Trapping Force Research Articles

Resonator nanophotonic standing-wave array trap for single-molecule manipulation and measurement

Nanophotonic tweezers represent emerging platforms with significant potential for parallel manipulation and measurements of single biological molecules on-chip. However, trapping force generation represents a substantial obstacle for their broader utility. Here, we present a resonator nanophotonic standing-wave array trap (resonator-nSWAT) that demonstrates significant force enhancement. This platform integrates a critically-coupled resonator design to the nSWAT and incorporates a novel trap reset scheme. The nSWAT can now perform standard single-molecule experiments, including stretching DNA molecules to measure their force-extension relations, unzipping DNA molecules, and disrupting and mapping protein-DNA interactions. These experiments have realized trapping forces on the order of 20 pN while demonstrating base-pair resolution with measurements performed on multiple molecules in parallel. Thus, the resonator-nSWAT platform now meets the benchmarks of a table-top precision optical trapping instrument in terms of force generation and resolution. This represents the first demonstration of a nanophotonic platform for such single-molecule experiments.

Analysis of trapping force exerted on multi-layered chiral sphere induced by laser sheet

Theoretical study on optical trapping of multi-layered chiral sphere has attracted more and more attention for its important applications in many frontier scientific fields such as chemical engineering, biomedicine, optical tweezers, micro/nano lithography etc. In order to trap and manipulate chiral multi-layered particles efficiently, the present paper aims at developing the theoretical research of trapping force (TF) exerted on a multi-layered chiral sphere induced by laser sheet which might have great potential to improve the light performance in optical trapping as well as capture, suspension, and high-precision delivery of chiral cells. Here, based on the Generalized Lorenz Mie theory and the completeness of spherical vector wave functions (SVWFs), the electromagnetic field of incident laser sheet are expanded in terms of SVWFs. Accordingly, by introducing the beam scattering theory and the conservation law of electromagnetic momentum (EM), the analysis of TF exerted on multi-layered chiral sphere can be analytically expressed in terms of the incident and scattering coefficients. Taking the chiral cell as an example, the TF induced by laser sheet is simulated numerically. Numerical effects of the varying chirality, polarization states, beam waist width, inner material loss and outmost size on the TF induced by laser sheet are analyzed and compared with those by circular Gaussian beam incidence in detail. It is found that the introduction of chirality parameter may reduce the axial TF exerted on chiral multi-layered cell. Thus, it is more difficult to trap and manipulate stratified chiral cells than to trap general isotropic cells. Also it is shown that the TF of chiral cells can be significantly discriminatory in nature, depending upon both the handedness of the interacting particles and the polarization of the incident light. Thus, an appropriately polarized beam should be considered in trapping chiral cells. For chiral multi-layered cells with small loss in the inner layer, when the inner refractive indices are less than the outmost refractive index, the TF of multi-layered chiral cell becomes stronger with the outmost radius decreasing. Conversely, for the inner refractive indices are greater than the outer refractive index, TF becomes weaker as the outmost radius decreases. Besides, compared with the traditional circular Gaussian beam, the strong convergence of elliptical Gaussian beam can be easier to achieve three-dimensional capture of stratified chiral cells, which may provide a recipe to understand the light interaction with more complex chiral cells with the aid of the analytical approach and could be a promising avenue for the design of optical trapping systems.

3D-printed capillary force trap reactors (CFTRs) for multiphase catalytic flow chemistry

Figure of 3D illustration of a capillary trap force reactor (CFTR) with transiently trapped liquid nanoparticle catalysts in dimple-shaped capillary traps in the presence of a gas–liquid segmented flow, for the hydrogenation of 1-hexene to n-hexane.

Synthesis of Germanium Nanospheres as High-Precision Optical Tweezers Probes.

