Radiation torque and force on optically trapped linear nanostructures

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.

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.

3D printing colloidal crystal microstructures via sacrificial-scaffold-mediated two-photon lithography

The orderly arrangement of nanomaterials’ tiny units at the nanometer-scale accounts for a substantial part of their remarkable properties. Maintaining this orderness and meanwhile endowing the nanomaterials with highly precise and free-designed 3D micro architectures will open an exciting prospect for various novel applications. In this paper, we developed a sacrificial-scaffold-mediated two-photon lithography (TPL) strategy that enables the fabrication of complex 3D colloidal crystal microstructures with orderly-arranged nanoparticles inside. We show that, with the help of a degradable hydrogel scaffold, the disturbance effect of the femtosecond laser to the nanoparticle self-assembling could be overcome. Therefore, hydrogel-state and solid-state colloidal crystal microstructures with diverse compositions, free-designed geometries and variable structural colors could be easily fabricated. This enables the possibility to create novel colloidal crystal microsensing systems that have not been achieved before.

Colloidal crystals are widely applied in the fabrication of optoelectronic devices, but realizing freedom of design, such as in 3D printing, in colloidal crystal fabrication remains challenging. Here, the authors demonstrate a sacrificial-scaffold-mediated two-photon lithography strategy that enables the fabrication of complex 3D colloidal crystal microstructures with orderly arranged nanoparticles in the bulk.

Optically oriented attachment of nanoscale metal-semiconductor heterostructures in organic solvents via photonic nanosoldering

As devices approach the single-nanoparticle scale, the rational assembly of nanomaterial heterojunctions remains a persistent challenge. While optical traps can manipulate objects in three dimensions, to date, nanoscale materials have been trapped primarily in aqueous solvents or vacuum. Here, we demonstrate the use of optical traps to manipulate, align, and assemble metal-seeded nanowire building blocks in a range of organic solvents. Anisotropic radiation pressure generates an optical torque that orients each nanowire, and subsequent trapping of aligned nanowires enables deterministic fabrication of arbitrarily long heterostructures of periodically repeating bismuth-nanocrystal/germanium-nanowire junctions. Heat transport calculations, back-focal-plane interferometry, and optical images reveal that the bismuth nanocrystal melts during trapping, facilitating tip-to-tail “nanosoldering” of the germanium nanowires. These bismuth-semiconductor interfaces may be useful for quantum computing or thermoelectric applications. In addition, the ability to trap nanostructures in oxygen- and water-free organic media broadly expands the library of materials available for optical manipulation and single-particle spectroscopy.

The use of optical traps has been limited to materials dispersed in aqueous media, which restricts the materials and range of experiments. Here, the authors demonstrate the alignment and assembly of composite structures made of a bismuth nanocrystal and a germanium nanowire in organic solvents.

Interface-Dependent Radiative Lifetimes of Yb3+, Er3+ Co-doped Single NaYF4 Upconversion Nanowires

The development of upconversion nanomaterials for many photonic applications requires a detailed understanding of their radiative lifetimes that in turn depend critically on local environmental conditions. In this work, hexagonal (β-phase) sodium-yttrium-fluoride (NaYF₄) nanowires (NWs) were synthesized and substitutionally co-doped with a luminescent solid solution of trivalent erbium and ytterbium ions. A single-beam laser trapping instrument was used in tandem with a piezo-controlled, variable-temperature stage to precisely vary the nanowire's distance from the substrate. The spontaneous photoluminescence lifetime of the ⁴S_3/2 → ⁴I_15/2 transition from Er³⁺ ions was observed to change by >60% depending on the ions' separation distance from a planar (water/glass) dielectric interface. The ⁴S_3/2 state lifetime is observed to increase by a factor of 1.62 ± 0.01 as the distance from the quartz coverslip increases from ∼0 nm to ∼40 μm. Less significant changes in the luminescence lifetime (≤10%) were observed over a temperature range between 25 and 50 °C. The distance dependence of the lifetime is interpreted quantitatively in the context of classical electromagnetic coupling between Er³⁺ ions within the nanowire and the adjacent dielectric interface. We also demonstrate potential applications of the NaYF₄ NWs for both controlling and probing temperatures at nanometer scales by integrating them within a poly(dimethylsiloxane) composite matrix.

