Comparative study of methods to calibrate the stiffness of a single-beam gradient-force optical tweezers over various laser trapping powers

Opto-thermal manipulation with a 3 µm mid-infrared Er:ZBLAN fiber laser

Water has significantly high absorption around 3 µm wavelength region, originated by its fundamental OH vibrational modes. Here, we successfully demonstrate an opto-thermal manipulation of particles utilizing a 3 µm mid-infrared Er:ZBLAN fiber laser (adjustable from 2700 to 2826 nm) that can efficiently elevate the temperature at a laser focus with a low laser power. The 3 µm laser indeed accelerates the formation of the particle assembly by simply irradiating the laser into water. By altering the laser wavelengths, the assembling speed and size, instantaneous particle velocity, particle distribution, trapping stiffness and temperature elevation are evaluated systematically. We propose that the dynamics of particle assembly can be understood through thermo-osmotic slip flows, taking into account the effects of volume heating within the focal cone and point heating at the focus.

Trapping and manipulation of bubbles with holographic optical tweezers

A methodology to manipulate bubbles and measure adhesion forces is presented and validated. Holographic optical tweezers are employed to establish a circular array of high intensity points to effectively trap a gas bubble within a liquid medium. This approach includes an efficient calibration protocol based on a theoretical framework for the calculation of optical forces using a ray tracing algorithm, which allows enhancing the versatility of optical manipulation to micro-objects with a lower refractive index than the surrounding medium. As an initial application, the adhesion force between two stable bubbles at different sizes is measured, finding a minimum when they have the same diameter.

On-Axis Optical Trapping with Vortex Beams: The Role of the Multipolar Decomposition

Optical trapping is a well-established, decades old technology with applications in several fields of research. The most common scenario deals with particles that tend to be centered on the brightest part of the optical trap. Consequently, the optical forces keep the particle away from the dark zones of the beam. However, this is not the case when a focused doughnut-shaped beam generates on-axis trapping. In this system, the particle is centered on the intensity minima of the laser beam and the bright annular part lies on the periphery of the particle. Researchers have shown great interest in this phenomenon due to its advantage of reducing light interaction with trapped particles and the intriguing increase in the trapping strength. This work presents experimental and theoretical results that extend the analysis of on-axis trapping with light vortex beams. Specifically, in our experiments, we trap micron-sized spherical silica (SiO2) particles in water and we measure, through the power spectrum density method, the trap stiffness constant κ generated by vortex beams with different topological charge orders. The optical forces are calculated from the exact solutions of the electromagnetic fields provided by the generalized Lorentz-Mie theory. We show a remarkable agreement between the theoretical prediction and the experimental measurements of κ. Moreover, our numerical model gives us information about the electromagnetic fields inside the particle, offering valuable insights into the influence of the electromagnetic fields present in the vortex beam trapping scenario.

Optical Tweezers Apparatus Based on a Cost-Effective IR Laser-Hardware and Software Description

Optical tweezers (OT), or optical traps, are a device for manipulating microscopic objects through a focused laser beam. They are used in various fields of physical and biophysical chemistry to identify the interactions between individual molecules and measure single-molecule forces. In this work, we describe the development of a homemade optical tweezers device based on a cost-effective IR diode laser, the hardware, and, in particular, the software controlling it. It allows us to control the instrument, calibrate it, and record and process the measured data. It includes the user interface design, peripherals control, recording, A/D conversion of the detector signals, evaluation of the calibration constants, and visualization of the results. Particular stress is put on the signal filtration from noise, where several methods were tested. The calibration experiments indicate a good sensitivity of the instrument that is thus ready to be used for various single-molecule measurements.

Anapole-Assisted Low-Power Optical Trapping of Nanoscale Extracellular Vesicles and Particles

This study addresses the challenge of trapping nanoscale biological particles using optical tweezers without the photothermal heating effect and the limitation presented by the diffraction limit. Optical tweezers are effective for trapping microscopic biological objects but not for nanoscale specimens due to the diffraction limit. To overcome this, we present an approach that uses optical anapole states in all-dielectric nanoantenna systems on distributed Bragg reflector substrates to generate strong optical gradient force and potential on nanoscale biological objects with negligible temperature rise below 1 K. The anapole antenna condenses the accessible electromagnetic energy to scales as small as 30 nm. Using this approach, we successfully trapped nanosized extracellular vesicles and supermeres (approximately 25 nm in size) using low laser power of only 10.8 mW. This nanoscale optical trapping platform has great potential for single molecule analysis while precluding photothermal degradation.

