Optical trapping of nanotubes with cylindrical vector beams

Real-time Stokes polarimetry using a polarization camera

This Lab Note introduces the "Stokes Camera," a simple experimental arrangement for real-time measurement of spatial amplitude and polarization and thus spatially resolved Stokes parameters. It uses a polarization sensitive camera and a fixed quarter-wave plate, providing a one-shot, digital solution for polarization measurement that is only limited by the frame rate of the camera and the computation speed of the provided code. The note also provides background information on relevant polarization theory and vector vortex beams, which are used as a demonstration of the device.

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.

Multi-Function Reflective Vector Light Fields Generated by All-Dielectric Encoding Metasurface

Traditional optics usually studies the uniform polarization state of light. Compared with uniform vector beams, non-uniform vector beams have more polarization information. Most of the research on generating cylindrical vector beams using metasurfaces focuses on generating transmitted beams using the geometric phase. However, the geometric phase requires the incident light to be circularly polarized, which limits the design freedom. Here, an all-dielectric reflective metasurface is designed to generate different output light according to the different polarization states of the incident light. By combining the two encoding arrangements of the dynamic phase and the geometric phase, the output light is a radial vector beam when the linearly polarized light is incident along the x-direction. Under the incidence of linearly polarized light along the y-direction, the generated output light is an azimuthal vector beam. Under the incidence of left-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of -1. Under the incidence of right-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of +1. The proposed reflective metasurface has potential applications in generating vector beams with high integration.

Calibration of the Soleil–Babinet Compensator Based on the Vectorial Optical Field

The Soleil–Babinet compensator (SBC) is a variable retarder and has been used in a variety of application fields. A scheme based on the vectorial optical field is proposed to calibrate the SBC by transforming the change of the phase retardation into the visible rotation of the petal-like pattern. The relationship between the rotation angle of the petal-like pattern and the phase retardation of the SBC is established theoretically. In the experiment, the vector beam is generated by using the spiral phase plate (SPP) and the modified Mach–Zehnder interferometer based on the superposition principle of two orthogonal circularly polarized vortex beams with opposite topological charges. Taking advantage of the image processing method, the rotation angles of the acquired petal patterns are calculated, and the relationship between the phase retardation of the SBC and the displacements of its micrometer screw is determined. The measured phase retardation of the SBC ranges from −277.00° to 516.57°. By linearly fitting the experimental data, the phase sensitivity is 33.076 ± 0.147 °/mm, and the coefficient of determination value that shows the linearity of the experimental data is 0.9995. The experimental results agree well with the theoretical data.

Solution-processed two-dimensional materials for next-generation photovoltaics

In the ever-increasing energy demand scenario, the development of novel photovoltaic (PV) technologies is considered to be one of the key solutions to fulfil the energy request. In this context, graphene and related two-dimensional (2D) materials (GRMs), including nonlayered 2D materials and 2D perovskites, as well as their hybrid systems, are emerging as promising candidates to drive innovation in PV technologies. The mechanical, thermal, and optoelectronic properties of GRMs can be exploited in different active components of solar cells to design next-generation devices. These components include front (transparent) and back conductive electrodes, charge transporting layers, and interconnecting/recombination layers, as well as photoactive layers. The production and processing of GRMs in the liquid phase, coupled with the ability to "on-demand" tune their optoelectronic properties exploiting wet-chemical functionalization, enable their effective integration in advanced PV devices through scalable, reliable, and inexpensive printing/coating processes. Herein, we review the progresses in the use of solution-processed 2D materials in organic solar cells, dye-sensitized solar cells, perovskite solar cells, quantum dot solar cells, and organic-inorganic hybrid solar cells, as well as in tandem systems. We first provide a brief introduction on the properties of 2D materials and their production methods by solution-processing routes. Then, we discuss the functionality of 2D materials for electrodes, photoactive layer components/additives, charge transporting layers, and interconnecting layers through figures of merit, which allow the performance of solar cells to be determined and compared with the state-of-the-art values. We finally outline the roadmap for the further exploitation of solution-processed 2D materials to boost the performance of PV devices.

Shaping light in 3d space by counter-propagation

We extend the established transverse customization of light, in particular, amplitude, phase, and polarization modulation of the light field, and its analysis by the third, longitudinal spatial dimension, enabling the visualization of longitudinal structures in sub-wavelength (nm) range. To achieve this high-precision and three-dimensional beam shaping and detection, we propose an approach based on precise variation of indices in the superposition of higher-order Laguerre-Gaussian beams and cylindrical vector beams in a counter-propagation scheme. The superposition is analyzed experimentally by digital, holographic counter-propagation leading to stable, reversible and precise scanning of the light volume. Our findings show tailored amplitude, phase and polarization structures, adaptable in 3D space by mode indices, including sub-wavelength structural changes upon propagation, which will be of interest for advanced material machining and optical trapping.