Chiral optical tweezers for optically active particles in the T-matrix formalism

Modeling optical tweezers in the T-matrix formalism has been of key importance for accurate and efficient calculations of optical forces and their comparison with experiments. Here we extend this formalism to the modeling of chiral optomechanics and optical tweezers where chiral light is used for optical manipulation and trapping of optically active particles. We first use the Bohren decomposition to deal with the light scattering of chiral light on optically active particles. Thus, we show analytically that all the observables (cross sections, asymmetry parameters) are split into a helicity dependent and independent part and study a practical example of a complex resin particle with inner copper-coated stainless steel helices. Then, we apply this chiral T-matrix framework to optical tweezers where a tightly focused chiral field is used to trap an optically active spherical particle, calculate the chiral behaviour of optical trapping stiffnesses and their size scaling, and extend calculations to chiral nanowires and clusters of astrophysical interest. Such general light scattering framework opens perspectives for modeling optical forces on biological materials where optically active amino acids and carbohydrates are present.

Optical Trapping, Optical Binding, and Rotational Dynamics of Silicon Nanowires in Counter-Propagating Beams

Silicon nanowires are held and manipulated in controlled optical traps based on counter-propagating beams focused by low numerical aperture lenses. The double-beam configuration compensates light scattering forces enabling an in-depth investigation of the rich dynamics of trapped nanowires that are prone to both optical and hydrodynamic interactions. Several polarization configurations are used, allowing the observation of optical binding with different stable structure as well as the transfer of spin and orbital momentum of light to the trapped silicon nanowires. Accurate modeling based on Brownian dynamics simulations with appropriate optical and hydrodynamic coupling confirms that this rich scenario is crucially dependent on the non-spherical shape of the nanowires. Such an increased level of optical control of multiparticle structure and dynamics open perspectives for nanofluidics and multi-component light-driven nanomachines.

Single Cell Isolation Using Optical Tweezers

Optical tweezers offer a non-contact method for selecting single cells and translocating them from one microenvironment to another. We have characterized the optical tweezing of yeast S. cerevisiae and can manipulate single cells at 0.41 ± 0.06 mm/s using a 26.8 ± 0.1 mW from a 785 nm diode laser. We have fabricated and tested three cell isolation devices; a micropipette, a PDMS chip and a laser machined fused silica chip and we have isolated yeast, single bacteria and cyanobacteria cells. The most effective isolation was achieved in PDMS chips, where single yeast cells were grown and observed for 18 h without contamination. The duration of budding in S. cerevisiae was not affected by the laser parameters used, but the time from tweezing until the first budding event began increased with increasing laser energy (laser power × time). Yeast cells tweezed using 25.0 ± 0.1 mW for 1 min were viable after isolation. We have constructed a micro-consortium of yeast cells, and a co-culture of yeast and bacteria, using optical tweezers in combination with the PDMS network of channels and isolation chambers, which may impact on both industrial biotechnology and understanding pathogen dynamics.

Controlled Mechanical Motions of Microparticles in Optical Tweezers

Optical tweezers, formed by a highly focused laser beam, have intriguing applications in biology and physics. Inspired by molecular rotors, numerous optical beams and artificial particles have been proposed to build optical tweezers trapping microparticles, and extensive experiences have been learned towards constructing precise, stable, flexible and controllable micromachines. The mechanism of interaction between particles and localized light fields is quite different for different types of particles, such as metal particles, dielectric particles and Janus particles. In this article, we present a comprehensive overview of the latest development on the fundamental and application of optical trapping. The emphasis is placed on controllable mechanical motions of particles, including rotation, translation and their mutual coupling under the optical forces and torques created by a wide variety of optical tweezers operating on different particles. Finally, we conclude by proposing promising directions for future research.