Strain stiffening of Ndc80 complexes attached to microtubule plus ends

In the mitotic spindle, microtubules attach to chromosomes via kinetochores. The microtubule-binding Ndc80 complex is an integral part of kinetochores, and is essential for kinetochores to attach to microtubules and to transmit forces from dynamic microtubule ends to the chromosomes. The Ndc80 complex has a rod-like appearance with globular domains at its ends that are separated by a long coiled coil. Its mechanical properties are considered important for the dynamic interaction between kinetochores and microtubules. Here, we present a novel method that allows us to time trace the effective stiffness of Ndc80 complexes following shortening microtubule ends against applied force in optical trap experiments. Applying this method to wild-type Ndc80 and three variants (calponin homology (CH) domains mutated or Hec1 tail unphosphorylated, phosphorylated, or truncated), we reveal that each variant exhibits strain stiffening; i.e., the effective stiffness increases under tension that is built up by a depolymerizing microtubule. The strain stiffening relation is roughly linear and independent of the state of the microtubule. We introduce structure-based models that show that the strain stiffening can be traced back to the specific architecture of the Ndc80 complex with a characteristic flexible kink, to thermal fluctuations of the microtubule, and to the bending elasticity of flaring protofilaments, which exert force to move the Ndc80 complexes. Our model accounts for changes in the amount of load-bearing attachments at various force levels and reproduces the roughly linear strain stiffening behavior, highlighting the importance of force-dependent binding affinity.

Lightsheet optical tweezer (LOT) for optical manipulation of microscopic particles and live cells

Optical trapping and patterning cells or microscopic particles is fascinating. We developed a light sheet-based optical tweezer to trap dielectric particles and live HeLa cells. The technique requires the generation of a tightly focussed diffraction-limited light-sheet realized by a combination of cylindrical lens and high NA objective lens. The resultant field is a focussed line (along x-axis) perpendicular to the beam propagation direction (z-axis). This is unlike traditional optical tweezers that are fundamentally point-traps and can trap one particle at a time. Several spherical beads undergoing Brownian motion in the solution are trapped by the lightsheet gradient potential, and the time (to reach trap-centre) is estimated from the video captured at 230 frames/s. High-speed imaging of beads with increasing laser power shows a steady increase in trap stiffness with a maximum of 0.00118 pN/nm at 52.5 mW. This is order less than the traditional point-traps, and hence may be suitable for applications requiring delicate optical forces. On the brighter side, light sheet tweezer (LOT) can simultaneously trap multiple objects with the distinct ability to manipulate them in the transverse (xy) plane via translation and rotation. However, the trapped beads displayed free movement along the light-sheet axis (x-axis), exhibiting a single degree of freedom. Furthermore, the tweezer is used to trap and pattern live HeLa cells in various shapes and structures. Subsequently, the cells were cultured for a prolonged period of time (> 18 h), and cell viability was ascertained. We anticipate that LOT can be used to study constrained dynamics of microscopic particles and help understand the patterned cell growth that has implications in optical imaging, microscopy, and cell biology.

Directly Measuring Forces within Reconstituted Active Microtubule Bundles

Microtubule networks are employed in cells to accomplish a wide range of tasks, ranging from acting as tracks for vesicle transport to working as specialized arrays during mitosis to regulate chromosome segregation. Proteins that interact with microtubules include motors such as kinesins and dynein, which can generate active forces and directional motion, as well as non-motor proteins that crosslink filaments into higher-order networks or regulate filament dynamics. To date, biophysical studies of microtubule-associated proteins have overwhelmingly focused on the role of single motor proteins needed for vesicle transport, and significant progress has been made in elucidating the force-generating properties and mechanochemical regulation of kinesins and dyneins. However, for processes in which microtubules act both as cargo and track, such as during filament sliding within the mitotic spindle, much less is understood about the biophysical regulation of ensembles of the crosslinking proteins involved. Here, we detail our methodology for directly probing force generation and response within crosslinked microtubule minimal networks reconstituted from purified microtubules and mitotic proteins. Microtubule pairs are crosslinked by proteins of interest, one microtubule is immobilized to a microscope coverslip, and the second microtubule is manipulated by an optical trap. Simultaneous total internal reflection fluorescence microscopy allows for multichannel visualization of all the components of this microtubule network as the filaments slide apart to generate force. We also demonstrate how these techniques can be used to probe pushing forces exerted by kinesin-5 ensembles and how viscous braking forces arise between sliding microtubule pairs crosslinked by the mitotic MAP PRC1. These assays provide insights into the mechanisms of spindle assembly and function and can be more broadly adapted to study dense microtubule network mechanics in diverse contexts, such as the axon and dendrites of neurons and polar epithelial cells.

