Optical forces and torques in nonuniform beams of light

Magneto-optical-like effect in tight focusing of azimuthally polarized sine-Gaussian beams

Magneto-optical effects, which have been known for over a century, are among the most fundamental phenomena in physics and describe changes in the polarization state of light when it interacts with magnetic materials. When a polarized plane wave propagates in or through a homogeneous and isotropic transparent medium, it is generally accepted that its transverse polarization structure remains unchanged. However, we show that a strong radial polarization component can be generated when an azimuthally polarized sine-Gaussian plane wave is tightly focused by a high numerical aperture lens, resulting in a magneto-optical-like effect that does not require external magnetic field or magnetic medium. Calculations show that the intensity structure and polarization distribution of the highly confined electric field strongly depend on the parameters m and φ0 in the sinusoidal term, where m can be used to control the number of the multifocal spots and φ0 can be used to control the position of each focal spot. Finally, we show that this peculiar electric field distribution can be used to realize multiple particles trapping with controllable numbers and locations.

Optimized array nanostructure for plasmonically induced motion force generation

The growing demand to manipulate objects with long-range techniques has increasingly called for the development of techniques capable of intensifying and spatially concentrating electromagnetic fields with the aim of improving the electromagnetic forces acting on objects. In this context, one of the most interesting techniques is based on the use of plasmonic phenomena that have the ability to amplify and structure the electric field in very small areas. In this paper, we report the simulation analysis of a plasmonic nanostructure useful for optimizing the profile of the induced plasmonic field distribution and thus the motion dynamics of a nanoparticle, overcoming some limitations observed in the literature for similar structures. The elementary cell of the proposed nanostructure consists of two gold scalene trapezoids forming a planar V-groove. The spatial replication of this elementary cell to form linear or circular array sequences is used to improve the final nanoparticle velocity. The effect of the geometry variation on the plasmonic behaviour and consequently on the force generated, was analyzed in detail. The results suggest that this optimized plasmonic structure has the potential to efficiently propel macroscopic objects, with implications for various fields such as aerospace and biomedical research.

Stable optical lateral forces from inhomogeneities of the spin angular momentum

Transverse spin momentum related to the spin angular momentum (SAM) of light has been theoretically studied recently and predicted to generate an intriguing optical lateral force (OLF). Despite extensive studies, there is no direct experimental evidence of a stable OLF resulting from the dominant SAM rather than the ubiquitous spin-orbit interaction in a single light beam. Here, we theoretically unveil the nontrivial physics of SAM-correlated OLF, showing that the SAM is a dominant factor for the OLF on a nonabsorbing particle, while an additional force from the canonical (orbital) momentum is exhibited on an absorbing particle due to the spin-orbit interaction. Experimental results demonstrate the bidirectional movement of 5-μm-diameter particles on both sides of the beam with opposite spin momenta. The amplitude and sign of this force strongly depend on the polarization. Our optofluidic platform advances the exploitation of exotic forces in systems with a dominant SAM, facilitating the exploration of fascinating light-matter interactions.

Linear and angular momentum properties induced by radial- and azimuthal-variant polarized beams in a strongly focused optical system

Optical linear and angular momenta have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic fields and linear and angular momentum properties of tightly focused radial- and azimuthal-variant vector input beams. Calculations show that a uniform 3D optical cage can be achieved when the optical degree of freedom of polarization in the radial direction is introduced. Furthermore, the distributions of linear and angular momenta in the focal volume are revealed. Moreover, we numerically investigate the gradient, scattering, and total forces as well as spin and orbital torques on a Rayleigh particle generated by the optical cage. It is found that there are two equilibrium positions before and after the focal plane, both of which can achieve stable 3D particles capture. Most importantly, the longitudinal spin and orbital torques show the same patterns but in opposite directions in the two equilibrium positions, thus, the unwinding of the double helix can be expected to be achieved by virtue of this special optical torque.