Force spectroscopy on single molecular machines generating piconewton forces is often performed using optical tweezers. Since trapping forces scale with the particle volume, piconewton-force measurements so far required micron-sized probes practically limiting the spatiotemporal resolution. Here, we have overcome this limit by developing high-refractive index germanium nanospheres as ultraresolution trapping probes. With a refractive index of 4.4, their trapping efficiency and maximum force per power is more than 10-fold higher compared to silica spheres of equal size. Therefore, the use ofgermanium allows piconewton-force measurements with nanometer sized probes. Using 70-nm-diameter germanium nanospheres as trappable optical probes (GeNTOPs), we could show that kinesin-1 walks with 4-nm-center-of-mass steps. In the long-term, the application of these novel high-precision GeNTOPs will provide new insight into the working mechanism of molecular machines and are promising candidates for other applications in microscopy, optoelectronics, and nanophotonics.

Optical trapping forces of focused circular partially coherent beams on Rayleigh particles

The optical trapping forces of tightly-focused radially polarized circular partially coherent beams on Rayleigh particles are theoretically investigated. Numerical calculations are performed to study the optical trapping forces on Rayleigh particles for different initial coherent length of the incident circular partially coherent beams. The results show that the magnitude of the gradient force decreases with the reduction of the initial coherent length of the focused radially polarized circular partially coherent beams, while the balanced position (i.e., the position where the optical trapping forces becomes zero) stays constant. Moreover, the focused spot gradually elongates along the optical axis with the reduction of the initial coherent length, and the axial gradient force on Rayleigh particles also decreases gradually with the reduction of the intensity gradient in axial direction. As there exists an spherical aberrant in the focusing optical system, the focal spot in the direction of the optical axis becomes trumpet-shaped, and the optical trapping forces on Rayleigh particles change as well.

Trapping and revolving micron particles by transformable line traps of optical tweezers

Optical line tweezers have been an efficient tool for the manipulation of large micron particles. In this paper, we propose to create line traps with transformable configurations by using the transverse electromagnetic mode-like laser source. We designed an optical path to simulate the generation of the astigmatic beams and line traps with a series of lenses to realize the rotational transformation with respect to the rotation angle of cylindrical lenses. It is shown that the spherical particles with diameters ranging from 5 μm to 20 μm could be trapped, aligned, and revolved in experiment. The periodical trapping forces generated by transformable line traps might open an alternative way to investigate the mechanical properties of soft particles and biological cells.

Optical trapping force on two types of particles with a focused partially coherent Lommel-Gaussian beam

In order to explore the capture of two types of particles with different refractive-indexes with focused partially coherent Lommel-Gaussian beam (PCLGB), we numerically derived the expressions of the intensity, and its distribution is also simulated. We found that the focused PCLGB is able to capture two high refractive-index particles at different positions on the focal plane and a low refractive-index particle at the focus, respectively. when the orbital angular momentum (OAM)quantum number, lens focal length, asymmetry parameter decreased, and the spatial correlation length and beam waist increased, the transverse gradient force of the focused PCLGB increased; when the OAM quantum number, lens focal length, asymmetry parameter, spatial correlation length decreased and the beam waist increased, the axial gradient force and scattering force of the focused PCLGB increased. We can choose the optimum optical and lens parameters, a large range and stable trapping can be achieved. The obtained results have certain reference value for the focused PCLGB applied in micromanipulation technology and biotechnology.

Numerical Analysis of Optical Trapping Force Affected by Lens Misalignments

Geometrical optics approximation is a classic method for calculating the optical trapping force on particles whose sizes are larger than the wavelength of the trapping light. In this study, the effect of the lens misalignment on optical force was analyzed in the geometrical optics regime. We used geometrical optics to analyze the influence of off-axis placement and the tilt of the lens on the trapping position and stiffness in an optical trap. Numerical calculation results showed that lens tilting has a greater impact on the optical trap force than the off-axis misalignments, and both misalignments will couple with each other and cause a shift of the equilibrium point and the asymmetry of the optical trap stiffness in different ways. Our research revealed the asymmetry in optical traps caused by lens misalignment and can provide guidance for optimize lens placement in future experiments.

