Optical Trap Stiffness Research Articles

Probing the Nanonewton Mitotic Cell Deformation Force by Ion-Resonance-Enhanced Photonics Force Microscopy.

Mechanical forces are essential for regulating dynamic changes in cellular activities. A comprehensive understanding of these forces is imperative for unraveling fundamental mechanisms. Here, we develop a microprobe capable of facilitating the measurement of biological forces up to nanonewton levels in living cells. This probe is designed by coating the core of anatase titania particles with amorphous titania and silica shells and an upconversion nanoparticles (UCNPs) layer. Leveraging both antireflection and ion resonance effects from the shells, the optically trapped probe attains a maximum lateral optical trap stiffness of 14.24 pN μm-1 mW-1, surpassing the best reported value by a factor of 3. Employing this advanced probe in a photonic force microscope, we determine the elasticity modulus of mitotic HeLa cells as 1.27 ± 0.3 kPa. Nanonewton probes offer the potential to explore 3D cellular mechanics with unparalleled precision and spatial resolution, fostering a deeper understanding of the underlying biomechanical mechanisms.

Measurement of the optical stiffness of photophoretic force tweezers in air

We report on a method of measuring the stiffness in photophoretic force tweezers in air by using an experimental configuration with two counter-propagating hollow beams. By setting the optical traps of both beams in the same focal plane of the camera, we are able to record the flight procedure of a trapped particle into the other trap after the initial trapping beam is switched off. Then, the stiffness of optical trap can be obtained by fitting the relationship of particle position vs time during the flight procedure. It is found that the measurement is tolerant to the distance between the traps and laser power variation. In addition, the measured stiffness is demonstrated applicable in determining the size of aerosol particles. The reliable method provided in this work is not only useful in studying the physical behavior of signal particle under atmosphere condition but also meaningful in the applications of aerosol studies, such as in situ aerosol characterization and the local surrounding environment sensing.

Determination of liquid viscosity based on dual-frequency-band particle tracking

Abstract An optical-tweezers-based dual-frequency-band particle tracking system was designed and fabricated for liquid viscosity detection. On the basis of the liquid viscosity dependent model of the particle’s restricted Brownian motion with the Faxén correction taken into account, the liquid viscosity and optical trap stiffness were determined by fitting the theoretical prediction with the measured power spectral densities of the particle’s displacement and velocity that were derived from the dual-frequency-band particle tracking data. When the SiO2 beads were employed as probe particles in the measurements of different kinds of liquids, the measurement results exhibited a good agreement with the reported results, as well as a detection uncertainty better than 4.6%. This kind of noninvasive economical technique can be applied in diverse environments for both in situ and ex situ viscosity detection of liquids.

Optical trapping-enhanced probes designed by a deep learning approach

Realizing optical trapping enhancement is crucial in biomedicine, fundamental physics, and precision measurement. Taking the metamaterials with artificially engineered permittivity as photonic force probes in optical tweezers will offer unprecedented opportunities for optical trap enhancement. However, it usually involves multi-parameter optimization and requires lengthy calculations; thereby few studies remain despite decades of research on optical tweezers. Here, we introduce a deep learning (DL) model to attack this problem. The DL model can efficiently predict the maximum axial optical stiffness of Si/Si3N4 (SSN) multilayer metamaterial nanoparticles and reduce the design duration by about one order of magnitude. We experimentally demonstrate that the designed SSN nanoparticles show more than twofold and fivefold improvement in the lateral ( k x and k y ) and the axial ( k z ) optical trap stiffness on the high refractive index amorphous TiO2 microsphere. Incorporating the DL model in optical manipulation systems will expedite the design and optimization processes, providing a means for developing various photonic force probes with specialized functional behaviors.

Calculation and measurement of trapping stiffness in femtosecond optical tweezers.