Anti-Symmetric Medium Chirality Leading to Symmetric Field Helicity in Response to a Pair of Circularly Polarized Plane Waves in Counter-Propagating Configuration

We examine how a chiral medium responds to a pair of plane waves of circular polarizations. To this goal, we assume the chiral medium to be spatially homogeneous for simplicity. By assuming the medium to be a lossless, we provide analytic formulas of key bilinear parameters such as the pair of electromagnetic and reactive Poynting vectors in addition to the pair of electromagnetic and reactive helicities. By examining two obliquely colliding plane waves, we learned that most of those key parameters are asymmetric with respect to the medium chirality. Only for a counter-propagating pair, some of those key parameters are found to exhibit symmetry with respect to the medium chirality. We will discuss the implications of those asymmetries and symmetries from the viewpoints of typical applications in optics and physics.

Generally Applicable Holographic Torque Measurement for Optically Trapped Particles

We present a method to measure the optical torque applied to particles of arbitrary shape such as micrometer-sized micro-organisms or cells held in an optical trap, inferred from the change of angular momentum of light induced by the particle. All torque components can be determined from a single interference pattern recorded by a camera in the back focal plane of a high-NA condenser lens provided that most of the scattered light is collected. We derive explicit expressions mapping the measured complex field in this plane to the torque components. The required phase is retrieved by an iterative algorithm, using the known position of the optical traps as constraints. The torque pertaining to individual particles is accessible, as well as separate spin or orbital parts of the total torque.

Plasmonic Nanostructures for Optically Induced Movement

Optical forces generated at the nanoscale using electric field gradients have proven to be a powerful tool for trapping and moving nano-objects in a variety of application fields ranging from aerospace engineering to biology and medicine. Typically, to achieve this optical effect plasmonic resonant cavities that combine localized surface plasmon resonances and propagative surface plasmon polaritons are used. Indeed, these structures allow to engineer the distribution of the excited field hotspots, so inducing a precise movement of the nanoparticles interacting with the plasmonic field. In this paper, starting from the theoretical analysis of the surface plasmons, the potentialities of plasmonic nanostructures are reviewed, analysing the geometric conformation designed according to the application. The configurations with the most interesting performance, among those mentioned in the literature, are described in detail, examining their main characteristics and limitations. Finally, the future development and prospects of these plasmonic nanostructures are discussed.

Superhybrid Mode-Enhanced Optical Torques on Mie-Resonant Particles

Circularly polarized light carries spin angular momentum, so it can exert an optical torque on the polarization-anisotropic particle by the spin momentum transfer. Here, we show that giant positive and negative optical torques on Mie-resonant (gain) particles arise from the emergence of superhybrid modes with magnetic multipoles and electric toroidal moments, excited by linearly polarized beams. Anomalous positive and negative torques on particles (doped with judicious amount of dye molecules) are over 800 and 200 times larger than the ordinary lossy counterparts, respectively. Meanwhile, a rotational motor can be configured by switching the s- and p-polarized beams, exhibiting opposite optical torques. These giant and reversed optical torques are unveiled for the first time in the scattering spectrum, paving another avenue toward exploring unprecedented physics of hybrid and superhybrid multipoles in metaoptics and optical manipulations.

Angular momentum separation in focused fractional vector beams for optical manipulation

The generation, propagation, and applications of different types of integer vector beams have been extensively investigated. However, little attention focuses on the photophysical and photomechanical properties of the fractional vector beam (FVB). Herein, we theoretically and experimentally investigate the spin angular momentum (SAM) separation and propagation characteristics of weakly focused FVBs. It is demonstrated that such a beam carrying no SAM leads to both the transverse separation of SAM and the special intensity patterns in the focal region. Furthermore, we study the intensity, SAM, and orbital angular momentum (OAM) distributions of the tightly focused FVBs. It is shown that both three-dimensional SAM and OAM are spatially separated in the focal region of tightly focused FVBs. We investigate the optical forces, spin torques, and orbital torques on a dielectric Rayleigh particle produced by the focused FVBs. The results reveal that asymmetrical spinning and orbiting motions of optically trapped particles can be realized by manipulating FVBs.

Brownian dynamics simulations of sphere clusters in optical tweezers

Computationally modeling the behavior of wavelength-sized non-spherical particles in optical tweezers can give insight into the existence and stability of trapping equilibria as well as the optical manipulation of such particles more broadly. Here, we report Brownian dynamics simulations of non-spherical particles that account for detailed optical, hydrodynamic, and thermal interactions. We use a T-matrix formalism to calculate the optical forces and torques exerted by focused laser beams on clusters of wavelength-sized spheres, and we incorporate detailed diffusion tensors that capture the anisotropic Brownian motion of the clusters. For two-sphere clusters whose size is comparable to or larger than the wavelength, we observe photokinetic effects in elliptically-polarized beams. We also demonstrate that multiple trapping equilibria exist for a highly asymmetric chiral cluster of seven spheres. Our simulations may lead to practical suggestions for optical trapping and manipulation as well as a deeper understanding of the underlying physics.

