traditional schemes without and with reflection is carried out. Based on the s-PNJ, the physical concept of an optical tweezer integrated into the microfluidic device is proposed provided by the calculations of optical trapping forces of the trial gold nanosphere. Importantly, such an optical trap shows twice as high stability to Brownian motion of the captured nano-bead as compared to the conventional nanojet-based traps and can be relatively easy implemented.

Bichromatic dark trap immersed in a buffer gas with an admixture of resonant atoms

The quasiclassical kinetic theory of optical forces has been applied to describe the kinetics of accumulation, deep trapping and cooling of particles in a bichromatic dark trap (BDT), which is placed into a reservoir with a thermal gas at room temperature containing an admixture of resonant atoms. BDT (proposed in our previous works, Krasnov 2016 Laser Phys. 26 105 501, 2017 27 085 501) is a multiple-optical-beam dark trap, in which rectified gradient forces in a bichromatic light field are used to manipulate the particles. The purpose of the present study is to investigate the possibility of direct BDT loading from the equilibrium gas mixture which will result in trapping and cooling of a sufficiently great amount of atoms by BDT. We derived a reduced Fokker-Planck equation in the energy space (for the Wigner particle distribution function) including the collision term. This equation takes into account the optical trapping force, its quantum fluctuations, particle loss from the trap and weakly-dissipative nature of BDT. Its asymptotic solution allows one to describe the particle kinetics and obtain explicit formulas for the main characteristics of BDT (particle capture rate into BDT, temperature and number of the trapped particles). Ultimately, we demonstrate the high efficiency of the particle accumulation in BDT. In particular, the concentration of the trapped particles (with the temperature at least by four orders of magnitude lower than the room temperature) has been shown to be able to exceed the concentration of the ‘hot’ untrapped particles by several dozens of times, and it has been demonstrated that the accumulation efficiency can reach the values of the order of 103.

Accurate Estimation of Refractive Indices of Organic Microparticles in Dual-Beam Optical Trap.

The Refractive Index (RI) is an important parameter of characterizing optical properties of particles. In a dual-beam optical trap, two counter-propagating laser beams are used to trap micro-particles suspended in an aqueous medium. When a ray of light passes from one medium of lower RI (e.g. aqueous suspension medium) to another medium of higher RI (e.g. suspended particle), its momentum changes which exerts a proportional trapping force on the surface of the particle. Thus, accurate knowledge of RI of the particles and the surrounding medium is needed to determine the behavior of particles in an optical trap. The RI of micro-sized beads can be experimentally measured using traditional optical methods such as absorption microscopy. We developed an alternative theoretical method to estimate the RI of trapped particles based on non-contact optical trapping experimental outcomes. In our study, a theoretical model was formulated based on the experimentally measured minimum trapping powers for polystyrene and polyethylene beads using a dual-beam optical setup. The tendencies of trapping power-RI curves predicted by our model agreed very well with those measured experimentally. Our technique provides an alternative approach to determining the RI of a certain micro-size particle regardless of its size or density. Our method is especially advantageous over traditional methods to determine RI of biological particles which exhibit significant variations based on physiological and environmental conditions.

Synthesis of submicron-sized CdS particles using reverse micelles

We synthesized cadmium sulfide (CdS) submicron particles in reverse micelles. We chose the surfactants and the water-to-surfactant molar ratio to influence the formation of reverse micelles such that their average size was 100 nm. The actual size of the particles that we synthesized was consistent with the expected reverse micelle size. The synthesized CdS particles exhibited a strong photoluminescence that comprised an interband emission with a quantum confinement effect and a broad emission that originated from the surface trap states. When combined with the blueshifted absorption edge seen in the submicron particle solution, our prepared submicron particles were an aggregation of semiconductor quantum dots. The submicron-size semiconductor particle is appropriate as an optical trapping target in a variety environments and is beneficial for sophisticated resonant optical manipulation, including enhanced optical trapping force and recoil force manipulation.

Synergy of Intensity, Phase, and Polarization Enables Versatile Optical Nanomanipulation.

