Escape forces and trajectories in optical tweezers and their effect on calibration

Faster and More Accurate Geometrical-Optics Optical Force Calculation Using Neural Networks

Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks permits overcoming this limitation, obtaining not only faster but also more accurate simulations. We demonstrate this using an optically trapped spherical particle for which we obtain an analytical solution to use as ground truth. Then, we take advantage of the acceleration provided by neural networks to study the dynamics of ellipsoidal particles in a double trap, which would be computationally impossible otherwise.

Exploring Single-Nanoparticle Dynamics at High Temperature by Optical Tweezers

The experimental determination of the velocity of a colloidal nanoparticle (v_NP) has recently became a hot topic. The thermal dependence of v_NP is still left to be explored although it is a valuable source of information allowing, for instance, the discernment between ballistic and diffusive regimes. Optical tweezers (OTs) constitute a tool especially useful for the experimental determination of v_NP although they have only been capable of determining it at room temperature. In this work, we demonstrate that it is possible to determine the temperature dependence of the diffusive velocity of a single colloidal nanoparticle by analyzing the temperature dependence of optical forces. The comparison between experimental results and theoretical predictions allowed us to discover the impact that the anomalous temperature dependence of water properties has on the dynamics of colloidal nanoparticles in this temperature range.

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.

Calibration of force detection for arbitrarily shaped particles in optical tweezers

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

Microfluidic-based high-throughput optical trapping of nanoparticles

Optical tweezers have emerged as a powerful tool for multiparametric analysis of individual nanoparticles with single-molecule sensitivity. However, its inherent low-throughput characteristic remains a major obstacle to its applications within and beyond the laboratory. This limitation is further exacerbated when working with low concentration nanoparticle samples. Here, we present a microfluidic-based optical tweezers system that can 'actively' deliver nanoparticles to a designated microfluidic region for optical trapping and analysis. The active microfluidic delivery of nanoparticles results in significantly improved throughput and efficiency for optical trapping of nanoparticles. We observed a more than tenfold increase in optical trapping throughput for nanoparticles as compared to conventional systems at the same nanoparticle concentration. To demonstrate the utility of this microfluidic-based optical tweezers system, we further used back-focal plane interferometry coupled with a trapping laser for the precise quantitation of nanoparticle size without prior knowledge of the refractive index of nanoparticles. The development of this microfluidic-based active optical tweezers system thus opens the door to high-throughput multiparametric analysis of nanoparticles using precision optical traps in the future.

Broadband ultrafast nonlinear absorption and ultra-long exciton relaxation time of black phosphorus quantum dots

Black phosphorus (BP) has recently attracted significant attention for its brilliant physical and chemical features. The remarkable strong light-matter interaction and tunable direct wide range band-gap make it an ideal candidate in various application regions, especially saturable absorbers. In this paper, ultrasmall black phosphorus quantum dots (BPQDs), a unique form of phosphorus nanostructures, with average size of 5.7 ± 0.8 nm are synthesized. Compared with BP nanosheets (BPNs) with similar thickness, the ultrafast nonlinear optical (NLO) absorption properties and excited carrier dynamics are investigated in wide spectra. Beyond the saturation absorption (SA), giant two photon absorption (TPA) is observed in BPQDs. BPQDs exhibit quite different excitation intensity and wavelength dependent nonlinear optical (NLO) response from BPNs, which is attributed to the quantum confinement and edge effects. The BPQDs show broadband photon-induced absorption (PIA) under the probe wavelength from 470 nm to 850 nm and a fast and a slow decay time are obtained as long as 92 ± 10 ps and 1100 ± 100 ps, respectively. The substantial independence for ultra-long time scales of pump intensity and temperature reveals that the carrier recombination mechanism may be attributed to a defect-assisted Auger capture process. These findings will help to develop optoelectronic and photonic devices operating in the infrared and visible wavelength region.

Beyond the Hookean Spring Model: Direct Measurement of Optical Forces Through Light Momentum Changes

The ability to measure forces in the range of 0.1-100 pN is a key feature of optical tweezers used for biophysical and cell biological studies. Analysis of the interactions between biomolecules and the forces that biomolecular motors generate at the single-molecule level has provided valuable insights in the molecular mechanisms that govern key cellular functions such as gene expression and the long-distance transport of organelles. Methods for determining the minute forces that biomolecular motors generate exhibit notable constraints that limit their application for studies other than the well-controlled in vitro experiments (although recent advances have been made that permit more quantitative optical tweezers studies insight living cells). One constraint comes from the linear approximation of the distance vs. force relationship used to extract the force from the position of the bead in the trap. This commonly employed "indirect" approach, although usually sufficiently precise, restricts the use of optical tweezers to a limited range of displacements (typically up to ±150 nm for small beads). Measurements based on the detection of the light-momentum changes, on the other hand, offer a "direct" and precise way to determine forces even when the generated displacements reach the escape point, thus covering the complete force range developed by the trap. In this chapter, we detail the requirements for the design of a force-sensor instrument based on light-momentum changes using a high-numerical-aperture objective lens and provide insights into its construction. We further discuss the calibration of the system and the main steps for its routine operation.