Theory of optical tweezing of dielectric microspheres in chiral host media and its applications

We report for the first time the theory of optical tweezers of spherical dielectric particles embedded in a chiral medium. We develop a partial-wave (Mie) expansion to calculate the optical force acting on a dielectric microsphere illuminated by a circularly-polarized, highly focused laser beam. When choosing a polarization with the same handedness of the medium, the axial trap stability is improved, thus allowing for tweezing of high-refractive-index particles. When the particle is displaced off-axis by an external force, its equilibrium position is rotated around the optical axis by the mechanical effect of an optical torque. Both the optical torque and the angle of rotation are greatly enhanced in the presence of a chiral host medium when considering radii a few times larger than the wavelength. In this range, the angle of rotation depends strongly on the microsphere radius and the chirality parameter of the host medium, opening the way for a quantitative characterization of both parameters. Measurable angles are predicted even in the case of naturally occurring chiral solutes, allowing for a novel all-optical method to locally probe the chiral response at the nanoscale.

Azimuthal Imaginary Poynting Momentum Density

The momentum of light beams can possess azimuthal densities, circulating around the beam axis and inducing intriguing mechanical effects in local light-matter interaction. Belinfante's spin momentum loops in circularly polarized beams, while the canonical momentum spirals in helically phased beams. However, a similar behavior of their imaginary counterpart, the so-called imaginary Poynting momentum (IPM), has not yet emerged. The foremost purpose of the present work is to put forward the discovery of this IPM vortex. We show that a simple superposition of radially and azimuthally polarized beams can form an IPM of completely azimuthal density. Additionally, the azimuthal IPM density can exist with a donut beam-intensity distribution and even with a vanishing azimuthal component of all other momenta. This uncovers the existence of a new mechanical effect which broadens the area of optical micromanipulation by achieving optical rotation of isotropic spheres, in the absence of both spin and orbital angular momenta. Our findings enrich the local dynamic properties of electromagnetic fields, highlighting the rotational action of their IPM, and thus its mechanical effect on microparticles and nanoparticles.

Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities

We examine acoustic radiation force and torque on a small (subwavelength) absorbing isotropic particle immersed in a monochromatic (but generally inhomogeneous) sound-wave field. We show that by introducing the monopole and dipole polarizabilities of the particle, the problem can be treated in a way similar to the well-studied optical forces and torques on dipole Rayleigh particles. We derive simple analytical expressions for the acoustic force (including both the gradient and scattering forces) and torque. Importantly, these expressions reveal intimate relations to the fundamental field properties introduced recently for acoustic fields: the canonical momentum and spin angular momentum densities. We compare our analytical results with previous calculations and exact numerical simulations. We also consider an important example of a particle in an evanescent acoustic wave, which exhibits the mutually orthogonal scattering (radiation-pressure) force, gradient force, and torque from the transverse spin of the field.

Single ultra-high-definition spatial light modulator enabling highly efficient generation of fully structured vector beams

Ultra-high-definition (UHD) spatial light modulators (SLMs) enhance the degree of freedom in the versatile engineering of optical field. Among efforts to explore the capability of SLMs, enhancing the efficiency of light utilization is an everlasting quest to find SLM-based applications. We propose a new method to efficiently generate arbitrary vector beams with a phase-only UHD-SLM. By enabling the UHD-SLM with a rectangle window to work in an in-line and split-screen manner with the help of a polarizing beam splitter, the total conversion efficiency as high as 49% of light beams is realized. Several complex beams, including cylindrical vector beams and higher-order Poincaré sphere beams, are experimentally demonstrated. Our method can facilitate application of SLM in optical field manipulation.

Sectoral multipole focused beams

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are "sectoral" multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams.