Due to the characteristics of ultra-short pulse width and ultra-high peak power, femtosecond pulse laser can effectively induce nonlinear optical effects in trapped objects. As a result, it holds great value in the fields of micro and nano manipulation, microfluidics, and cell biology. However, the nonlinear optical effects on the stiffness of femtosecond optical traps remain unclear. Calibration of trap stiffness is crucial for accurately measuring forces and manipulating small particles. In this paper, we compare the stiffness between femtosecond optical traps and continuous wave optical traps. Experimental results demonstrate that the stiffness of the femtosecond optical trap in the splitting direction is greater than that in other directions and the stiffness of the continuous wave optical trap under the same laser power condition. Additionally, as the laser power increases, the stiffnesses of both the femtosecond optical trap and the continuous wave optical trap gradually increases. In contrast to a linear increase of the continuous wave optical trap, the stiffness of the femtosecond optical trap exhibits an exponential rise with increasing laser power. This research provides guidance and reference for improving the force measurement accuracy of femtosecond optical tweezer system.

Improved detection of particle displacement in optical traps using back focal plane interferometry and image processing

Optical tweezers play a crucial role in particle manipulation and force measurement. Therefore, it is essential to calibrate the force measurement parameters, such as the optical trap stiffness and the conversion factor of the sensor deflection signal to the actual displacement of the trapped particle. This calibration is necessary to achieve accurate and efficient parameter calibration. In this study, we employed a suitable image processing method, based on a low-frequency CMOS camera, to calibrate the Displacement Conversion Factor (DCF) of the optical tweezers system. The high accuracy of this image processing method makes it ideal for analyzing the actual displacement of optically trapped microspheres. Interestingly, we discovered that the normalized deflection signal captured by the quadrant photodiode (QPD) through back focal plane interferometry is primarily correlated with the axial height of the trapped microspheres, and is relatively unaffected by laser power variations. Building on this finding, we also examined the linear detection range of the trapped microspheres at different heights. These results address certain limitations associated with the use of optical tweezer systems and provide valuable guidance for utilizing this tool effectively.

Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces.

In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.

Laser writing of parabolic micromirrors with a high numerical aperture for optical trapping and rotation

On-chip optical trapping systems allow for high scalability and lower the barrier to access. Systems capable of trapping multiple particles typically come with high cost and complexity. Here, we present a technique for making parabolic mirrors with micrometer-size dimensions and high numerical apertures (NA > 1). Over 350 mirrors are made by simple CO2 laser ablation of glass followed by gold deposition. We fabricate mirrors of arbitrary diameter and depth at a high throughput rate by carefully controlling the ablation parameters. We use the micromirrors for three-dimensional optical trapping of microbeads in solution, achieving a maximum optical trap stiffness of 52 pN/μm/W. We, then, further demonstrate the viability of the mirrors as in situ optical elements through the rotation of a vaterite particle using reflected circularly polarized light. The method used allows for rapid and highly customizable fabrication of dense optical arrays.

Enhanced transverse optical gradient force on Rayleigh particles in two plane waves.

Based on the full wave simulation and the Maxwell stress tensor theory, we demonstrate an enhanced transverse optical gradient force acting on Rayleigh particles immersed in a simple optical field formed by two linearly polarized plane waves. The optical gradient force acting on a conventional dielectric particle can be enhanced by two orders of magnitude via coating an extremely thin silver shell, whose thickness is only about one-tenth of the dielectric core. The analytical results based on the multipole expansion theory reveal that the enhanced optical gradient force comes mostly from the interaction between the incident field and the electric quadrupole excited in the core-shell particle. It is worth noting that the force expression within the dipole approximation commonly used for Rayleigh particles is invalid in our situation, even the particle is within the Rayleigh regime. In addition, both the optical potential energy and the optical trapping stiffness for the core-shell particle exhibit a great enhancement by two orders of magnitude stronger than a conventional dielectric particle and thus is favorable to a stable optical trapping. These results may extend the application range of optical tweezers and enrich optical manipulation techniques.

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.