Real-time monitoring and visualization of the multi-dimensional motion of an anisotropic nanoparticle

As interest in anisotropic particles has increased in various research fields, methods of tracking such particles have become increasingly desirable. Here, we present a new and intuitive method to monitor the Brownian motion of a nanowire, which can construct and visualize multi-dimensional motion of a nanowire confined in an optical trap, using a dual particle tracking system. We measured the isolated angular fluctuations and translational motion of the nanowire in the optical trap, and determined its physical properties, such as stiffness and torque constants, depending on laser power and polarization direction. This has wide implications in nanoscience and nanotechnology with levitated anisotropic nanoparticles.

Optical Torques on Upconverting Particles for Intracellular Microrheometry

Precise knowledge and control over the orientation of individual upconverting particles is extremely important for full exploiting their capabilities as multifunctional bioprobes for interdisciplinary applications. In this work, we report on how time-resolved, single particle polarized spectroscopy can be used to determine the orientation dynamics of a single upconverting particle when entering into an optical trap. Experimental results have unequivocally evidenced the existence of a unique stable configuration. Numerical simulations and simple numerical calculations have demonstrated that the dipole magnetic interactions between the upconverting particle and trapping radiation are the main mechanisms responsible of the optical torques that drive the upconverting particle to its stable orientation. Finally, how a proper analysis of the rotation dynamics of a single upconverting particle within an optical trap can provide valuable information about the properties of the medium in which it is suspended is demonstrated. A proof of concept is given in which the laser driven intracellular rotation of upconverting particles is used to successfully determine the intracellular dynamic viscosity by a passive and an active method.

Photonic Torque Microscopy of the Nonconservative Force Field for Optically Trapped Silicon Nanowires

We measure, by photonic torque microscopy, the nonconservative rotational motion arising from the transverse components of the radiation pressure on optically trapped, ultrathin silicon nanowires. Unlike spherical particles, we find that nonconservative effects have a significant influence on the nanowire dynamics in the trap. We show that the extreme shape of the trapped nanowires yields a transverse component of the radiation pressure that results in an orbital rotation of the nanowire about the trap axis. We study the resulting motion as a function of optical power and nanowire length, discussing its size-scaling behavior. These shape-dependent nonconservative effects have implications for optical force calibration and optomechanics with levitated nonspherical particles.

Laser-Directed Assembly of Aligned Carbon Nanotubes in Three Dimensions for Multifunctional Device Fabrication

Laser-directed assembly of multiwalled carbon nanotubes (MWNTs) in 3D space is investigated via a two-photon polymerization technique. MWNT-thiol-acrylate (MTA) composite resins are developed with high MWNT concentrations up to 0.2 wt%, over one order of magnitude higher than previously published work. Significantly enhanced electrical and mechanical properties of the 3D micro-/nanostructures are achieved. Microelectronic devices made of the MTA resins are demonstrated.

Three-dimensional optical trapping of a plasmonic nanoparticle using low numerical aperture optical tweezers

It was previously believed that larger metal nanoparticles behave as tiny mirrors that are pushed by the light beam radiative force along the direction of beam propagation, without a chance to be confined. However, several groups have recently reported successful optical trapping of gold and silver particles as large as 250 nm. We offer a possible explanation based on the fact that metal nanoparticles naturally occur in various non-spherical shapes and their optical properties differ significantly due to changes in localized plasmon excitation. We demonstrate experimentally and support theoretically three-dimensional confinement of large gold nanoparticles in an optical trap based on very low numerical aperture optics. We showed theoretically that the unique properties of gold nanoprisms allow an increase of trapping force by an order of magnitude at certain aspect ratios. These results pave the way to spatial manipulation of plasmonic nanoparticles using an optical fibre, with interesting applications in biology and medicine.