Custom flow in overdamped Brownian dynamics

When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex, and obtaining a detailed physical understanding often requires case-by-case considerations. To facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence, compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

Negative optical torque on a microsphere in optical tweezers

We show that the optical force field in optical tweezers with elliptically polarized beams has the opposite handedness for a wide range of particle sizes and for the most common configurations. Our method is based on the direct observation of the particle equilibrium position under the effect of a transverse Stokes drag force, and its rotation around the optical axis by the mechanical effect of the optical torque. We find overall agreement with theory, with no fitting, provided that astigmatism, which is characterized separately, is included in the theoretical description. Our work opens the way for characterization of the trapping parameters, such as the microsphere complex refractive index and the astigmatism of the optical system, from measurements of the microsphere rotation angle.

Transverse spin forces and non-equilibrium particle dynamics in a circularly polarized vacuum optical trap

We provide a vivid demonstration of the mechanical effect of transverse spin momentum in an optical beam in free space. This component of the Poynting momentum was previously thought to be virtual, and unmeasurable. Here, its effect is revealed in the inertial motion of a probe particle in a circularly polarized Gaussian trap, in vacuum. Transverse spin forces combine with thermal fluctuations to induce a striking range of non-equilibrium phenomena. With increasing beam power we observe (i) growing departures from energy equipartition, (ii) the formation of coherent, thermally excited orbits and, ultimately, (iii) the ejection of the particle from the trap. As well as corroborating existing measurements of spin momentum, our results reveal its dynamic effect. We show how the under-damped motion of probe particles in structured light fields can expose the nature and morphology of optical momentum flows, and provide a testbed for elementary non-equilibrium statistical mechanics.

Here, the authors provide a vivid demonstration of the dynamic effect of transverse spin momentum in an optical beam in free space revealed by placing a dielectric bead in a counter-propagating optical beam trap in vacuum.

Spin and Orbital Rotation of Plasmonic Dimer Driven by Circularly Polarized Light

The plasmon-enhanced spin and orbital rotation of Au dimer, two optically bound nanoparticles (NPs), induced by a circularly polarized (CP) light (plane wave or Gaussian beam) were studied theoretically. Through the optomechanical performances of optical forces and torques, the longitudinal/transverse spin-orbit coupling (SOC) of twisted electromagnetic fields was investigated. The optical forces show that for the long-range interaction, there exist some stable-equilibrium orbits for rotation, where the stable-equilibrium interparticle distances are nearly the integer multiples of wavelength in medium. In addition, the optical spin torque drives each NP to spin individually. For a plane wave, the helicities of the longitudinal spin and orbital rotation of the coupled NPs are the same at the stable-equilibrium orbit, consistent with the handedness of plane wave. In contrast, for a focused Gaussian beam, the helicity of the orbital rotation of dimer could be opposite to the handedness of the incident light due to the negative optical orbital torque at the stable-equilibrium interparticle distance; additionally, the transverse spin of each NP becomes profound. These results demonstrate that the longitudinal/transverse SOC is significantly induced due to the twisted optical field. For the short-range interaction, the mutual attraction between two NPs is induced, associated with the spinning and spiral trajectory; eventually, the two NPs will collide. The borderline of the interparticle distance between the long-range and short-range interactions is approximately at a half-wavelength in medium.

Theoretical investigation on asymmetrical spinning and orbiting motions of particles in a tightly focused power-exponent azimuthal-variant vector field

We generate a new kind of azimuthal-variant vector field with a distribution of states of polarization (SoPs) described by the square of the azimuthal angle. Owing to asymmetrical SoPs distribution of this localized linearly polarized vector field, the tightly focused field exhibits a double half-moon shaped pattern with the localized elliptical polarization in the cross section of field at the focal plane. Moreover, we study the three-dimensional distributions of spin and orbital linear and angular momenta in the focal region. We numerically investigate the gradient force, radiation force, spin torque, and orbital torque on a dielectric Rayleigh particle produced by the tightly focused vector field. It is found that asymmetrical spinning and orbiting motions of trapped Rayleigh particles can be realized by the use of a tight vector field with power-exponent azimuthal-variant SoPs.