Microsphere kinematics from the polarization of tightly focused nonseparable light

Recently, it was shown that vector beams can be utilized for fast kinematic sensing via measurements of their global polarization state [Optica2, 864 (2015)10.1364/OPTICA.2.000864]. The method relies on correlations between the spatial and polarization degrees of freedom of the illuminating field which result from its nonseparable mode structure. Here, we extend the method to the nonparaxial regime. We study experimentally and theoretically the far-field polarization state generated by the scattering of a dielectric microsphere in a tightly focused vector beam as a function of the particle position. Using polarization measurements only, we demonstrate position sensing of a Mie particle in three dimensions. Our work extends the concept of back focal plane interferometry and highlights the potential of polarization analysis in optical tweezers employing structured light.

Laguerre-Gaussian modes generated vector beam via nonlinear magneto-optical rotation

Laguerre-Gaussian (LG) beams contain a helical phase front with a doughnut-like intensity profile. We use the LG beam to introduce a rather simple method for generation of a vector beam (VB), a beam with spatially-dependent polarization in the beam cross section, via the nonlinear magneto-optical rotation (NMOR). We consider the NMOR of the polarization of a linearly polarized probe field passing through an inverted Y-type four-level quantum system interacting with a LG control field and a static magnetic field. It is shown that the polarization of the transmitted field is spatially distributed by the orbital angular momentum (OAM) of the LG control field, leading to generation of the VB with azimuthally symmetric polarization distribution. We show that the polarization and intensity distributions of the VB spatially vary by changing the OAMs of the LG control field. Moreover, the radial index of the LG control field has a major role in more spatially polarization distributing of the VB. It is shown that the intensity of the generated VBs in different points of the beam cross section can be controlled by the OAM as well as the radial index of the LG control field. However, the VB with highly spatially distributed can be generated for higher values of the radial index of LG control field. The analytical calculations determine the contribution of the different nonlinear (cross-Kerr effect) phenomena on the generation of the VB. We show that the VB is mainly generated via birefringence induced by the applied fields. Finally, we use asymmetric LG (aLG) beams for making the VBs with asymmetric polarization distribution. It is shown that by applying aLG beams, the azimuthal symmetry of the polarization distribution breaks and the asymmetric polarization distribution can be controlled by OAM and radial index of the aLG control field. The obtained results may find more interesting applications in fiber/free space optical communication to enhance the capacity of the information transmission.

Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams

Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication between mobile nodes for many critical applications. While the spatial modes of light offer a degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we demonstrate experimentally a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can reliably transmit high-dimensional information through a turbulent channel without the need of any adaptive optics for beam compensation. In a proof-of-principle experiment with a controllable turbulence cell, we measure a channel capacity of 4.84 bits per pulse using 34 vector modes through a turbulent channel with a scintillation index of 1.09, and 4.02 bits per pulse using 18 vector modes through even stronger turbulence corresponding to a scintillation index of 1.54.

Resistance to turbulence is an ongoing challenge for point-to-point freespace communications. Here the authors present a protocol for encoding a large amount of information in vector beams that are transmittable through a moderately strong turbulent channel without adaptive beam compensation.

Optimized anti-reflection core-shell microspheres for enhanced optical trapping by structured light beams

In this paper, we study the optical trapping of anti-reflection core-shell microspheres by regular Gaussian beam and several structured beams including radially polarized Gaussian, petal, and hard-aperture-truncated circular Airy beams. We show that using an appropriate anti-reflection core-shell microsphere for the optical trapping by several structured light beams can dramatically enhance the strength of the trap compared to the trapping by the common Gaussian beam. The optimal core-shell thickness ratio that minimizes the scattering force is obtained for polystyrene-silica and anatase-amorphous titania microspheres, such that the core-shells act as anti-reflection coated microspheres. We show that the trapping strength of the anti-reflection coated microparticles trapped by the common Gaussian beam is enhanced up to 2-fold compared to that of trapped uncoated microparticles, while the trapping of anti-reflection coated microparticles, by the radially polarized beam, is strengthened up to 4-fold in comparison to that of the trapped uncoated microparticles by the Gaussian beam. Our results indicate that for anatase-amorphous titania microparticles highest trap strength is obtained by radially polarized beam, while for the polystyrene-silica microparticles, the strongest trapping is achieved by the petal beam.