Morphological Characteristics, Hemoglobin Content, and Membrane Mechanical Properties of Red Blood Cell Delivery Systems

Red blood cell (RBC)-based systems are under extensive development as platforms for the delivery of various biomedical agents. While the importance of the membrane biochemical characteristics in relation to circulation kinetics of RBC delivery systems has been recognized, the membrane mechanical properties of such carriers have not been extensively studied. Using optical methods in conjunction with image analysis and mechanical modeling, we have quantified the morphological and membrane mechanical characteristics of RBC-derived microparticles containing the near-infrared cargo indocyanine green (ICG). We find that these particles have a significantly lower surface area, volume, and deformability as compared to normal RBCs. The residual hemoglobin has a spatially distorted distribution in the particles. The membrane bending modulus of the particles is about twofold higher as compared to normal RBCs and exhibits greater resistance to flow. The induced increase in the viscous characteristics of the membrane is dominant over the elastic and entropic effects of ICG. Our results suggest that changes to the membrane mechanical properties are a result of impaired membrane-cytoskeleton attachment in these particles. We provide a mechanistic explanation to suggest that the compromised membrane-cytoskeleton attachment and altered membrane compositional and structural asymmetry induce curvature changes to the membrane, resulting in mechanical remodeling of the membrane. These findings highlight the importance of membrane mechanical properties as an important criterion in the design and engineering of future generations of RBC-based delivery systems to achieve prolonged circulation.

Flagellar rotational features of an optically confined bacterium at high frequency and temporal resolution reveal the microorganism's response to changes in the fluid environment

Rotations of the flagella control the movement of a peritrichous (multiflagellar) bacterium in fluids, the run and tumble events being caused through modulations in the flagella's collective rotation speed and pattern. Observing such modulations is a challenge in free swimming bacteria. In this work, we present a setup to measure the collective flagellar rotational features of an optically confined Bacillus subtilis bacterium. We adopt a Continuous Wavelet Technique (CWT) while monitoring the rotational patterns in frequency and time, thus achieving optimal resolution in both the domains. This enables in marking the events wherein subtle changes in the flagellar rotational pattern occur. These studies unravel a fact, hitherto unknown, that variations in swimming speed that are seen in pure run sequences are also caused by modulations in the rotating flagella. Further, we have monitored the flagellar rotation for durations over a minute and observe a gradual slowing down of the rotation before ceasing completely due to the trapping laser induced photodamage. We have observed a significant alteration in the rate of rotational fall off in real time with changes in pH or the nutrient concentration in the fluid. This work serves to demonstrate the advantage of optical confinement of a bacterium in its pristine form for carrying out such studies and can serve as a marker for work that assesses membrane photodamage in active matter. Details on the role of flagella in propulsion and on other factors influencing the rotations, can be of significance in the design of artificial microswimmers.

Multimodal regulation of myosin VI ensemble transport by cargo adaptor protein GIPC

A range of cargo adaptor proteins are known to recruit cytoskeletal motors to distinct subcellular compartments. However, the structural impact of cargo recruitment on motor function is poorly understood. Here, we dissect the multimodal regulation of myosin VI activity through the cargo adaptor GAIP-interacting protein, C terminus (GIPC), whose overexpression with this motor in cancer enhances cell migration. Using a range of biophysical techniques, including motility assays, FRET-based conformational sensors, optical trapping, and DNA origami-based cargo scaffolds to probe the individual and ensemble properties of GIPC-myosin VI motility, we report that the GIPC myosin-interacting region (MIR) releases an autoinhibitory interaction within myosin VI. We show that the resulting conformational changes in the myosin lever arm, including the proximal tail domain, increase the flexibility of the adaptor-motor linkage, and that increased flexibility correlates with faster actomyosin association and dissociation rates. Taken together, the GIPC MIR-myosin VI interaction stimulates a twofold to threefold increase in ensemble cargo speed. Furthermore, the GIPC MIR-myosin VI ensembles yield similar cargo run lengths as forced processive myosin VI dimers. We conclude that the emergent behavior from these individual aspects of myosin regulation is the fast, processive, and smooth cargo transport on cellular actin networks. Our study delineates the multimodal regulation of myosin VI by the cargo adaptor GIPC, while highlighting linkage flexibility as a novel biophysical mechanism for modulating cellular cargo motility.