Enhancement of the 'tractor-beam' pulling force on an optically bound structure

Recently, increasing attention has been devoted to mastering a new technique of optical delivery of micro-objects tractor-beam'1, 2, 3, 4, 5, 6, 7, 8, 9. Such beams have uniform intensity profiles along their propagation direction and can exert a negative force that, in contrast to the familiar pushing force associated with radiation pressure, pulls the scatterer toward the light source. It was experimentally observed that under certain circumstances, the pulling force can be significantly enhanced6 if a non-spherical scatterer, for example, a linear chain of optically bound objects10, 11, 12, is optically transported. Here we demonstrate that motion of two optically bound objects in a tractor beam strongly depends on theirs mutual distance and spatial orientation. Such configuration-dependent optical forces add extra flexibility to our ability to control matter with light. Understanding these interactions opens the door to new applications involving the formation, sorting or delivery of colloidal self-organized structures.

Tailoring Optical Gradient Force and Optical Scattering and Absorption Force

The introduction of the concept of gradient force and scattering and absorption force is an important milestone in optical trapping. However the profiles of these forces are usually unknown, even for standard setups. Here, we successfully calculated them analytically via multipole expansion and numerically via Mie theory and fast Fourier transform. The former provides physical insight, while the latter is highly accurate and efficient. A recipe to create truly conservative energy landscapes is presented. These may open up qualitatively new features in optical manipulation.

Design of a compact device to generate and test beams with orbital angular momentum in the EUV

We present a compact design to generate and test optical-vortex beams with possible applications in the extreme ultraviolet (EUV) region of the electromagnetic spectrum. The device consists of a diffractive mask where both the beam with orbital angular momentum and the reference wavefront to test its phase are generated. In order to show that the proposal would work in the EUV, simulations and proof-of-principle experiments were performed, using typical parameters for EUV holography scaled to visible wavelengths. As the simplest case, we consider the well-known Laguerre-Gaussian (LG)-like beams, which have a single vortex in the propagation axis. To further test the versatility of the device, we consider Mathieu beams, more complex structured beams that may contain several vortices. In the experiment, a spatial light modulator was used to display the mask. As examples, we show the results for a LG-like beam with topological charge ℓ=1 and Mathieu beams with topological charge ℓ=2 and ellipticity q=2. These results show the potential of the device to generate a variety of beam shapes at EUV wavelengths.

Shaping of optical vector beams in three dimensions

We present a method of shaping three-dimensional (3D) vector beams with prescribed intensity distribution and controllable polarization state variation along arbitrary curves in three dimensions. By employing a non-iterative 3D beam-shaping method developed for the scalar field, we use two curved laser beams with mutually orthogonal polarization serving as base vector components with a high-intensity gradient and controllable phase variation, so that they are collinearly superposed to produce a 3D vector beam. We experimentally demonstrate the generation of 3D vector beams that have a polarization gradient (spatially continuous variant polarization state) along 3D curves, which may find applications in polarization-mediated processes, such as to drive the motion of micro-particles.

Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum

The theory of photokinetic effects expresses the forces and torques exerted by a beam of light in terms of experimentally accessible amplitude and phase profiles. We use this formalism to develop an intuitive explanation for the performance of optical tweezers operating in the Rayleigh regime, including effects arising from the influence of light's angular momentum. First-order dipole contributions reveal how a focused beam can trap small objects, and what features limit the trap's stability. The first-order force separates naturally into a conservative intensity-gradient term that forms a trap and a non-conservative solenoidal term that drives the system out of thermodynamic equilibrium. Neither term depends on the light's polarization; light's spin angular momentum plays no role at dipole order. Polarization-dependent effects, such as trap-strength anisotropy and spin-curl forces, are captured by the second-order dipole-interference contribution to the photokinetic force. The photokinetic expansion thus illuminates how light's angular momentum can be harnessed for optical micromanipulation, even in the most basic optical traps.This article is part of the themed issue 'Optical orbital angular momentum'.

Spinning and orbiting motion of particles in vortex beams with circular or radial polarizations

Focusing fields of optical vortex (OV) beams with circular or radial polarizations carry both spin angular momentum (SAM) and orbital angular momentum (OAM), and can realize non-axial spinning and orbiting motion of absorptive particles. Using the T-matrix method, we evaluate the optical forces and torques exerted on micro-sized particles induced by the OV beams. Numerical results demonstrate that the particle is trapped on the circle of intensity maxima, and experiences a transverse spin torque along azimuthal direction, a longitudinal spin torque, and an orbital torque, respectively. The direction of spinning motion is not only related to the sign of topological charge of the OV beam, but also to the polarization state. However, the topological charge controls the direction of orbiting motion individually. Optically induced rotations of particles with varying sizes and absorptivity are investigated in OV beams with different topological charges and polarization states. These results may be exploited in practical optical manipulation, especially for optically induced rotations of micro-particles.