Micromanipulation by optical tweezers mainly relies on the trapping force derived from the intensity gradient of light. Here we show that the synergy of intensity, phase, and polarization in structured light allows versatile optical manipulation of nanostructures. When a metal nanoparticle is confined by a linearly polarized laser field, the sign of optical force depends on the particle shape and the laser intensity, phase, and polarization profiles. By tuning these parameters in optical line traps, optical trapping, transporting, and sorting of silver nanostructures have been demonstrated. These findings inspired us to control the motion of nanostructures with designed intensity, phase, and polarization of light using holographic optical tweezers with advanced beam shaping techniques. This work provides a new perspective on active colloidal nanomanipulation in fully controlled optical landscapes, which largely expands the existing optical manipulation toolbox.

Optical manipulations via auxiliary substrates

We report flexible optomechanical manipulations by the help of surface and volumetric modes of the substrate. Optical binding effect can be sufficiently enhanced due to both surface plasmon-polariton and hyperbolic modes of the structure. Volumetric modes of the structure provide optical pulling force for inclined incident plane wave, while surface waves cause enhancement of the optical trapping force under Gaussian beam illumination. Moreover, antitrapping effect can occur for specific positions of the beam waist.

Theory of acoustic trapping of microparticles in capillary tubes.

We present a semianalytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of the quality factor of the two-dimensional (2D) cross-section resonance mode. This axial variation is determined analytically based on the numerical solution to the eigenvalue problem in the 2D cross section. The analysis is developed in two steps: First, we generalize a recently published expression for the 2D standing-wave resonance modes in a rectangular cross section to arbitrary shapes, including the viscous boundary layer. Second, based on these 2D modes, we derive analytical expressions in three dimensions for the acoustic pressure, the acoustic radiation and trapping force, as well as the acoustic energy flux density. We validate the theory by comparison to three-dimensional numerical simulations.

Tunable emission and optical trapping of upconverting LiYF4:Yb,Er nanocrystal

Present work investigates about hydrothermally prepared LiYF4:Yb,Er nanocrystals with novel tunable emission and optical trapping results. Optical trapping effect of LiYF4:Yb,Er upconversion nanocrystal under 980 nm diode laser interaction is reported and a single nanoparticle trapping is demonstrated. Optical trapping force of 10.8 fN is exerted on LiYF4:Yb,Er upconversion nanocrystal of size ~238 nm at laser power 50 mW and the result is in agreement with the reported values. At 980 nm excitation, tunable green to red upconversion emission is achieved by calcination. It depends on orthorhombic and tetragonal phases that confirmed by XRD. The nanocrystals calcined at 450 and 600 °C resulted in a decay time of 26 and 19 µs respectively and the upconversion emission mechanism is explained. FESEM and HRTEM examinations showed the hydrothermally synthesized nanocrystals are in trapezohedral, pyramidal, bi-pyramidal and tetragonal morphologies. The differential scanning calorimetry revealed the tetragonal phase formation temperature is lower at 450 °C compared to the reported value of 750 °C. The UV–VIS-NIR spectra of LiYF4:Yb,Er showed high absorption at 380, 480, 520 and 660 nm due to Er3+ ion and the broad absorption from 900 to 1000 nm centered at 980 nm is owing to Yb3+ ion. The crystalline phase, morphology, upconversion emission and optical trapping behaviors of LiYF4:Yb,Er nanocrystal are explained elaborately.

Dual optical trap created by tightly focused circularly polarized ring Airy beam

The dual focus property of focused circularly polarized ring Airy beam (RAB) under the action of tightly focused lens is demonstrated in this paper. The radiation forces at two foci of tightly focused RAB are calculated, the numerical results show that the particle could be longitudinally and transversely trapped at the two foci. By varying corresponding parameters, we could control the property of two traps. The trapping force increases with NA and the scaling parameter w; and an appropriate initial radius r0 is necessary for the enhancement of either trap. The two traps could move closer as w increases or r0 decreases. To realize the dual optical trap, we should choose a smaller decaying parameter a and a larger NA, or the dual optical trap would degenerate into a single optical trap. Moreover, because of the influence of the Brownian motion and the scattering force, the size of the particle should be in a special range.

Selective Manipulation of Biomolecules with Insulator-Based Dielectrophoretic Tweezers.