Longitudinal Motion Modeling and Experimental Verification of a Microrobot Subject to Liquid Laminar Flow

This study presents an untethered magnetic manipulation technique for controlling a microrobot position under high rate laminar flows up to 4.5 mL/min. An increase in flow rate exponentially increases the drag force on the microrobot and negatively impacts its positioning accuracy. Increasing the longitudinal force generated by the microrobot's driving apparatus helps in overcoming the disruptive effects of the fluid flow and increases longitudinal motion stability. To this end, we propose a magnetic configuration with two ring-shaped magnets, one above and the other below the microfluidic channel. This configuration causes the magnetic field lines emanating from the ring-shaped magnets to converge on both sides of the microrobot. Thus, the magnetic trapping forces that hold the microrobot in position are increased. To the best of our knowledge, no prior study exists on investigating the longitudinal motion for high flow velocities (>5 mm/s). Investigating the longitudinal forces (along the x-axis) that affect a magnetically-driven microrobot is a novel research topic that has many potential application areas such as cell research, micromanipulation, and lab-on-a-chip systems. The microrobot's dynamical motion is modeled as a second-order system, and using this model as a guideline, we demonstrate the ability of a microrobot in a square-shaped microfluidic channel 900 m 900 m to follow a linear trajectory with a relative velocity up to 132.6 mm/s. A straight and longitudinal trajectory of 4000 m has been successfully followed in the same and opposite directions to the flow for different flow rates (1-4.5 mL/min) and different robot speeds (10-50 mm/s).

Optical Trapping Separation of Chiral Nanoparticles by Subwavelength Slot Waveguides.

Enantiomer separation opens great opportunities to develop the technologies of pharmaceutics, chemicals, and biomedicine, but faces daunting challenges. Here, we discover a considerable chiral-dependent trapping force to separate nanometer-scale enantiomers in a new silicon-based waveguide platform. The electromagnetic chirality gradient of strongly confined evanescent fields can be largely enhanced by the counterpropagating slot waveguides so that the resulting chiral gradient forces can shift the trapping equilibrium positions of dielectric gradient forces. Especially, there exists a transitional width for the slot waveguides to exchange the trapping equilibrium positions between two opposite enantiomers. Our thoroughly numerical investigations demonstrate that the chiral-separable slot waveguides here can offer high efficiency and feasibility of separating chiral nanoparticles, and may pave a route toward new on-chip chiral optical tweezers or optofluidic transport systems for large-scale chiral separation.

Towards non-blind optical tweezing by finding 3D refractive index changes through off-focus interferometric tracking

In modern 3D microscopy, holding and orienting arbitrary biological objects with optical forces instead of using coverslips and gel cylinders is still a vision. Although optical trapping forces are strong enough and related photodamage is acceptable, the precise (re-) orientation of large specimen with multiple optical traps is difficult, since they grab blindly at the object and often slip off. Here, we present an approach to localize and track regions with increased refractive index using several holographic optical traps with a single camera in an off-focus position. We estimate the 3D grabbing positions around several trapping foci in parallel through analysis of the beam deformations, which are continuously measured by defocused camera images of cellular structures inside cell clusters. Although non-blind optical trapping is still a vision, this is an important step towards fully computer-controlled orientation and feature-optimized laser scanning of sub-mm sized biological specimen for future 3D light microscopy.

A Miniature Optical Force Dual-Axis Accelerometer Based on Laser Diodes and Small Particles Cavities.

