Extending calibration-free force measurements to optically-trapped rod-shaped samples

Temperature Measurement of Trapped, Thermally Sensitive Single Particles in an Optical Trap Using Raman Spectroscopy

Single particles trapped in an optical trap may experience temperature elevation, yet direct measurement of temperature and its distribution inside the optical trap of several to hundreds of microns in size remains a big challenge. We introduce a method that can measure the temperature inside a universal optical trap (UOT) using Raman spectroscopy of single trapped particles of high thermal conductivity. We measured temperature and temperature distributions inside the UOT using Raman shifts of single-walled carbon nanotubes (SWCNTs) and micron-sized diamonds (MSDs), which are heated by trapping laser beams directly or indirectly, depending on the location of the particle in the trap. We show that the temperature at the center of the UOT is much lower than the temperature along the hollow beams that form a hollow, cage-shaped UOT. In the range of the trapping laser power of 200-2950 mW, the surface temperature of particles trapped at the center of a UOT changes from 322 K to 830 K, correspondingly. This result gives a heating rate as a high thermal-absorbing particle trapped in the center of the UOT with 18.3 ± 0.4 °C/100 mW. In addition, the temperature gradient outside the UOT was also characterized by trapping SWCNT particles outside the UOT. Results show that when a light-absorbing particle is trapped for the study of material property, phase transitions, surface equilibrium process, chemical reactions, etc., this method can be used to measure temperature distribution and its variations in the trap and its surroundings.

Visualization of Optical Vortex Forces Acting on Au Nanoparticles Transported in Nanofluidic Channels

The optical manipulation of nanoscale objects via structured light has attracted significant attention for its various applications, as well as for its fundamental physics. In such cases, the detailed behavior of nano-objects driven by optical forces must be precisely predicted and controlled, despite the thermal fluctuation of small particles in liquids. In this study, the optical forces of an optical vortex acting on gold nanoparticles (Au NPs) are visualized using dark-field microscopic observations in a nanofluidic channel with strictly suppressed forced convection. Manipulating Au NPs with an optical vortex allows the evaluation of the three optical force components, namely, gradient, scattering, and absorption forces, from the in-plane trajectory. We develop a Langevin dynamics simulation model coupled with Rayleigh scattering theory and compare the theoretical results with the experimental ones. Experimental results using Au NPs with diameters of 80-150 nm indicate that our experimental method can determine the radial trapping stiffness and tangential force with accuracies on the order of 0.1 fN/nm and 1 fN, respectively. Our experimental method will contribute to broadening not only applications of the optical-vortex manipulation of nano-objects, but also investigations of optical properties on unknown nanoscale materials via optical force analyses.

Positioning Accuracy in Holographic Optical Traps

Spatial light modulators (SLMs) have been widely used to achieve dynamic control of optical traps. Often, holographic optical tweezers have been presumed to provide nanometer or sub-nanometer positioning accuracy. It is known that some features concerning the digitalized structure of SLMs cause a loss in steering efficiency of the optical trap, but their effect on trap positioning accuracy has been scarcely analyzed. On the one hand, the SLM look-up-table, which we found to depend on laser power, produces positioning deviations when the trap is moved at the micron scale. On the other hand, phase quantization, which makes linear phase gratings become phase staircase profiles, leads to unexpected local errors in the steering angle. We have tracked optically trapped microspheres with sub-nanometer accuracy to study the effects on trap positioning, which can be as high as 2 nm in certain cases. We have also implemented a correction strategy that enabled the reduction of errors down to 0.3 nm.

Optical Tweezers Exploring Neuroscience

Over the past decade, optical tweezers (OT) have been increasingly used in neuroscience for studies of molecules and neuronal dynamics, as well as for the study of model organisms as a whole. Compared to other areas of biology, it has taken much longer for OT to become an established tool in neuroscience. This is, in part, due to the complexity of the brain and the inherent difficulties in trapping individual molecules or manipulating cells located deep within biological tissue. Recent advances in OT, as well as parallel developments in imaging and adaptive optics, have significantly extended the capabilities of OT. In this review, we describe how OT became an established tool in neuroscience and we elaborate on possible future directions for the field. Rather than covering all applications of OT to neurons or related proteins and molecules, we focus our discussions on studies that provide crucial information to neuroscience, such as neuron dynamics, growth, and communication, as these studies have revealed meaningful information and provide direction for the field into the future.

Acousto-holographic optical tweezers

Acousto-optic deflectors (AODs) allow the creation of multiple optical traps by time-sharing, that is, by rapidly cycling the laser focus between designated spatial locations. The traps thus formed are not permanent. In this Letter, we successfully demonstrate the creation of multiple and permanent traps by means of AODs driven by specially encoded radio frequency signals. The generation of complex acoustic signals allows us to treat such devices as super-fast spatial light modulators. Using this technique, it is possible to generate several static optical trap arrays and switch them at kilohertz (kHz) rates, allowing independent control of each trap group. Additionally, we discuss the compatibility of this method with precise force and position measurements, and the improvement in their frequency bandwidth compared to time-sharing optical tweezers, especially when many objects are trapped.

Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity

How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and out-of-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.

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".

Influence of experimental parameters on the laser heating of an optical trap

In optical tweezers, heating of the sample due to absorption of the laser light is a major concern as temperature plays an important role at microscopic scale. A popular rule of thumb is to consider that, at the typical wavelength of 1064 nm, the focused laser induces a heating rate of B = 1 °C/100 mW. We analysed this effect under different routine experimental conditions and found a remarkable variability in the temperature increase. Importantly, we determined that temperature can easily rise by as much as 4 °C at a relatively low power of 100 mW, for dielectric, non-absorbing particles with certain sets of specific, but common, parameters. Heating was determined from measurements of light momentum changes under drag forces at different powers, which proved to provide precise and robust results in watery buffers. We contrasted the experiments with computer simulations and obtained good agreement. These results suggest that this remarkable heating could be responsible for changes in the sample under study and could lead to serious damage of live specimens. It is therefore advisable to determine the temperature increase in each specific experiment and avoid the use of a universal rule that could inadvertently lead to critical changes in the sample.