Variable transformation of singular cylindrical vector beams using anisotropic crystals

We demonstrated and investigated, both theoretically and experimentally, the transformation of cylindrical vector beams with an embedded phase singularity under the condition of focusing perpendicularly to the axis of the anisotropic calcite crystal. Theoretical and numerical analysis, performed on the basis of decomposing the light field into a set of plane waves for an anisotropic medium, allowed us to study the dependence of the structural transformation of the initial laser beam on the polarisation and phase state in detail. The proposed approach allows one to perform the visual recognition of cylindrically-polarised vector beams of various orders and can be used for the demultiplexing of information channels in the case of polarisation-division multiplexing. The experimentally-obtained results agree with the theoretical findings and demonstrate the reliability of the approach.

Efficient optical trapping with cylindrical vector beams

Radially and azimuthally polarized beams can create needle-like electric and magnetic fields under tight focusing conditions, respectively, and thus have been highly recommended for optical manipulation. There have been reports on the superiority of these beams over the conventional Gaussian beam for providing a larger optical force in single beam optical trap. However, serious discrepancies in their experimental results prevent one from concluding this superiority. Here, we theoretically and experimentally study the impact of different parameters - such as spherical aberration, the numerical aperture of the focusing lens, and the particles' size - on optical trapping stiffness of radially, azimuthally, and linearly polarized beams. The result of calculations based on generalized Lorenz-Mie theory, which is in good agreement with the experiment, reveals that the studied parameters determine which polarization state has the superiority for optical trapping. Our findings play a crucial role in the development of optical tweezers setups and, in particular, in biophysical applications when laser-induced heating in the optical tweezers applications is the main concern.

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.

A vector holographic optical trap

The invention of optical tweezers almost forty years ago has triggered applications spanning multiple disciplines and has also found its way into commercial products. A major breakthrough came with the invention of holographic optical tweezers (HOTs), allowing simultaneous manipulation of many particles, traditionally done with arrays of scalar beams. Here we demonstrate a vector HOT with arrays of digitally controlled Higher-Order Poincaré Sphere (HOPS) beams. We employ a simple set-up using a spatial light modulator and show that each beam in the array can be manipulated independently and set to an arbitrary HOPS state, including replicating traditional scalar beam HOTs. We demonstrate trapping and tweezing with customized arrays of HOPS beams comprising scalar orbital angular momentum and cylindrical vector beams, including radially and azimuthally polarized beams simultaneously in the same trap. Our approach is general enough to be easily extended to arbitrary vector beams, could be implemented with fast refresh rates and will be of interest to the structured light and optical manipulation communities alike.

Optical force decoration of 3D microstructures with plasmonic particles

Optical forces are used to push and aggregate gold nanorods onto several substrates creating surface-enhanced Raman scattering (SERS) active hot spots for Raman-based identification of proteins. By monitoring the increase of the protein SERS signal, we observe different aggregation times for different curvatures of the substrates. The slower aggregation dynamics on curved surfaces is justified by a simple geometrical model. In particular, this technique is used to decorate three-dimensional microstructures and to quickly realize hybrid micro/nanosensors for highly sensitive detection of biological material directly in a liquid environment.

Tighter focus for ultrashort pulse vector light beams: change of the relative contribution of different field components to the focal spot upon pulse shortening

We investigate the focusing of Poisson-spectrum few cycle pulsed light beams for linear, circular, azimuthal, and radial input polarizations with and without a first-order vortex. It is shown that, for all the considered cases, the focal spot is tighter when compared to long pulses due to the increased blue frequency content in the ultrashort pulses spectrum. More significantly, we show, for what we believe is the first time, that upon pulse shortening different focused beam vector components associated with different Bessel functions J₀ and J₁ undergo a change in the relative weight of their respective contribution to the focal spot size. This effect is caused by the different spectral dependencies of J₀ and J₁ near the focus. This newly discovered property of broadband ultrashort pulses could be exploited in light-matter interactions advantageously.

Analyzing characteristics of spiral vector beams generated by mixing of orthogonal LP11 modes in a few-mode optical fiber

We have demonstrated a method for the generation of spiral vector beams using a few-mode optical fiber. The beams are generated due to the combination of orthogonal linearly polarized modes with a tilted polarization vector in the few-mode optical fiber. The excitation of these modes is controlled by the incident state of polarization and coupling conditions at the input end of the fiber. The beams with clockwise and counterclockwise nature of spiral polarization are generated, and switching between them is demonstrated. The obtained results emphasize the strong dependency of polarization of generated spiral vector beams and other orthogonal linearly polarized modes on the input state of polarization. The simulated results of mode mixing are verified experimentally with good agreement.