Optically driven oscillations of ellipsoidal particles. Part I: experimental observations

We report experimental observations of the mechanical effects of light on ellipsoidal micrometre-sized dielectric particles, in water as the continuous medium. The particles, made of polystyrene, have shapes varying between near disk-like (aspect ratio k = 0.2) to very elongated needle-like (k = 8). Rather than the very tightly focused beam geometry of optical tweezers, we use a moderately focused laser beam to manipulate particles individually by optical levitation. The geometry allows us varying the longitudinal position of the particle, and to capture images perpendicular to the beam axis. Experiments show that moderate-k particles are radially trapped with their long axis lying parallel to the beam. Conversely, elongated (k > 3) or flattened (k < 0.3) ellipsoids never come to rest, and permanently "dance" around the beam, through coupled translation-rotation motions. The oscillations are shown to occur in general, be the particle in bulk water or close to a solid boundary, and may be periodic or irregular. We provide evidence for two bifurcations between static and oscillating states, at k ≈ 0.33 and k ≈ 3 for oblate and prolate ellipsoids, respectively. Based on a recently developed 2-dimensional ray-optics simulation (Mihiretie et al., EPL 100, 48005 (2012)), we propose a simple model that allows understanding the physical origin of the oscillations.

Direct laser writing of 3D architectures of aligned carbon nanotubes

Direct laser writing through two-photon polymerization lithography is used to fabricate 3D nanostructures containing aligned single-wall carbon nanotubes (SWCNTs). SWCNTs are aligned in the laser scanning directions while they are embedded in the structure. The alignment is induced by spatial confinement, volume shrinkage, and the optical gradient force. This method is expected to lead to new applications based on aligned SWCNTs.

5D-Tracking of a nanorod in a focused laser beam--a theoretical concept

Back-focal plane (BFP) interferometry is a very fast and precise method to track the 3D position of a sphere within a focused laser beam using a simple quadrant photo diode (QPD). Here we present a concept of how to track and recover the 5D state of a cylindrical nanorod (3D position and 2 tilt angles) in a laser focus by analyzing the interference of unscattered light and light scattered at the cylinder. The analytical theoretical approach is based on Rayleigh-Gans scattering together with a local field approximation for an infinitely thin cylinder. The approximated BFP intensities compare well with those from a more rigorous numerical approach. It turns out that a displacement of the cylinder results in a modulation of the BFP intensity pattern, whereas a tilt of the cylinder results in a shift of this pattern. We therefore propose the concept of a local QPD in the BFP of a detection lens, where the QPD center is shifted by the angular coordinates of the cylinder tilt.

Optical trapping and manipulation of nanostructures

Optical trapping and manipulation of micrometre-sized particles was first reported in 1970. Since then, it has been successfully implemented in two size ranges: the subnanometre scale, where light-matter mechanical coupling enables cooling of atoms, ions and molecules, and the micrometre scale, where the momentum transfer resulting from light scattering allows manipulation of microscopic objects such as cells. But it has been difficult to apply these techniques to the intermediate - nanoscale - range that includes structures such as quantum dots, nanowires, nanotubes, graphene and two-dimensional crystals, all of crucial importance for nanomaterials-based applications. Recently, however, several new approaches have been developed and demonstrated for trapping plasmonic nanoparticles, semiconductor nanowires and carbon nanostructures. Here we review the state-of-the-art in optical trapping at the nanoscale, with an emphasis on some of the most promising advances, such as controlled manipulation and assembly of individual and multiple nanostructures, force measurement with femtonewton resolution, and biosensors.

Resolving stable axial trapping points of nanowires in an optical tweezers using photoluminescence mapping

Axially resolved microphotoluminescence mapping of semiconductor nanowires held in an optical tweezers reveals important new experimental information regarding equilibrium trapping points and trapping stability of high aspect ratio nanostructures. In this study, holographic optical tweezers are used to scan trapped InP nanowires along the beam direction with respect to a fixed excitation source and the luminescent properties are recorded. It is observed that nanowires with lengths on the range of 3-15 μm are stably trapped near the tip of the wire with the long segment positioned below the focus in an inverted trapping configuration. Through the use of trap multiplexing we investigate the possibility of improving the axial stability of the trapped nanowires. Our results have important implication for applications of optically assisted nanowire assembly and optical tweezers based scanning probes microscopy.