Reverse engineering approach to focus shaping

We propose and experimentally demonstrate an inverse design for the complete shaping of the optical focal field with the prescribed distribution of intensity, phase, and polarization. The input field that yields the desired focal field is obtained through a fast noniterative calculation procedure, in which the focal field is configured at will and then back-propagates to the input plane. The experiments have verified that all parameters of the focal field can be controlled simultaneously and independently. Furthermore, using this inverse design, we generate in focal region a kind of "perfect polarization vortex" field that has a shape independent of the topological charge of vortex. This target-oriented scheme holds the potential for applications requiring a complex focal field.

Spin-controlled orbital motion in tightly focused high-order Laguerre-Gaussian beams

Spin angular momentum can contribute to both optical force and torque exerted on spheres. Orbit rate of spheres located in tightly focused LG beams with the same azimuthal mode index l is spin-controlled due to spin-orbit coupling. Laguerre-Gaussian beams with high-order azimuthal mode are used here to study the orbit rate of dielectric spheres. Orbit rates of spheres with varying sizes and refravtive indices are investigated as well as optical forces acting on spheres in LG beams with different azimuthal modes. These results would be much helpful to investigation on optical rotation and transfer of spin and orbital angular momentum.

Rotation of millimeter-sized objects using ordinary light

The ability to optically rotate bodies offers new degrees of control of micro-objects with applications in various domains, including microelectromechanical systems (MEMS), biomanipulations, or optofluidics. Here we demonstrate the optically-induced rotation of simple asymmetric two-dimensional objects using plane waves originating either from ordinary laser sources or from black body radiation. The objects are floating on an air/water interface. We observe a steady-state rotation depending on the light intensity and on the asymmetry of the object. We interpret this rotation in terms of light diffraction by the edges of the object. Such systems could be easily implemented in optofluidic devices to induce liquid flow without the need for special light sources.

Spin Textures of Exciton-Polaritons in a Tunable Microcavity with Large TE-TM Splitting

We report an extended family of spin textures of zero-dimensional exciton-polaritons spatially confined in tunable open microcavity structures. The transverse-electric-transverse-magnetic (TE-TM) splitting, which is enhanced in the open cavity structures, leads to polariton eigenstates carrying quantized spin vortices. Depending on the strength and anisotropy of the cavity confining potential and of the TE-TM induced splitting, which can be tuned via the excitonic or photonic fractions, the exciton-polariton emissions exhibit either spin-vortex-like patterns or linear polarization, in good agreement with theoretical modeling.

Simple method for generation of vector beams using a small-angle birefringent beam splitter

A simple and practical system for generation of vector beams with arbitrary polarization and complex-amplitude distributions is proposed. The system mainly consists of a scalar computer-generated hologram (CGH), a small-angle birefringent beam splitter (BBS), and a Fourier lens with a filtering aperture (FA). The CGH is placed in front of the Fourier lens. The BBS is inserted between the CGH and the Fourier lens. When the CGH specially designed according to the method described in this Letter is illuminated by a plane beam or a Gaussian beam, a desired vector beam can be obtained through the FA placed at the back focal plane of the Fourier lens. Because no coupling element and half-wave plate are to be placed between the CGH and the BBS, the extinction ratios of both the two orthogonal polarization components for the vector beam can be better than 10(-5) and so high-quality vector beams can be generated.

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.

Complete shaping of optical vector beams

We propose and experimentally demonstrate the complete and simultaneous modulation of the amplitude, phase and arbitrary state of polarization of optical beams. Based on a 4-f system including a spatial light modulator (SLM), two orthogonally polarized beams serving as the base vector components are produced by a computer generated hologram. The complex amplitude of orthogonal components is realized by a macro-pixel encoding technique purposely designed for phase-only SLMs. Vector beams can be created from the coaxial superposition of the two base beams. This enables us to design optical fields with arbitrarily structured amplitude, phase and polarization by using only one SLM, and thus provides an easy-to-implement route for exploring the novel effects and expanding the functionality of vector beams with space-variant parameters.