Insulator-based dielectrophoretic (iDEP) trapping, separating, and concentrating nanoscale objects is carried out using a non-metal, unbiased, mobile tip acing as a tweezers. The spatial control and manipulation of fluorescently-labeled polystyrene particles and DNA were performed to demonstrate the feasibility of the iDEP tweezers. Frequency-dependent iDEP tweezers' strength and polarity were quantitatively determined using two theoretical approaches to DNA, which resulted in a factor of 2 ~ 40 differences between them. In either approach, the strength of iDEP was at least 4-order of magnitude stronger than the thermal force, indicating iDEP was a dominant force for trapping, holding, and separating DNA. The trapping strength and volume of the iDEP tweezers were also determined, which further supports direct capture and manipulation of DNA at the tip end.

Waveguiding and focusing in a bio-medium with an optofluidic cell chain

Long-distance waveguiding and submicron focusing of light in a bio-medium are crucial for biomedical sensing and imaging. Disordered bio-mediums usually exhibit high scattering and absorption, which limits effective waveguiding and focusing. Here, we demonstrate an optofluidic cell chain, assembled via an optical trapping force from an optical fiber probe, to achieve long-distance waveguiding and submicron light focusing in a disordered bio-medium. By applying a trapping light at 980 nm to generate an optical force, stable binding of E. faecalis cells was achieved in a fluid to assemble cell chains of different lengths. The length could reach up to 360 µm and the incident light (at 675, 532 and 473 nm) could be focused into a beam with a waist radius of 400 nm. As a potential practical application, backscattered signals from human red blood cells were detected using the cell chains, which is expected to benefit biomedical sensing and single cell analysis. Statement of significanceWith the assistance of optofluidic techniques, we assembled an E. faecalis cell chain with a length up to 360 µm to achieve long-distance waveguiding and submicron focusing at a propagation loss of 0.03 dB/µm in the bio-medium. Visible lights were launched into the cell chain and the incident lights can converge into a beam with a waist radius of 400 nm. The cell chain was further used to detect the backscattering signals from human red blood cells (RBCs), and the results indicate that the cell chain can be applied as a fully biocompatible extension of the probe for the real-time detection of RBCs in healthy and pathological states.

Photonic crystal nanobeam/micro-ring hybrid-cavities for optical trapping

We propose a new type of hybrid-cavity structure for trapping nanoscale particles. The hybrid cavity is based on a ring waveguide with the incorporation of a photonic crystal nanobeam cavity (PCNC). We design the cavity and investigate the influence of geometric parameters on its performance and optical trapping ability. The numerical results show that high quality factor, low mode volume and strong optical trapping ability can be achieved. The radii of holes are quadratically tapered from the center to two sides with a smaller period in the mirrors of the PCNC and the optical trapping force is proportional to (1−T)Q/V of the cavity. Furthermore, a hybrid cavity with optimal trapping ability is realized with quality factor up to 1.98×106, mode volume as low as 1.90(λ∕nSi)3 and its optical trapping force can be as high as −855 pN/mW, which is 15 times enhanced compared to that of a microring resonator with the same radius.

A study of metastable ion Coulomb crystals in a polychromatic all-optical trap

Metastable ion Coulomb crystal (ICC) in the polychromatic optical superlattice (OSL) created by so-called rectified gradient forces is studied. Our analysis is based on the numerical solution of the nonlinear stochastic differential equations taking into account the trapping and dissipative forces, their quantum fluctuations, and Coulomb repulsion of ions. The key question is how long will this metastable highly ordered crystalline structure persist. The critical parameter determining the ICC destruction times td is the OSL period L (at fixed intensity values of the optical fields). Our simulations demonstrate that td of the ICC, consisting of several tens of mercury ions, experiences giant changes (by four orders of magnitude) at relatively slight variations of the optical superlattice period L in the range from 0.35 to 0.70 mm. We have shown that the dependence td (L) can be approximated by the Arrhenius-like equation with an effective activation energy which is nonlinearly dependent on the OSL period L. These results explain the ultrahigh sensitivity td (L) to the OSL period L and show how to adjust L to ensure all-optical confinement of ICC in the OSL from a fraction of a second to one and half minutes.