Trapping volume control in optical tweezers using cylindrical vector beams

We present the result of an investigation into the optical trapping of spherical microparticles using laser beams with a spatially inhomogeneous polarization direction [cylindrical vector beams (CVBs)]. We perform three-dimensional tracking of the Brownian fluctuations in the position of a trapped particle and extract the trap spring constants. We characterize the trap geometry by the aspect ratio of spring constants in the directions transverse and parallel to the beam propagation direction and evaluate this figure of merit as a function of polarization angle. We show that the additional degree of freedom present in CVBs allows us to control the optical trap strength and geometry by adjusting only the polarization of the trapping beam. Experimental results are compared with a theoretical model of optical trapping using CVBs derived from electromagnetic scattering theory in the T-matrix framework.

Nanowire heating by optical electromagnetic irradiation

The dissipative absorption of electromagnetic energy by 1D nanoscale structures at optical frequencies is applicable to several important phenomena, including biomedical photothermal theranostics, nanoscale photovoltaic materials, atmospheric aerosols, and integrated photonic devices. Closed-form analytical calculations are presented for the temperature rise within infinite circular cylinders with nanometer-scale diameters (nanowires) that are irradiated at right angles by a continuous-wave laser source polarized along the nanowire's axis. Solutions for the heat source are compared to both numerical finite-difference time domain (FDTD) simulations and well-known Mie scattering cross sections for infinite cylinders. The analysis predicts that the maximum temperature increase is affected not only by the cylinder's composition and porosity but also by morphology-dependent resonances (MDRs) that lead to significant spikes in the local temperature at particular diameters. Furthermore, silicon nanowires with high thermal conductivities are observed to exhibit extremely uniform internal temperatures during electromagnetic heating to 1 part in 10(6), including cases where there are substantial fluctuations of the internal electric-field source term that generates the Joule heating. For a highly absorbing material such as carbon, much higher temperatures are predicted, the internal temperature distribution is nonuniform, and MDRs are not encountered.

Optical trapping of nanotubes with cylindrical vector beams

We use laser beams with radial and azimuthal polarization to optically trap carbon nanotubes. We measure force constants and trap parameters as a function of power showing improved axial trapping efficiency with respect to linearly polarized beams. The analysis of the thermal fluctuations highlights a significant change in the optical trapping potential when using cylindrical vector beams. This enables the use of polarization states to shape optical traps according to the particle geometry, as well as paving the way to nanoprobe-based photonic force microscopy with increased performance compared to a standard linearly polarized configuration.

Optical alignment and confinement of an ellipsoidal nanorod in optical tweezers: a theoretical study

Within the Rayleigh approximation, we investigate the behavior of an individual ellipsoidal metal nanorod that is optically confined in three dimensions using a single focused laser beam. We focus on the description of the optical torque and optical force acting upon the nanorod placed into a linearly polarized Gaussian beam (scalar description of the electric field) or a strongly focused beam (vector field description). The study comprises the influence of the trapping laser wavelength, the angular aperture of focusing optics, the orientation of the ellipsoidal nanorod, and the aspect ratio of its principal axes. The results reveal a significantly different behavior of the nanorod if the trapping wavelength is longer or shorter than the wavelength corresponding to the longitudinal plasmon resonance mode. Published experimental observations are compared with our theoretical predictions with satisfactory results.

Effect of finite terms on the truncation error of Mie series

The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori the number of the most significant terms needed to evaluate the scattering cross section. Here, we obtain an improved formula, which includes the number of terms needed for determining the scattering cross section within a prescribed relative error. This is accomplished using extended precision computation for a wide range of commonly used size parameters and indices of refraction. The revised formula for the finite number of terms can be a promising and valuable approach for efficient modeling light scattering phenomena.