Upconversion, MRI imaging and optical trapping studies of silver nanoparticle decorated multifunctional NaGdF4:Yb,Er nanocomposite

The multifunctional upconversion nanoparticles (UCNPs) are fascinating tool for biological applications. In the present work, photon upconverting NaGdF4:Yb,Er and Ag nanoparticles decorated NaGdF4:Yb,Er (NaGdF4:Yb,Er@Ag) nanoparticles were prepared using a simple polyol process. Rietveld refinement was performed for detailed crystal structural and phase fraction analysis. The morphology of the NaGdF4:Yb,Er@Ag was examined using high-resolution transmission electron microscope, which reveals silver nanoparticles of 8 nm in size were decorated over spherical shaped NaGdF4:Yb,Er nanoparticles with a mean particle size of 90 nm. The chemical compositions were confirmed by EDAX and inductively coupled plasma-optical emission spectrometry analyses. The upconversion luminescence (UCL) of NaGdF4:Yb,Er at 980 nm excitation showed an intense red emission. After incorporating the silver nanoparticles, the UCL intensity decreased due to weak scattering and surface plasmon resonance effect. The VSM magnetic measurement indicates both the UCNPs possess paramagnetic behaviour. The NaGdF4:Yb,Er@Ag showed computed tomography imaging. Magnetic resonance imaging study exhibited better T1 weighted relaxivity in the NaGdF4:Yb,Er than the commercial Gd-DOTA. For the first time, the optical trapping was successfully demonstrated for the upconversion NaGdF4:Yb,Er nanoparticle at near-infrared 980 nm light using an optical tweezer setup. The optically trapped UCNP possessing paramagnetic property exhibited a good optical trapping stiffness. The UCL of trapped single UCNP is recorded to explore the effect of the silver nanoparticles. The multifunctional properties for the NaGdF4:Yb,Er@Ag nanoparticle are demonstrated.

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.

Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events.

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

Bessel beam optical tweezers for manipulating superparamagnetic beads.

We propose a Bessel beam optical tweezers setup that can stably trap superparamagnetic beads. The trap stiffness measured is practically independent of the radius of the Bessel beam and of the bead height (distance from the coverlip of the sample chamber), indicating that the beads can be trapped with high accuracy within a wide range of such parameters. On the other hand, the trap stiffness exhibits the expected linear increase with the laser power, despite the non-negligible absorption coefficient of the superparamagnetic beads. A geometrical optics model that considers spherical aberration and light absorption by the beads was used to predict the optical forces and trap stiffness, showing excellent agreement with the experimental data. We believe the results presented here advance the field of optical trapping manipulation of absorbing magnetic particles, and future applications will involve, for example, the design of new hybrid optomagnetic tweezers.

Optical tweezers beyond refractive index mismatch using highly doped upconversion nanoparticles.

Optical tweezers are widely used in materials assembly1, characterization2, biomechanical force sensing3,4 and the in vivo manipulation of cells5 and organs6. The trapping force has primarily been generated through the refractive index mismatch between a trapped object and its surrounding medium. This poses a fundamental challenge for the optical trapping of low-refractive-index nanoscale objects, including nanoparticles and intracellular organelles. Here, we report a technology that employs a resonance effect to enhance the permittivity and polarizability of nanocrystals, leading to enhanced optical trapping forces by orders of magnitude. This effectively bypasses the requirement of refractive index mismatch at the nanoscale. We show that under resonance conditions, highly doping lanthanide ions in NaYF4 nanocrystals makes the real part of the Clausius-Mossotti factor approach its asymptotic limit, thereby achieving a maximum optical trap stiffness of 0.086 pN μm-1 mW-1 for 23.3-nm-radius low-refractive-index (1.46) nanoparticles, that is, more than 30 times stronger than the reported value for gold nanoparticles of the same size. Our results suggest a new potential of lanthanide doping for the optical control of the refractive index of nanomaterials, developing the optical force tag for the intracellular manipulation of organelles and integrating optical tweezers with temperature sensing and laser cooling7 capabilities.

Probing Ligand-Receptor Interaction in Living Cells Using Force Measurements With Optical Tweezers.