Temperature Quantification and Temperature Control in Optical Tweezers

Optical tweezers are widely used to investigate biomolecules and biomolecular interactions. In these investigations, the biomolecules of interest are typically coupled to microscopic beads that can be optically trapped. Since high-intensity laser beams are required to trap such microscopic beads, laser-induced heating due to optical absorption is typically unavoidable. This chapter discusses how to identify, quantify, and control thermal effects in optical tweezers. We provide a brief overview of the reported causes and effects of unwanted heating in optical tweezers systems. Specific details are provided on methods to perform a temperature-independent trap calibration procedure. Finally, an effective temperature-control system is presented, and we discuss the operation of this system as well as the methods to measure the temperature at the optically trapped particle.

Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides

Liquid-liquid phase separation of multivalent proteins and RNAs drives the formation of biomolecular condensates that facilitate membrane-free compartmentalization of subcellular processes. With recent advances, it is becoming increasingly clear that biomolecular condensates are network fluids with time-dependent material properties. Here, employing microrheology with optical tweezers, we reveal molecular determinants that govern the viscoelastic behavior of condensates formed by multivalent Arg/Gly-rich sticker-spacer polypeptides and RNA. These condensates behave as Maxwell fluids with an elastically-dominant rheological response at shorter timescales and a liquid-like behavior at longer timescales. The viscous and elastic regimes of these condensates can be tuned by the polypeptide and RNA sequences as well as their mixture compositions. Our results establish a quantitative link between the sequence- and structure-encoded biomolecular interactions at the microscopic scale and the rheological properties of the resulting condensates at the mesoscale, enabling a route to systematically probe and rationally engineer biomolecular condensates with programmable mechanics.

Particle Classification through the Analysis of the Forward Scattered Signal in Optical Tweezers

The ability to select, isolate, and manipulate micron-sized particles or small clusters has made optical tweezers one of the emergent tools for modern biotechnology. In conventional setups, the classification of the trapped specimen is usually achieved through the acquired image, the scattered signal, or additional information such as Raman spectroscopy. In this work, we propose a solution that uses the temporal data signal from the scattering process of the trapping laser, acquired with a quadrant photodetector. Our methodology rests on a pre-processing strategy that combines Fourier transform and principal component analysis to reduce the dimension of the data and perform relevant feature extraction. Testing a wide range of standard machine learning algorithms, it is shown that this methodology allows achieving accuracy performances around 90%, validating the concept of using the temporal dynamics of the scattering signal for the classification task. Achieved with 500 millisecond signals and leveraging on methods of low computational footprint, the results presented pave the way for the deployment of alternative and faster classification methodologies in optical trapping technologies.

Optical microlever assisted DNA stretching

Optical microrobotics is an emerging field that has the potential to improve upon current optical tweezer studies through avenues such as limiting the exposure of biological molecules of interest to laser radiation and overcoming the current limitations of low forces and unwanted interactions between nearby optical traps. However, optical microrobotics has been historically limited to rigid, single-body end-effectors rather than even simple machines, limiting the tasks that can be performed. Additionally, while multi-body machines such as microlevers exist in the literature, they have not yet been successfully demonstrated as tools for biological studies, such as molecule stretching. In this work we have taken a step towards moving the field forward by developing two types of microlever, produced using two-photon absorption polymerisation, to perform the first lever-assisted stretches of double-stranded DNA. The aim of the work is to provide a proof of concept for using optical micromachines for single molecule studies. Both styles of microlevers were successfully used to stretch single duplexes of DNA, and the results were analysed with the worm-like chain model to show that they were in good agreement.

Multi-frequency passive and active microrheology with optical tweezers

Optical tweezers have attracted significant attention for microrheological applications, due to the possibility of investigating viscoelastic properties in vivo which are strongly related to the health status and development of biological specimens. In order to use optical tweezers as a microrheological tool, an exact force calibration in the complex system under investigation is required. One of the most promising techniques for optical tweezers calibration in a viscoelastic medium is the so-called active–passive calibration, which allows determining both the trap stiffness and microrheological properties of the medium with the least a-priori knowledge in comparison to the other methods. In this manuscript, we develop an optimization of the active–passive calibration technique performed with a sample stage driving, whose implementation is more straightforward with respect to standard laser driving where two different laser beams are required. We performed microrheological measurements over a broad frequency range in a few seconds implementing an accurate multi-frequency driving of the sample stage. The optical tweezers-based microrheometer was first validated by measuring water, and then exemplarily applied to more viscous medium and subsequently to a viscoelastic solution of methylcellulose in water. The described method paves the way to microrheological precision metrology in biological samples with high temporal- and spatial-resolution allowing for investigation of even short time-scale phenomena.