In recent years, the optical accelerometer based on the optical trapping force effect has gradually attracted the attention of researchers for its high sensitivity and high measurement accuracy. However, due to its large size and the complexity of optical path adjustment, the optical force accelerometers reported are only suitable for the laboratory environment up to now. In this paper, a miniature optical force dual-axis accelerometer based on the miniature optical system and a particles cavity which is prepared by Micro-Electro-Mechanical Systems (MEMS) technology is proposed. The overall system of the miniature optical levitation including the miniature optical system and MEMS particles cavity is a cylindrical structure with a diameter of about 10 mm and a height of 33 mm (Φ 10 mm × 33 mm). Moreover, the size of this accelerometer is 200 mm × 100 mm × 100 mm. Due to the selected light source being a laser diode light source with elliptical distribution, it is sensitive to the external acceleration in both the long axis and the short axis. This accelerometer achieves a measurement range of ±0.17 g–±0.26 g and measurement resolution of 0.49 mg and 1.88 mg. The result shows that the short-term zero-bias stability of the two orthogonal axes of the optical force accelerometer is 4.4 mg and 9.2 mg, respectively. The main conclusion that can be drawn is that this optical force accelerometer could provide an effective solution for measuring acceleration with an optical force effect for compact engineering devices.

Method for evaluating the polarization performance of cylindrical vector polarized beams

Cylindrical vector polarized (CVP) beams are widely used in many applications due to their special polarized distribution and highly focused properties. It is crucial to evaluate the polarization performance of CVP beams. This paper proposes several polarization parameters for comprehensively evaluating the overall polarization performance and spatial polarization symmetry of CVP beams. To verify this method, several different CVP beams are simulated, and the polarization performance of these beams are indicated. In addition, the trapping models are built to compare trapping capacities of the beams with different polarization performance. The results indicate that the ideal CVP beams demonstrated a higher trapping force than the non-ideal ones, and the trapping force was sensitive to the spatial polarization symmetry of the beams. This evaluation method plays an important role in applications that are susceptible to the polarization performance of the beams.

Bessel-modulated autofocusing beams for optimal trapping implementation

Abruptly autofocusing beams were proposed and tested for a variety of applications such as optical manipulation, yet their trapping performance associated with the optical forces and trap stiffness remains largely unexplored. In this work, we design and demonstrate specially modulated autofocusing beams. We theoretically and experimentally show improved properties of such beams and their trapping capabilities as compared to their unmodulated counterparts. In particular, an autofocusing beam tailored with a Bessel function exhibits a shorter focal length and a much stronger peak intensity than that of an unmodulated circular Airy beam. Moreover, we perform optical tweezer experiments using both the modulated and unmodulated autofocusing beams to trap microbeads and red blood cells for direct comparison, and find that the Bessel-modulated beam displays an enhanced trapping capability, thanks to a stronger optical trapping force due to its peculiar intensity landscape. Compared with the conventional circular Airy beams, optical tweezers based on our modulated autofocusing beams exhibit a superior performance, which may lead to new photonic tools for optical trapping and manipulation.

FIB-milled plasmonic nanoapertures allow for long trapping times of individual proteins

SummaryWe have developed a fabrication methodology for label-free optical trapping of individual nanobeads and proteins in inverted-bowtie-shaped plasmonic gold nanopores. Arrays of these nanoapertures can be reliably produced using focused ion beam (FIB) milling with gap sizes of 10–20 nm, single-nanometer variation, and with a remarkable stability that allows for repeated use. We employ an optical readout where the presence of the protein entering the trap is marked by an increase in the transmission of light through the nanoaperture from the shift of the plasmonic resonance. In addition, the optical trapping force of the plasmonic nanopores allows 20-nm polystyrene beads and proteins, such as beta-amylase and Heat Shock Protein (HSP90), to be trapped for very long times (approximately minutes). On demand, we can release the trapped molecule for another protein to be interrogated. Our work opens up new routes to acquire information on the conformation and dynamics of individual proteins.