Acoustic manipulation of large solid objects for medical applications

Most progress in acoustic manipulation through radiation forces has been achieved in the trapping and levitation of small and low-density objects. We are developing traps to manipulate large dense objects. Such technology could be used to noninvasively steer a kidney stone along a complex path in the kidney fluid space to pass a small stone before it is symptomatic. In this work various acoustic beams were generated with a focused, 1.5-MHz, 256-element array and used to trap, levitate, and manipulate in three-dimensions (3-D) 3-5 mm glass spheres. The radiation forces from these beams were simulated and measured for different target and trap sizes. Good agreement between calculations and measurements of the forces was found, with an average discrepancy of 12 %. At 10-W acoustic power, the lateral trapping forces were 0.5–3 times the gravitational forces in water. 3-D stability and off-axis steering were achievable only when the ratio of beam diameter to the target diameter was ≳1. Glass spheres placed in the focus of the array were manipulated over a preprogrammed 3-D path at pressure and intensity levels safe for clinical exposure. [Work supported by NIH P01-DK043881, K01-DK104854, R01-EB007643, and RBBR 17-02-00261.]

Waveguiding and Focusing in a Bio-Medium with an Optofluidic Cell Chain

Long-distance waveguiding and submicron focusing of light in a bio-medium are crucial for biomedical sensing and imaging. Disordered bio-mediums usually exhibit high scattering and absorption, which limits effective waveguiding and focusing. Here, we demonstrate an optofluidic cell chain, assembled via an optical trapping force from an optical fiber probe, to achieve long-distance waveguiding and submicron light focusing in a disordered bio-medium. By applying a trapping light at 980 nm to generate an optical force, stable binding of E. faecalis cells was achieved in a fluid to assemble cell chains of different lengths. The length could reach up to 360 μm and the incident light (at 675, 532 and 473 nm) could be focused into a beam with a waist radius of 400 nm. As a potential practical application, backscattered signals from human red blood cells were detected using the cell chains, which is expected to benefit biomedical sensing and single cell analysis.

Thermo-Electro-Mechanics at Individual Particles in Complex Colloidal Systems

It has been well established that thermoelectric (TE) field can arise from different Soret coefficients of salt ions in the aqueous solution under constant temperature gradient. Despite their high relevance to cellular biology and particle manipulations, understanding and controlling of TE field in complex colloidal systems that involve micro/nanoparticles, salt ions and molecules have remained challenging. In such colloidal systems, the challenge arises from the thermal interactions with charged micro/nanoparticles that distort the TE field around the particles. Herein, we provide a framework for TE field in colloidal suspensions with various ions and surfactants at the single-nanoparticle level. In particular, we reveal the spatial variation of TE field around a dielectric particle under temperature gradient to determine the thermoelectric trapping force on the particle. Our theoretical results on the trapping force predicted from the TE force profile match well with the experimental opto-thermoelectric trapping stiffness of particles in the solutions where the temperature gradient was well-controlled by a laser beam. With their insight into TE field and force in complex systems, our framework and methodology can be extended to engineer the TE field for versatile opto-thermoelectric manipulations of arbitrarily shaped particles with non-uniform surface morphology and to advance the scientific research in cellular biology.

Solenoidal optical forces from a plasmonic Archimedean spiral.

The optical forces generated by a right-handed plasmonic Archimedean spiral (PAS) have been mapped and analyzed. By changing the handedness of the circularly polarized excitation, the structure can switch from a trapping force profile to a rotating force profile. The Helmholtz-Hodge decomposition method has been used to separate the solenoidal component and the conservative component of the force and quantify their relative magnitude. It is shown that the for right-hand circularly polarized excitation, the PAS creates a significant amount of solenoidal forces. Using the decomposed force components, an intuitive explanation of the motion of micro- and nanoparticles in the force field is presented. Vector field topology is used to visualize the force components. The analysis is found to be consistent with numerical and experimental results. Due to the intuitive nature of the analysis, it can be used in the initial design process of complex laboratory-on-a-chip systems where a rigorous analysis is computationally expensive.