Optical trapping and optical force positioning of two-dimensional materials

In recent years, considerable effort has been devoted to the synthesis and characterization of two-dimensional materials. Liquid phase exfoliation (LPE) represents a simple, large-scale method to exfoliate layered materials down to mono- and few-layer flakes. In this context, the contactless trapping, characterization, and manipulation of individual nanosheets hold perspectives for increased accuracy in flake metrology and the assembly of novel functional materials. Here, we use optical forces for high-resolution structural characterization and precise mechanical positioning of nanosheets of hexagonal boron nitride, molybdenum disulfide, and tungsten disulfide obtained by LPE. Weakly optically absorbing nanosheets of boron nitride are trapped in optical tweezers. The analysis of the thermal fluctuations allows a direct measurement of optical forces and the mean flake size in a liquid environment. Measured optical trapping constants are compared with T-matrix light scattering calculations to show a quadratic size scaling for small size, as expected for a bidimensional system. In contrast, strongly absorbing nanosheets of molybdenum disulfide and tungsten disulfide are not stably trapped due to the dominance of radiation pressure over the optical trapping force. Thus, optical forces are used to pattern a substrate by selectively depositing nanosheets in short times (minutes) and without any preparation of the surface. This study will be useful for improving ink-jet printing and for a better engineering of optoelectronic devices based on two-dimensional materials.

Probing the degenerate states of V-point singularities

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

Cylindrical vector resonant modes achieved in planar photonic crystal cavities with enlarged air-holes

We reveal a triangular-lattice planar photonic crystal supports Bloch modes with radially and azimuthally symmetric electric field distributions at the top band-edge of the first photonic band. Bifurcated from the corresponding Bloch modes, two cylindrical vector resonant modes are achieved by simply enlarging the central air-hole of the planar photonic crystal, which have high quality factors around 3,000 and small mode volume of (λ/n)³. The far-field radiations of the two resonant modes present high-quality cylindrical vector beam profiles. The resonant modes could be optimized by modifying the six nearest neighboring air-holes around the central defect. The cylindrically symmetric characteristics of the resonant mode's near- and far-fields might provide a new view to investigate light-matter interactions and device developments in planar photonic crystal cavities.

Diffraction of V-point singularities through triangular apertures

In this paper we present experimental studies on diffraction of V-point singularities through equilateral and isosceles right triangular apertures. When V-point index, also called Poincare-Hopf index (η), of the optical field is +1, the diffraction disintegrates it into two monstars/lemons. When V-point index η is -1, diffraction produces two stars. The diffraction pattern, unlike phase singularity, is insensitive to polarity of the polarization singularity and the intensity pattern remains invariant. Higher order V-point singularities are generated using Sagnac interferometer and it is observed that the diffraction disintegrates them into lower order C-points.

Beam quality measure for vector beams

Vector beams have found a myriad of applications, from laser materials processing to microscopy, and are now easily produced in the laboratory. They are usually differentiated from scalar beams by qualitative measures, for example, visual inspection of beam profiles after a rotating polarizer. Here we introduce a quantitative beam quality measure for vector beams and demonstrate it on cylindrical vector vortex beams. We show how a single measure can be defined for the vector quality, from 0 (purely scalar) to 1 (purely vector). Our measure is derived from a quantum toolkit, which we show applies to classical vector beams.

Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincaré beam

It is theoretically predicted in [Opt. Lett.37, 1553 (2012)] that a full Poincaré (FP) beam can significantly reduce turbulence-induced scintillation. In this paper, we propose a method for synthesizing a FP beam for different beam orders and report experimental generation of the first-, second- and third-order FP beams. Furthermore, we carry out experimental measurement of the scintillation index of a FP beam passing through thermally induced turbulence. It is demonstrated that the FP beam indeed can significantly reduce the scintillation index compared to a Gaussian beam under certain conditions. Our results will be useful in long-distance free-space optical communications.

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces

A novel method is proposed to generate vector beams with arbitrary spatial variation of phase and linear polarization at the nanoscale using compact plasmonic metasurfaces with rectangular nanoapertures. The physical mechanism underlying the simultaneous control of light polarization and phase is explained. Vector beams with different spiral phasefronts are obtained by manipulating the local orientation and geometric parameters of the metasurfaces. In addition, radially and azimuthally polarized vector beams and double-mode vector beams are achieved through completely compensating for the Berry phase, which provides additional degrees of freedom for beam manipulation.

