Single-Crystal Rutile TiO2 Nanocylinders are Highly Effective Transducers of Optical Force and Torque

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

Optical Torque Calculations and Measurements for DNA Torsional Studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping, but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

SIGNIFICANCE

We developed a simulation platform based on the finite element method for force and torque calculation for particles in an angular optical trap (AOT), with considerations of tightly focused Gaussian beam, spherical aberrations, and optically anisotropic particles. Experimental measurements of focal shift ratio, force, and torque under multiple conditions were in good agreement with predictions from the simulations. We also demonstrated that intrinsic DNA torsional properties can be robustly measured under different AOT measurement conditions, strongly validating our simulations and calibrations. Our platform can facilitate trapping particle design for single-molecule assays using the AOT.

Simulation and Experiment of the Trapping Trajectory for Janus Particles in Linearly Polarized Optical Traps

The highly focused laser beam is capable of confining micro-sized particle in its focus. This is widely known as optical trapping. The Janus particle is composed of two hemispheres with different refractive indexes. In a linearly polarized optical trap, the Janus particle tends to align itself to an orientation where the interface of the two hemispheres is parallel to the laser propagation as well as the polarization direction. This enables a controllable approach that rotates the trapped particle with fine accuracy and could be used in partial measurement. However, due to the complexity of the interaction of the optical field and refractive index distribution, the trapping trajectory of the Janus particle in the linearly polarized optical trap is still uncovered. In this paper, we focus on the dynamic trapping process and the steady position and orientation of the Janus particle in the optical trap from both simulation and experimental aspects. The trapping process recorded by a high speed camera coincides with the simulation result calculated using the T-matrix model, which not only reveals the trapping trajectory, but also provides a practical simulation solution for more complicated structures and trapping motions.

Synthesis of Germanium Nanospheres as High-Precision Optical Tweezers Probes

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

Versatile Multilayer Metamaterial Nanoparticles with Tailored Optical Constants for Force and Torque Transduction

The ability to apply force and torque directly to micro- and nanoscale particles in optical traps has a wide range of applications. While full control of both force and torque in three dimensions has been realized using top-down fabrication of rod-shaped particles composed of birefringent crystalline materials, widespread usage of such particles is limited as the optical constants of the predominant birefringent materials (quartz SiO2 and rutile TiO2) preclude coverage of the full application space of optical trapping. Here, we show that multilayer metamaterial nanoparticles provide access to a wide range of optical constants that can be specifically tuned for each application. Selecting the material pair Nb2O5/SiO2 from the library of amorphous dielectrics as our metamaterial, we show that its refractive index and birefringence can be designed by adapting the ratio of layer thicknesses. Using a robust top-down fabrication process, we show that uniformly sized, free-floating Nb2O5/SiO2 particles with high birefringence at moderate refractive index are obtained at high yield. Using an optical torque wrench, we show that these particles function as joint force and torque transducers while maintaining excellent stability in aqueous solutions and can be controllably optimized for particular physical characteristics such as maximal torque transfer or rapid response time. We expect that such customizable birefringent metamaterial nanoparticles whose properties surpass those of conventional crystalline particles will provide a means to unleash the full potential of optical trapping applications.

High-Resolution Photonic Force Microscopy Based on Sharp Nanofabricated Tips

Although near-field imaging techniques reach sub-nanometer resolution on rigid samples, it remains extremely challenging to image soft interfaces, such as biological membranes, due to the deformations induced by the probe. In photonic force microscopy, optical tweezers are used to manipulate and measure the scanning probe, allowing imaging of soft materials without force-induced artifacts. However, the size of the optically trapped probe still limits the maximum resolution. Here, we show a novel and simple nanofabrication protocol to massively produce optically trappable quartz particles which mimic the sharp tips of atomic force microscopy. Imaging rigid nanostructures with our tips, we resolve features smaller than 80 nm. Scanning the membrane of living malaria-infected red blood cells reveals, with no visible artifacts, submicron features termed knobs, related to the parasite activity. The use of nanoengineered particles in photonic force microscopy opens the way to imaging soft samples at high resolution.