This work probes the binding kinetics of COOH-terminus of Clostridium perfringens enterotoxin (c-CPE) and claudin expressing MCF-7 cells using force spectroscopy with optical tweezers. c-CPE is of high biomedical interest due to its ability to specifically bind to claudin with high affinity as well as reversibly disrupt tight junctions whilst maintaining cell viability. We observed single-step rupture events between silica particles functionalized with c-CPE and MCF-7 cells. Extensive calibration of the optical tweezers’ trap stiffness and displacement of the particle from trap center extracted a probable bond rupture force of ≈ 18 pN. The probability of rupture events with c-CPE functionalized silica particles increased by 50% compared to unfunctionalized particles. Additionally, rupture events were not observed when probing cells not expressing claudin with c-CPE coated particles. Overall, this work demonstrates that optical tweezers are invaluable tools to probe ligand-receptor interactions and their potential to study dynamic molecular events in drug-binding scenarios.

Gold cauldrons as efficient candidates for plasmonic tweezers

In this report, gold cauldrons are proposed and proved as efficient candidates for plasmonic tweezers. Gold cauldrons benefit from high field localization in the vicinity of their apertures, leading to particle trapping by a reasonably low power source. The plasmonic trapping capability of a single gold cauldron and a cauldrons cluster are studied by investigating the plasmon-induced variations of the optical trap stiffness in a conventional optical tweezers configuration. This study shows that the localized plasmonic fields and the consequent plasmonic forces lead to enhanced trap stiffness in the vicinity of the cauldrons. This observation is pronounced for the cauldrons cluster, due to the additive plasmonic fields of the neighboring cauldrons. Strong direct plasmonic tweezing by the gold cauldrons cluster is also investigated and confirmed by our simulations and experimental results. In addition to the presented plasmonic trapping behavior, gold cauldrons benefit from a low cost and simple fabrication process with acceptable controllability over the structural average dimensions and plasmonic behavior, making them attractive for emerging lab-on-a-chip optophoresis applications.

Optimizing optical trap stiffness for Rayleigh particles with an Airy array beam

Airy array beams are attractive for optical manipulation of particles owing to their non-diffraction and auto-focusing properties. An Airy array beam is composed of N Airy beams that accelerate mutually and symmetrically in opposite directions, for different ballistics trajectories, i.e., with different initial launch angles. Based on this, we investigate the optical force distribution acting on Rayleigh particles. Results show that it is possible to obtain greater stability for optical trapping by increasing the number of beams in the array. Also, the intensity focal point and gradient and scattering force of the array on Rayleigh particles can be controlled through a launch angle parameter.

Propagation characteristics and optical forces exerted upon a Rayleigh dielectric sphere for a controllable dark-hollow beam

Propagation characteristics and optical forces exerted upon a Rayleigh dielectric sphere for a novel controllable dark-hollow beam (CDHB) are analyzed theoretically and illustrated numerically. In view of the unique focusing characteristics that a sharp, peak-centered, and adjustable configuration would be produced in the focal region, a tightly focused CDHB could be exploited to trap and manipulate particles with high-refractive index in the focal vicinity. Furthermore, it is significant that the CDHB tweezers’ trapping efficiency and optical trap stiffness could be finely controlled by adjusting either the targeted beam’s order or the central dark size controlling parameter. Finally, the trapping stability conditions are analyzed. The results obtained here are of interest and importance in optical manipulations and investigations for a CDHB.

Efficient optical trapping with cylindrical vector beams.

Radially and azimuthally polarized beams can create needle-like electric and magnetic fields under tight focusing conditions, respectively, and thus have been highly recommended for optical manipulation. There have been reports on the superiority of these beams over the conventional Gaussian beam for providing a larger optical force in single beam optical trap. However, serious discrepancies in their experimental results prevent one from concluding this superiority. Here, we theoretically and experimentally study the impact of different parameters - such as spherical aberration, the numerical aperture of the focusing lens, and the particles' size - on optical trapping stiffness of radially, azimuthally, and linearly polarized beams. The result of calculations based on generalized Lorenz-Mie theory, which is in good agreement with the experiment, reveals that the studied parameters determine which polarization state has the superiority for optical trapping. Our findings play a crucial role in the development of optical tweezers setups and, in particular, in biophysical applications when laser-induced heating in the optical tweezers applications is the main concern.