Perturbative theory for Brownian vortexes

Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Laser optical separation of chiral molecules

The optical trapping of molecules with an off-resonant laser beam involves a forward-Rayleigh scattering mechanism. It is shown that discriminatory effects arise on irradiating chiral molecules with circularly polarized light; the complete representation requires ensemble-weighted averaging to account for the influence of the trapping beam on the distribution of molecular orientations. Results of general application enable comparisons to be drawn between the results for two limits of the input laser intensity. It emerges that, in a racemic mixture, there is a differential driving force whose effect, at high laser intensities, is to produce differing local concentrations of the two enantiomers.

Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector

In this Letter, the optical forces on an electric dipole generated by a beam made up of two circularly polarized Hermite-Gaussian modes have been analyzed. When the intensity of the two modes is not the same, the mechanical action of the scattering force is completely different from the behavior of the Poynting vector. The dynamics of resonant metallic nanoparticles under this field have been calculated by means of Langevin molecular dynamic simulations. This configuration could be useful to experimentally verify how radiation pressure on a Rayleigh particle is due to the transfer of linear momentum coming solely from the orbital part of the Poynting vector.

Surface angular momentum of light beams

Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded transversely and longitudinally while a beam has, in principle, an infinite extent along the direction of propagation, renders incomplete the textbook calculation of the spin/orbital separation of the angular momentum of a light beam. In this work we demonstrate that a novel, extra surface part must be added in order to preserve the gauge invariance of the optical angular momentum per unit length. The impact of this extra term is quantified by means of two examples: a Laguerre-Gaussian and a Bessel beam, both circularly polarized.

Selective trapping or rotation of isotropic dielectric microparticles by optical near field in a plasmonic archimedes spiral

We demonstrate selective trapping or rotation of optically isotropic dielectric microparticles by plasmonic near field in a single gold plasmonic Archimedes spiral. Depending on the handedness of circularly polarized excitation, plasmonic near fields can be selectively engineered into either a focusing spot for particle trapping or a plasmonic vortex for particle rotation. Our design provides a simple solution for subwavelength optical manipulation and may find applications in micromechanical and microfluidic systems.

Electromagnetically induced torque on a large ring in the microwave range

We report on the exchange of orbital angular momentum between an electromagnetic wave and a 30 cm diameter ring. Using a turnstile antenna in the GHz range, we induce a torque on a suspended copper strip of the order of 10(-8)  N m. Rotations of a few degrees and accelerations up to 4×10(-4) °/s2 are observed. A linear dependence of the acceleration as a function of the applied power is found. There are many applications in the detection of angular momentum in electromagnetics, in acoustics, and also in the magnetization of nanostructures.

Nanolithography by plasmonic heating and optical manipulation of gold nanoparticles

Noble-metal particles feature intriguing optical properties, which can be utilized to manipulate them by means of light. Light absorbed by gold nanoparticles, for example, is very efficiently converted into heat, and single particles can thus be used as a fine tool to apply heat to a nanoscopic area. At the same time, gold nanoparticles are subject to optical forces when they are irradiated with a focused laser beam, which renders it possible to print, manipulate, and optically trap them in two and three dimensions. Here, we demonstrate how these properties can be used to control the polymerization reaction and thermal curing of polydimethylsiloxane (PDMS) at the nanoscale and how these findings can be applied to synthesize polymer nanostructures such as particles and nanowires with subdiffraction limited resolution.

Refractive optical wing oscillators with one reflective surface

An optical wing is a cambered rod that experiences a force and torque owing to the reflection and transmission of light from the surface. Here we address how such a wing may be designed to maintain an efficient thrust from radiation pressure (RP) while also providing a torque that returns the wing to a source facing orientation. The torsional stiffness of two different wing cross-sections is determined from numerical ray-tracing analyses. These results demonstrate the potential to construct a passive sun-tracking, space flight system or a microscopic surface measurement device based on RP force and torque.

Optical conveyors: a class of active tractor beams

We experimentally demonstrate a class of tractor beams created by coherently superposing coaxial Bessel beams. These optical conveyors have periodic intensity variations along their axes that act as highly effective optical traps for micrometer-scale objects. Trapped objects can be moved selectively upstream or downstream along the conveyor by appropriately changing the Bessel beams' relative phase. The same methods used to project a single optical conveyor can project arrays of independent optical conveyors, allowing bidirectional transport in three dimensions.