We study the Brownian motion (BM) of optically trapped graphene flakes. These orient orthogonal to the light polarization, due to the optical constants anisotropy. We explain the flake dynamics, measure force and torque constants and derive a full electromagnetic theory of optical trapping. The understanding of two dimensional BM paves the way to light-controlled manipulation and all-optical sorting of biological membranes and anisotropic macromolecules.The random motion of microscopic particles in a fluid was first observed in the late eighteenth century, and goes by the name of Brownian motion(BM) [1]. This was ascribed to thermal agitation[2], leading to Einstein's predictions of the resulting particle displacements [3]. BM is ubiquitous throughout physics, chemistry, biology, and even finance. It can be harnessed to produce directed motion [4]. It was also suggested that thermally activated BM may be responsible for the movement of molecular motors, such as myosin and kinesin [5]. When a Brownian particle (BP), i.e. a particle undergoing BM, is subject to an external field, e.g. a confining potential, the fluid damps the BM and, in a high damping regime, such as for a BP in water, the confining potential acts as a cut-off to the BM dynamics. This is free for short times (high frequency limit), while is frozen at longer times (low frequency limit) [8]. These processes have perfect ground in experiments with optical traps, where a BP is held by a focused laser beam, i.e. an optical tweezers [9]. In this context, BM can be utilized to investigate the properties of the surrounding environment [10,11], as well as of the trapped particle, and for accurate calibration of the spring constants of the optical harmonic potential [12,13].Dimensionality plays a special role in nature. From phase transitions [14], to transport phenomena[15], twodimensional (2d) systems often exhibit a strikingly different behavior [14]. Nanomaterials are an attractive target for optical trapping [16][17][18]. This can lead to top-down organization of composite nano-assemblies[16], sub-wavelength imaging by the excitation and scanning of nano-optical probes [17], photonic force microscopy with increased space and force resolution [18]. Graphene[19] is the prototype 2d material, and, as such, has unique mechanical, thermal, electronic and optical properties [20]. Here, we use graphene as prototype material to unravel the consequences of BM in 2d.Graphene is dispersed by processing graphite in a water-surfactant solution, Fig.1a. We do not use any functionalization nor oxidation, to retain the pristine electronic structure in the exfoliated monolayers [21][22][23]. We use di-hydroxy sodium deoxycholate surfactant. High resolution Transmission Electron Microscopy (HRTEM) shows∼10-40nm flakes. Fig.1b is an image of one such flake, with the typical honeycomb lattice. By analyzing over a hundred flakes, we find∼ 60% single-layer (SLG), much higher than previous aqueous [22] and nonaqueous dispersions [21], and the remainder bi-and trilayers (Fi...

We study the optical trapping of highly elongated linear nanostructures in the focal region of a high-numerical aperture lens (optical tweezers). The radiation torque and trapping force on these nanostructures that are modeled as chains of identical spherical scatterers are calculated by means of multipole field expansions in the framework of the transition matrix approach. We investigate both orientational and trapping stability and calculate force constants and trap parameters in order to clarify the role of the linear geometry in the optical trapping mechanism. Furthermore, we calculate optical trapping of nanowires of different materials and compare our theoretical findings with available experimental results.

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.

We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive, fast and maskless process compatible with Si technology. The structure allows for a high light-trapping efficiency across the entire visible range, attaining total reflectance values as low as 0.1% when the wavelength in the medium matches the length scale of maximum heterogeneity in the system. We show that the random fractal structure of our nanowire array is responsible for a strong in-plane multiple scattering, which is related to the material refractive index fluctuations and leads to a greatly enhanced Raman scattering and a bright photoluminescence. These strong emissions are correlated on all length scales according to the refractive index fluctuations. The relevance and the perspectives of the reported results are discussed as promising for Si-based photovoltaic and photonic applications.

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.

The theory of the trapping of nonspherical particles in the focal region of a high-numerical-aperture optical system is formulated in the framework of the transition matrix approach. Both the case of an unaberrated lens and the case of an aberrated one are considered. The theory is applied to single latex spheres of various sizes and, when the results are compared with the available experimental data, a fair agreement is attained. The theory is also applied to binary clusters of spheres of latex with a diameter of 220nm in various orientations. Although, in this case we have no experimental data to which our results can be compared, we get useful indications for the trapping of nonspherical particles. In particular, we find substantial agreement with recent results on the trapping of prolate spheroids in aberrated gaussian fields [S. H. Simpson and S. Hanna, J. Opt.Soc. Am. A 24, 430 (2007)].

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The optical trapping of polymeric nanofibers and the characterization of the rotational dynamics are reported. A strategy to apply a torque to a polymer nanofiber, by tilting the trapped fibers using a symmetrical linear polarized Gaussian beam is demonstrated. Rotation frequencies up to 10 Hz are measured, depending on the trapping power, the fiber length and the tilt angle. A comparison of the experimental rotation frequencies in the different trapping configurations with calculations based on optical trapping and rotation of linear nanostructures through a T-Matrix formalism, accurately reproduce the measured data, providing a comprehensive description of the trapping and rotation dynamics.PACS numbers: 87.80.Cc; 45.20.da; 42.50.Wk; 07.10.Pz * Corresponding author: antonio.neves@unisalento.it † marago@its.me.cnr.it 2 Optical forces are currently employed to study a range of chemical, physical and biological problems, by trapping microscale objects and measuring sub pico-Newton forces [1,2]. In particular, optical trapping of elongated nanoparticles, including nanowires [3] and nanotubes [4], is gaining an increasing interest because of the high shape anisotropy and unique physical properties of these systems. Among linear nanostructures, polymeric nanofibers are novel nanomaterials with many strategic applications ranging from scaffolding for tissue-engineering to integrated photonics [5,6] and electronics [7,8]. However, optical trapping and manipulation of polymer nanofibers has never been reported, despite the understanding of the optical forces and torques acting on these objects as well as their trapping dynamics might open a new range of applications, exploiting the polymeric fibers as local probes or active elements in microrheology [9] and microfluidics [10], and in next generation Photonic Force Microscopy [3]. Furthermore, the nanofibers are characterized by subwavelength diameters and lengths in the range 10-100 m, therefore constituting ideal systems for studying effects occurring in the intermediate regime between the Rayleigh scattering and geometrical optics.A laser beam can carry intrinsic (spin) or extrinsic (orbital) angular momentum, associated to the polarization and to the light beam phase structure, respectively [11]. Either trapping beams with elliptical polarization or with a rotating linear polarization can be exploited to apply a torque to trapped objects. Rotation in trapped particles can also be induced by exploiting the phase structure or the astigmatism of the trapping laser beam [12 and references therein]. The rotatable object can be spherical, exhibiting a birefringence or a slight absorption, or it can have more complex shapes, as in microfabricated propellers by two-photon polymerization [13] or cylinders with inclined faces [14].In this work we trap polymeric nanofibers and characterize their rotational dynamics in different trapping configurations by a different method. We employ a strategy to rotate a dielectric cylinder with flat end faces, based on a non-rotat...