Devil's lens optical tweezers

We demonstrate an optical tweezers using a laser beam on which is imprinted a focusing phase profile generated by a Devil's staircase fractal structure (Cantor set). We show that a beam shaped in this way is capable of stably trapping a variety of micron- and submicron-sized particles and calibrate the optical trap as a function of the control parameters of the fractal structure, and explain the observed variation as arising from radiation pressure exerted by unfocused parts of the beam in the region of the optical trap. Experimental results are complemented by calculation of the structure of the focus in the regime of high numerical aperture.

Scanning metallic nanosphere microscopy for vectorial profiling of optical focal spots

Recent years have witnessed fast progress in the development of spatially variant states of polarization under high numerical aperture focusing, and intensive exploration of their applications. We report a vectorial, broadband, high contrast and subwavelength resolution method for focal spot profiling. In this experiment, a 100 nm diameter gold nanosphere on a silica aerogel substrate is raster scanned across the focal spots, and the orthogonal polarization components can be obtained simultaneously by measuring the scattering far field in a confocal manner. The metallic-nanosphere-on-aerogel structure ensures negligible distortion to the focal spots, low crosstalk between orthogonal polarization components (1/39 in experiment), and a low level background noise (1/80 of peak intensity in experiment), while high contrast imaging is not limited by the resonance bandwidth.

Determination of the polarization states of an arbitrary polarized terahertz beam: vectorial vortex analysis

Vectorial vortex analysis is used to determine the polarization states of an arbitrarily polarized terahertz (0.1-1.6 THz) beam using THz achromatic axially symmetric wave (TAS) plates, which have a phase retardance of Δ = 163° and are made of polytetrafluorethylene. Polarized THz beams are converted into THz vectorial vortex beams with no spatial or wavelength dispersion, and the unknown polarization states of the incident THz beams are reconstructed. The polarization determination is also demonstrated at frequencies of 0.16 and 0.36 THz. The results obtained by solving the inverse source problem agree with the values used in the experiments. This vectorial vortex analysis enables a determination of the polarization states of the incident THz beam from the THz image. The polarization states of the beams are estimated after they pass through the TAS plates. The results validate this new approach to polarization detection for intense THz sources. It could find application in such cutting edge areas of physics as nonlinear THz photonics and plasmon excitation, because TAS plates not only instantaneously elucidate the polarization of an enclosed THz beam but can also passively control THz vectorial vortex beams.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Elliptic-symmetry vector optical fields

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

Generation of vector beams in planar photonic crystal cavities with multiple missing-hole defects

We propose a novel method to generate vector beams in planar photonic crystal cavities with multiple missing-hole defects. Simulating the resonant modes in the cavities, we observe that the optical fields in each defect have different phase and polarization state distributions, which promise the compositions of vector beams by the scattered light from the defects. The far-field radiation patterns of the cavity modes calculated via the Sommerfeld diffraction theory present vector beams possessing hollow intensity profiles and polarization singularities. In addition, the extraction efficiencies of the vector beams from the cavities could be improved by modifying the air-holes surrounding the defects. This planar photonic crystal cavity-based vector beam generator may provide useful insights for the on-chip controlling of vector beams in their propagations and interactions with matter.

Application of flat-top focus to 2D trapping of large particles

The 2D optical trapping ability of larger-than average-particles is compared for three different beam types: a flat-top, a Gaussian beam, and a donut shaped beam. Optical force-displacement curves are calculated in four different size regimes of particle diameters (1.5-20 μm). We find that the trapping efficiency increases linearly with ratio of particle diameter to wavelength for all three beams. As the ratio reaches a specific threshold value, the flat-top focus exhibits the largest trapping efficiency compared to the other two beam types. We experimentally demonstrate that flat-top focusing provides the largest transverse trapping efficiency for particles as large as 20 μm in diameter for our given experimental conditions. The overall trend in our experimental results follows that observed in our simulation model. The results from this study could facilitate light manipulation of large particles.

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.

Long-distance axial trapping with focused annular laser beams

Focusing an annular laser beam can improve the axial trapping efficiency due to the reduction of the scattering force, which enables the use of a lower numerical aperture (NA) objective lens with a long working distance to trap particles in deeper aqueous medium. In this paper, we present an axicon-to-axicon scheme for producing parallel annular beams with the advantages of higher efficiency compared with the obstructed beam approach. The validity of the scheme is verified by the observation of a stable trapping of silica microspheres with relatively low NA microscope objective lenses (NA = 0.6 and 0.45), and the axial trapping depth of 5 mm is demonstrated in experiment.

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.