Cubic-Phase Metasurface for Three-Dimensional Optical Manipulation

The optical tweezer is one of the important techniques for contactless manipulation in biological research to control the motion of tiny objects. For three-dimensional (3D) optical manipulation, shaped light beams have been widely used. Typically, spatial light modulators are used for shaping light fields. However, they suffer from bulky size, narrow operational bandwidth, and limitations of incident polarization states. Here, a cubic-phase dielectric metasurface, composed of GaN circular nanopillars, is designed and fabricated to generate a polarization-independent vertically accelerated two-dimensional (2D) Airy beam in the visible region. The distinctive propagation characteristics of a vertically accelerated 2D Airy beam, including non-diffraction, self-acceleration, and self-healing, are experimentally demonstrated. An optical manipulation system equipped with a cubic-phase metasurface is designed to perform 3D manipulation of microscale particles. Due to the high-intensity gradients and the reciprocal propagation trajectory of Airy beams, particles can be laterally shifted and guided along the axial direction. In addition, the performance of optical trapping is quantitatively evaluated by experimentally measured trapping stiffness. Our metasurface has great potential to shape light for compact systems in the field of physics and biological applications.

Electrothermoplasmonic Trapping and Dynamic Manipulation of Single Colloidal Nanodiamond

Low-power trapping of nanoscale objects can be achieved by using the enhanced fields near plasmonic nanoantennas. Unfortunately, in this approach the trap site is limited to the position of the plasmonic hotspots and continuous dynamic manipulation is not feasible. Here, we report a low-frequency electrothermoplasmonic tweezer (LFET) that provides low-power, high-stability and continuous dynamic manipulation of a single nanodiamond. LFET harnesses the combined action of the laser illumination of a plasmonic nanopillar antenna array and low-frequency alternating current (ac) electric field to establish an electrohydrodynamic potential capable of the stable trapping and dynamic manipulation of single nanodiamonds. We experimentally demonstrate the fast transport, trapping, and dynamic manipulation of a single nanodiamond using a low-frequency ac field below 5 kHz and low-laser power of 1 mW. This nanotweezer platform for nanodiamond manipulation holds promise for the scalable assembly of single photon sources for quantum information processing and low noise quantum sensors.

Determining Trap Compliances, Microsphere Size Variations, and Response Linearities in Single DNA Molecule Elasticity Measurements with Optical Tweezers

We previously introduced the use of DNA molecules for calibration of biophysical force and displacement measurements with optical tweezers. Force and length scale factors can be determined from measurements of DNA stretching. Trap compliance can be determined by fitting the data to a nonlinear DNA elasticity model, however, noise/drift/offsets in the measurement can affect the reliability of this determination. Here we demonstrate a more robust method that uses a linear approximation for DNA elasticity applied to high force range (25-45 pN) data. We show that this method can be used to assess how small variations in microsphere sizes affect DNA length measurements and demonstrate methods for correcting for these errors. We further show that these measurements can be used to check assumed linearities of system responses. Finally, we demonstrate methods combining microsphere imaging and DNA stretching to check the compliance and positioning of individual traps.

Quantitative analysis of the three-dimensional trap stiffness of a dielectrophoretic corral trap

Dielectrophoresis is a robust approach for the manipulation and separation of (bio)particles using microfluidic platforms. We developed a dielectrophoretic corral trap in a microfluidic device that utilizes negative dielectrophoresis to capture single spherical polystyrene particles. Circular-shaped micron-size traps were employed inside the device and the three-dimensional trap stiffness (restoring trapping force from equilibrium trapping location) was analyzed using 4.42 μm particles and 1 MHz of an alternating electric field from 6 V_P-P to 10 V_P-P . The trap stiffness increased exponentially in the x- and y-direction, and linearly in the z-direction. Image analysis of the trapped particle movements revealed that the trap stiffness is increased 608.4, 539.3, and 79.7% by increasing the voltage from 6 V_P-P to 10 V_P-P in the x-, y-, and z-direction, respectively. The trap stiffness calculated from a finite element simulation of the device confirmed the experimental results. This analysis provides important insights to predict the trapping location, strength of the trapping, and optimum geometry for single particle trapping and its applications such as single-molecule analysis and drug discovery.

Increasing AFM colloidal probe accuracy by optical tweezers

A precise determination of the cantilever spring constant is the critical point of all colloidal probe experiments. Existing methods are based on approximations considering only cantilever geometry and do not take into account properties of any object or substance attached to the cantilever. Neglecting the influence of the colloidal sphere on the cantilever characteristics introduces significant uncertainty in a spring constant determination and affects all further considerations. In this work we propose a new method of spring constant calibration for 'colloidal probe' type cantilevers based on the direct measurement of force constant. The Optical Tweezers based calibration method will help to increase the accuracy and repeatability of the AFM colloidal probe experiments.