Optical trapping force and torque on a Rayleigh spheroidal particle by a non-diffracting optical needle

Optical trapping force and torque on a Rayleigh spheroidal particle by a non-diffracting optical needle

Trapped two-nucleon system in energy-dependent effective field theory

We discuss how to connect the energy levels of two-particle systems trapped by a harmonic-oscillator force to scattering amplitudes, with nucleon-nucleon scattering phase shifts in uncoupled channels as the application. At the center of the proposed framework is the energy-dependent effective field theory that aims to expand observables in a neighborhood around each reference energy, often taken to be one of the energy levels. We also investigate how to disentangle the trapping force at short distances and the intrinsic interaction between the particles.

Dynamical gravastars from the interaction between scalar fields and matter

Gravastars are configurations of compact singularity-free gravitational objects which are interesting alternatives to classical solutions in the strong gravitational field regime. Although there are no static star-like solutions of the Einstein–Klein–Gordon equations for real scalar fields, we show that dynamical gravastars solutions arise through the direct interaction of a scalar field with matter. Two configurations presented here show that, within the internal zone, the scalar field plays a role similar to a cosmological constant, while it decays at large distances as the Yukawa potential. Like classical gravastars, these solutions exhibit small values of the temporal metric component near a transitional radial value, although this behaviour is not determined by the de Sitter nature of the internal space-time, but rather by a slowly-varying scalar field. The scalar field-matter interaction is able to define trapping forces that rigorously confine the polytropic gases to the interior of a sphere. At the surface of these spheres, pressures generated by the field-matter interaction play the role of “walls” preventing the matter from flowing out. These solutions predict a stronger scattering of the accreting matter with respect to Schwarzschild black holes.

Elastic property of sickle cell anemia and sickle cell trait red blood cells.

.Significance: We introduce a model for better calibration of the trapping force using an equal but oppositely directed drag force acting on a trapped red blood cell (RBC). We demonstrate this approach by studying RBCs’ elastic properties from deidentified sickle cell anemia (SCA) and sickle cell trait (SCT) blood samples.Aim: A laser trapping (LT) force was formulated and analytically calculated in a cylindrical model. Using this trapping force relative percent difference, the maximum (longitudinal) and minimum (transverse) radius rate and stiffness were used to study the elasticity.Approach: The elastic property of SCA and SCT RBCs was analyzed using LT technique with computer controlled piezo-driven stage, in order to trap and stretch the RBCs.Results: For all parameters, the results show that the SCT RBC samples have higher elastic property than the SCA RBCs. The higher rigidity in the SCA cell may be due to the lipid composition of the membrane, which was affected by the cholesterol concentration.Conclusions: By developing a theoretical model for different trapping forces, we have also studied the elasticity of RBCs in SCT (with hemoglobin type HbAS) and in SCA (with hemoglobin type HbSS). The results for the quantities describing the elasticity of the cells consistently showed that the RBCs in the SCT display lower rigidity and higher deformability than the RBCs with SCA.

Magnetic levitation force and trapped field properties of multiseeded YBCO with triangular arrangement of seeds

AbstractAlthough there are studies in literature using different number of seeds with different arrangements, especially line and rectangular, it is seen that there is no detailed study handling the levitation force together with trapped field properties of triangular arrangement of seed in YBCO. Therefore, to further investigate the magnetic properties of seeded YBCO superconductors, we have fabricated cylindrical YBCO (YBa2Cu3O7) superconductors with triangular arrangement of the seeds with different seed distances. Maximum levitation force values were obtained as 39.4 N and 57.1 N, while the maximum guidance force values were obtained as −4.6 N, and −8.7 N, respectively, with single‐seeded and triangular‐seeded samples with seed distance of 14 mm. It was determined that the trapped field, levitation force, and guidance force firstly decreased from the single‐seeded sample to the triangular‐seeded sample with small seed distance and then increased with increasing seed distance. Increased field trapping and levitation force performances in the triangular‐seeded samples with suitable seed distance indicate that the triangular arrangement of seeds is an eligible method to produce larger dimension YBCO samples with bigger shielding current radius and bigger averaged trapped field values.