Equilibrium orientations and positions of non-spherical particles in optical traps

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

Stability analysis and thermal motion of optically trapped nanowires

We investigate the stability and thermal motion of optically trapped nanowires, with aspect ratios in the range 10-100. A simple analytical model is used to determine qualitative features of the system, assuming that the nanowire is weakly scattering and the incident beam is paraxial. As expected, the model predicts that the nanowire will align with the beam axis. In this configuration the translational stiffness coefficients of the trap approach their limiting values for long nanowires like O(L(-3)), where L is the nanowire length, the limit for the stiffness parallel to the beam axis being zero. The rotational stiffness coefficients vary more slowly, according to O(L(-1)). Also, it is predicted that defocusing decreases the translational stiffness perpendicular to the beam, while increasing rotational stiffness. These findings are reinforced by comparison with rigorous electromagnetic calculations which additionally reveal the effects of radiation pressure and finite scattering. A strong polarization effect is observed in the numerical simulations and coupled translational and rotational motions arise which influence the trap stability. The use of nanowire traps for force sensing is discusse.

Size-scaling in optical trapping of silicon nanowires

We investigate size-scaling in optical trapping of ultrathin silicon nanowires showing how length regulates their Brownian dynamics, optical forces, and torques. Force and torque constants are measured on nanowires of different lengths through correlation function analysis of their tracking signals. Results are compared with a full electromagnetic theory of optical trapping developed in the transition matrix framework, finding good agreement.

FDTD simulation of trapping nanowires with linearly polarized and radially polarized optical tweezers

In this paper a model of the trapping force on nanowires is built by three dimensional finite-difference time-domain (FDTD) and Maxwell stress tensor methods, and the tightly focused laser beam is expressed by spherical vector wave functions (VSWFs). The trapping capacities on nanoscale-diameter nanowires are discussed in terms of a strongly focused linearly polarized beam and radially polarized beam. Simulation results demonstrate that the radially polarized beam has higher trapping efficiency on nanowires with higher refractive indices than linearly polarized beam.

Plasmon-enhanced optical trapping of gold nanoaggregates with selected optical properties

We show how light forces can be used to trap gold nanoaggregates of selected structure and optical properties obtained by laser ablation in liquid. We measure the optical trapping forces on nanoaggregates with an average size range 20-750 nm, revealing how the plasmon-enhanced fields play a crucial role in the trapping of metal clusters featuring different extinction properties. Force constants of the order of 10 pN/nmW are detected, the highest measured on a metal nanostructure. Finally, by extending the transition matrix formalism of light scattering theory to the optical trapping of metal nanoaggregates, we show how the plasmon resonances and the fractal structure arising from aggregation are responsible for the increased forces and wider trapping size range with respect to individual metal nanoparticles.

Brownian motion of graphene

Brownian motion is a manifestation of the fluctuation-dissipation theorem of statistical mechanics. It regulates systems in physics, biology, chemistry, and finance. We use graphene as prototype material to unravel the consequences of the fluctuation-dissipation theorem in two dimensions, by studying the Brownian motion of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics in the optical trap and measure force and torque constants from the correlation functions of the tracking signals, as well as comparing experiments with a full electromagnetic theory of optical trapping. The understanding of optical trapping of two-dimensional nanostructures gained through our Brownian motion analysis paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.

Angular and position stability of a nanorod trapped in an optical tweezers

We analyze the trap stiffness and trapping force potential for a nano-cylinder trapped in the optical tweezers against its axial and lateral shift and tilt associated to the natural Brownian motion. We explain the physical properties of the optical trapping by computing and integrating the radiation stress distribution on the nano-cylinder surfaces using the T-matrix approach. Our computation shows that the force stiffness to the lateral shift is several times higher than that to the axial shift of the nano-cylinder, and lateral torque due to the stress on the side-face is 1-2 orders of magnitude higher than that on the end-faces of a nano-cylinder with the aspect ratio of 2 - 20. The torque due to the stress on the nano-cylinder surface is 2-3 orders of magnitude higher than the spin torque. We explain why a nano-cylinder of low aspect ratio is trapped and aligned normal to the trapping beam axis.