Optical Manipulation of Lanthanide-Doped Nanoparticles: How to Overcome Their Limitations

Since Ashkin's pioneering work, optical tweezers have become an essential tool to immobilize and manipulate microscale and nanoscale objects. The use of optical tweezers is key for a variety of applications, including single-molecule spectroscopy, colloidal dynamics, tailored particle assembly, protein isolation, high-resolution surface studies, controlled investigation of biological processes, and surface-enhanced spectroscopy. In recent years, optical trapping of individual sub-100-nm objects has got the attention of the scientific community. In particular, the three-dimensional manipulation of single lanthanide-doped luminescent nanoparticles is of great interest due to the sensitivity of their luminescent properties to environmental conditions. Nevertheless, it is really challenging to trap and manipulate single lanthanide-doped nanoparticles due to the weak optical forces achieved with conventional optical trapping strategies. This limitation is caused, firstly, by the diffraction limit in the focusing of the trapping light and, secondly, by the Brownian motion of the trapped object. In this work, we summarize recent experimental approaches to increase the optical forces in the manipulation of lanthanide-doped nanoparticles, focusing our attention on their surface modification and providing a critical review of the state of the art and future prospects.

Optical trapping in the presence of laser-induced thermal effects

The inclusion of thermal effects in optical manipulation has been explored in diverse experiments, increasing the possibilities for applications in diverse areas. In this Letter, the results of combined optical and thermal manipulation in the vicinity of a highly absorbent hydrogenated amorphous silicon layer, which induces both the generation of convective currents and thermophoresis, are presented. In combination with the optical forces, thermal forces help reduce the optical power required to trap and manipulate micrometric polystyrene beads. Moreover, the inclusion of these effects allows the stacking and manipulation of multiple particles with a single optical trap along with the beam propagation, providing an extra tool for micromanipulation of a variety of samples.

Measurement of the capillary interaction force between Janus colloidal particles trapped at a flat air/water interface

The capillary interaction force between spherical Janus particles trapped at the air-water interface is measured using a time-sharing optical tweezer (bond number ≪ 1). One face of the particles is hydrophilic, and the other one, hydrophobic. Measured force goes from almost pure quadrupolar to almost pure hexapolar interaction due to the three-phase contact line corrugation. Measured force curves are modeled as a sum of power laws, Ar^-α + Br^-β + Cr^-γ, obtained from an expansion in capillary multipoles. The mean values for the exponents of particle pairs of 3 μm are 〈α〉 = 5.05 ± 0.12, 〈β〉 = 7.02 ± 0.03, and 〈γ〉 = 5.96 ± 0.03. For particles pairs of 5 μm, we find 〈α〉 = 5.02 ± 0.04, 〈β〉 = 6.94 ± 0.06, and 〈γ〉 = 5.80 ± 0.05. In both cases, A < 0, B < 0, and C > 0.

Trap stiffness modification of an optically trapped microsphere through directed motion of nanoparticles

We report an enhancement in the corner frequency of an optically trapped non-magnetic microsphere in the plane perpendicular to the laser propagation direction on addition of ferrofluid to the suspension medium. We conjecture that a directed motion of the nanoparticles toward the trap in this plane is responsible for the augmentation. Changes in the corner frequency in the presence of external magnetic field gradients lend credence to this conjecture. Corner frequency augmentation is also observed when zinc oxide nanoparticles are used. Here, however, no further changes are seen in the presence of magnetic field gradients.

Video microscopy-based accurate optical force measurement by exploring a frequency-changing sinusoidal stimulus

Optical tweezers are constantly evolving micromanipulation tools that can provide piconewton force measurement accuracy and greatly promote the development of bioscience at the single-molecule scale. Consequently, there is an urgent need to characterize the force field generated by optical tweezers in an accurate, cost-effective, and rapid manner. Thus, in this study, we conducted a deep survey of optically trapped particle dynamics and found that merely quantifying the response amplitude and phase delay of particle displacement under a sine input stimulus can yield sufficiently accurate force measurements. In addition, Nyquist-Shannon sampling theorem suggests that the entire recovery of the accessible particle sinusoidal response is possible, provided that the sampling theorem is satisfied, thereby eliminating the requirement for high-bandwidth (typically greater than 10 kHz) detectors. Based on this principle, we designed optical trapping experiments by loading a sinusoidal signal into the optical tweezers system and recording the trapped particle responses with 45 frames per second (fps) charge-coupled device (CCD) and 163 fps complementary metal-oxide-semiconductor (CMOS) cameras for video microscopy imaging. The experimental results demonstrate that the use of low-bandwidth detectors is suitable for highly accurate force quantification, thereby greatly reducing the complexity of constructing optical tweezers. The trap stiffness increases significantly as the frequency increases, and the experimental results demonstrate that the trapped particles shifting along the optical axis boost the transversal optical force.