Rotational dynamics of optically trapped nanofibers

We report on the experimental evidence of tilted polymer nanofiber rotation, using a highly focused linear polarized Gaussian beam. Torque is controlled by varying trapping power or fiber tilt angle. This suggests an alternative strategy to previously reported approaches for the rotation of nano-objects, to test fundamental theoretical aspects. We compare experimental rotation frequencies to calculations based on T-Matrix formalism, which accurately reproduces measured data, thus providing a comprehensive description of trapping and rotation dynamics of the linear nanostructures.

Rotation detection in light-driven nanorotors

We analyze the rotational dynamics of light driven nanorotors, made of nanotube bundles and gold nanorods aggregates, with nonsymmetric shapes, trapped in optical tweezers. We identify two different regimes depending on dimensions and optical properties of the nanostructures. These correspond to alignment with either the laser propagation axis or the dominant polarization direction, or rotational motions caused by either unbalanced radiation pressure or polarization torque. By analyzing the motion correlations of the trapped nanostructures, we measure with high accuracy both the optical trapping parameters and the rotation frequency induced by the radiation pressure. Our results pave the way to improved all-optical detection, control over rotating nanomachines, and rotation detection in nano-optomechanics.

Controlled assembly of In2O3 nanowires on electronic circuits using scanning optical tweezers

In(2)O(3) nanowires can be used effectively as building blocks in the production of electronic circuits used in transparent and flexible electronic devices. The fabrication of these devices requires a controlled assembly of nanowires at crucial places and times. However, this kind of controlled assembly, which results in the fusion of nanowires to circuits, is still very difficult to execute. In this study, we demonstrate the benefits of using various lengths of In(2)O(3) nanowires by using non-contact mechanisms, such as scanning optical tweezers, to place them on designated targets during the fabrication process. Furthermore, these nanowires can be stabilized at both ends of the conducting wires using a focused laser, and later in the process, the annealed technique, so that proper flow of electrons is affected.

Parallel trapping of multiwalled carbon nanotubes with optoelectronic tweezers

Here we report the use of optoelectronic tweezers and dynamic virtual electrodes to address multiwalled carbon nanotubes (MWCNTs) with trap stiffness values of approximately 50 fNmum. Both high-speed translation (>200 mums) of individual-MWCNTs and two-dimensional trapping of MWCNT ensembles are achieved using 100,000 times less optical power density than single beam laser tweezers. Modulating the virtual electrode's intensity enables tuning of the MWCNT ensemble's number density by an order of magnitude on the time scale of seconds promising a broad range of applications in MWCNT science and technology.

Optical trapping calculations for metal nanoparticles. Comparison with experimental data for Au and Ag spheres

We calculate the optical forces on Au and Ag nanospheres through a procedure based on the Maxwell stress tensor. We compare the theoretical and experimental force constants obtained for gold and silver nanospheres finding good agreement for all particles with r < 80 nm. The trapping of the larger particles recently demonstrated in experiments is not foreseen by our purely electromagnetic theory based on fixed dielectric properties. Since the laser power produces a heating that may be large for the largest spheres, we propose a model in which the latter particles are surrounded by a steam bubble. This model foresees the trapping of these particles and the results turn out to be in reasonable agreement with the experimental data.

Femtonewton force sensing with optically trapped nanotubes

We extract the distribution of both center-of-mass and angular fluctuations from three-dimensional tracking of optically trapped nanotubes. We measure the optical force and torque constants from autocorrelation and cross-correlation of the tracking signals. This allows us to isolate the angular Brownian motion. We demonstrate that nanotubes enable nanometer spatial and femtonewton force resolution in photonic force microscopy, the smallest to date. This has wide implications in nanotechnology, biotechnology, nanofluidics, and material science.