Drag controlled formation of polymeric colloids with optical traps

Optical trapping is a powerful optical manipulation technique for controlling various mesoscopic systems that allows formation of tailor-made polymeric micro-sized colloids by directed coalescence of nucleation sites. However, control over the size of a single colloid requires constant monitoring of the growth process and deactivation of the optical trap once it reaches the required dimensions. Moreover, producing more than one colloid requires moving the sample to a pristine location where the process must be repeated. Here, we present a novel method for continuous control over formation of polydimethylsiloxane colloids based on directed coalescence induced by optical traps under flow inside microfluidic channels. Once the drag force on a growing colloid exceeds the trapping force, it leaves the optical trap, and a new colloid starts to form at the same location. We demonstrate repeatability of the process and selectively produce colloids with radii of ∼1-14 μm by controlling the laser intensity and flow rate. In addition, holographic optical tweezers are used to show how multiple optical traps in 3D could be used to influence a significant cross section of the micro-channel, thus forming a light-controlled assembly line for colloidal formation.

Optical vacuum cleaner by optomechanical manipulation of nanoparticles using nanostructured mesoscale dielectric cuboid

Here, we propose the concept of an "optical vacuum cleaner" for optomechanical manipulation of nanoparticles. We utilize a dielectric cuboid to generate an optical gradient force exerted on the nanoparticles for particle's hovering and trapping. We show that the permittivity contrast between the particle and the nanohole leads to the deep subwavelength light confinement and enhancement at the opening of the nanohole located at the shadow surface of the particle. The proposed "optical vacuum cleaner" can be utilized in optomechanical manipulations on particles such as noble metal nanoparticles adsorbed on surfaces or controlling the particles taking part in cellular uptake.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Near-field optical trapping in a non-conservative force field

The force-field generated by a near-field optical trap is analyzed. A C-shaped engraving on a gold film is considered as the trap. By separating out the conservative component and the solenoidal component of the force-field using Helmholtz-Hodge decomposition, it was found that the force is non-conservative. Conventional method of calculating the optical potential from the force-field is shown to be inaccurate when the trapping force is not purely conservative. An alternative method is presented to accurately estimate the potential. The positional statistics of a trapped nanoparticle in this non-conservative field is calculated. A model is proposed that relates the position distribution to the conservative component of the force. The model is found to be consistent with numerical and experimental results. In order to show the generality of the approach, the same analysis is repeated for a plasmonic trap consisting of a gold nanopillar. Similar consistency is observed for this structure as well.

Optical Manipulation along an Optical Axis with a Polarization Sensitive Meta-Lens

The ability to manipulate small objects with focused laser beams opens a broad spectrum of opportunities in fundamental and applied studies, for which precise control over mechanical path and stability is required. Although conventional optical tweezers are based on refractive optics, the development of compact trapping devices that could be integrated within fluid cells is in high demand. Here, a plasmonic polarization-sensitive metasurface-based lens, embedded within a fluid, is demonstrated to provide several stable trapping centers along the optical axis. The position of a particle is controlled with the polarization of the incident light, interacting with plasmonic nanoscale patch antennas, organized within overlapping Fresnel zones of the lens. While standard diffractive optical elements face challenges in trapping objects in the axial direction outside the depth of focus, bifocal Fresnel meta-lens demonstrates the capability to manipulate a bead along a 4 μm line. An additional fluorescent module, incorporated within the optical trapping setup, was implemented and enabled the accurate mapping of optical potentials via a particle-tracking algorithm. Auxiliary micro- and nanostructures, integrated within fluidic devices, provide numerous opportunities to achieve flexible optomechanical manipulation, including transport, trapping, and sorting, which are in high demand for lab-on-a-chip applications and many others.

Depth-resolved measurement of optical radiation-pressure forces with optical coherence tomography

A weakly focused laser beam can exert sufficient radiation pressure to manipulate microscopic particles over a large depth range. However, depth-resolved continuous measurement of radiation-pressure force profiles over an extended range about the focal plane has not been demonstrated despite decades of research on optical manipulation. Here, we present a method for continuous measurement of axial radiation-pressure forces from a weakly focused beam on polystyrene micro-beads suspended in viscous fluids over a depth range of 400 μm, based on real-time monitoring of particle dynamics using optical coherence tomography (OCT). Measurements of radiation-pressure forces as a function of beam power, wavelength, bead size, and refractive index are consistent with theoretical trends. However, our continuous measurements also reveal localized depth-dependent features in the radiation-pressure force profiles that deviate from theoretical predictions based on an aberration-free Gaussian beam. The combination of long-range radiation pressure and OCT offers a new mode of quantitative optical manipulation and detection with extended spatial coverage. This may find applications in the characterization of optical tractor beams, or volumetric optical manipulation and interrogation of beads in viscoelastic media.

Objective-lens-free Fiber-based Position Detection with Nanometer Resolution in a Fiber Optical Trapping System

Position detection with high accuracy is crucial for force calibration of optical trapping systems. Most existing position detection methods require high-numerical-aperture objective lenses, which are bulky, expensive, and difficult to miniaturize. Here, we report an affordable objective-lens-free, fiber-based position detection scheme with 2 nm spatial resolution and 150 MHz bandwidth. This fiber based detection mechanism enables simultaneous trapping and force measurements in a compact fiber optical tweezers system. In addition, we achieved more reliable signal acquisition with less distortion compared with objective based position detection methods, thanks to the light guiding in optical fibers and small distance between the fiber tips and trapped particle. As a demonstration of the fiber based detection, we used the fiber optical tweezers to apply a force on a cell membrane and simultaneously measure the cellular response.

Scanning holographic optical tweezers

The aim of this Letter is to introduce a new optical tweezers approach, called scanning holographic optical tweezers (SHOT), which drastically increases the working area (WA) of the holographic-optical tweezers (HOT) approach, while maintaining tightly focused laser traps. A 12-fold increase in the WA is demonstrated. The SHOT approach achieves its utility by combining the large WA of the scanning optical tweezers (SOT) approach with the flexibility of the HOT approach for simultaneously moving differently structured optical traps in and out of the focal plane. This Letter also demonstrates a new heuristic control algorithm for combining the functionality of the SOT and HOT approaches to efficiently allocate the available laser power among a large number of traps. The proposed approach shows promise for substantially increasing the number of particles that can be handled simultaneously, which would enable optical tweezers additive fabrication technologies to rapidly assemble microgranular materials and structures in reasonable build times.

Optical tweezer calibration by using a part of the intensity distribution of a trapped particle

In this paper, we demonstrated that an optical tweezer setup can be calibrated by using a part of the symmetric intensity distribution of the trapped particle in digital video microscopy. First, we modified the radial symmetry center method, which was a recently proposed position detection algorithm. This algorithm uses gradient vectors of the particle intensity distribution, which allows us to use a part of the symmetric intensity distribution in the calculation of the particle center. We applied the modified algorithm to different camera image configurations, which are obtained by cutting the same experimental video frames. We further calibrated the trap stiffness for each camera configuration. Then we compared the trap stiffness values and the position distributions. As a result, we can conclude that optical tweezer setups can be calibrated by using a part of the intensity distribution of the trapped particle.

Combined optical micromanipulation and interferometric topography (COMMIT)

Optical tweezers have emerged as a prominent light-based tool for pico-Newton (pN) force microscopy in mechanobiological studies. However, the efficacy of optical tweezers are limited in applications where concurrent metrology of the nano-sized structures under interrogation is essential to the quantitative analysis of its mechanical properties and various mechanotransduction events. We have developed an all-optical platform delivering pN force resolution in parallel with nano-scale structural imaging of the biological sample by combining optical tweezers with interferometric quantitative phase microscopy. These capabilities allow real-time micromanipulation and label-free measurement of sample's nanostructures and nanomechanical responses, opening avenues to a wide range of new research possibilities and applications in biology.

Evanescent wave optical binding forces on spherical microparticles

In this Letter, we demonstrate stable optical binding of spherical microparticles in counter-propagating evanescent optical fields formed by total reflection at a dielectric interface. The microspheres are observed to form one-dimensional chains oriented parallel to the direction of propagation of the beams. We characterize the strength of the optical binding interaction by measuring the extent of Brownian position fluctuations of the optically bound microspheres and relating this to a binding spring constant acting between adjacent particles. A stronger binding interaction is observed for particles near the middle of the chain, and the dependence of the binding strength on incident laser power and number of particles in the chain is determined.