Azimuthal Imaginary Poynting Momentum Density

Revealing the Electric and Magnetic Nature of the Scattered Light

The multipolar expansion of the electromagnetic field plays a key role in the study of light-matter interactions. All the information about the radiation and coupling between the incident wavefield and the object is embodied in the electric and magnetic scattering coefficients of the expansion. However, the experimental determination of requires measuring the components of the scattered field in all directions, something that is exceptionally challenging. Here, we demonstrate that a single measurement of the Stokes vector unlocks access to the quadrivector . Thus, our Stokes polarimetry method allows us to capture and separately, a distinction that can not be achieved by measuring the total energy of the scattered field via an integrating sphere. Moreover, the determination of enables us to infer the amplitude of the scattered field at all points of the radiation zone, including the amplitude of the near-field distribution generated by the objects. Importantly, we demonstrate the robustness of our Stokes polarimetry method, showing its fidelity with just two measurements of the Stokes vector at different scattering angles.

Gradient and curl optical torques

Optical forces and torques offer the route towards full degree-of-freedom manipulation of matter. Exploiting structured light has led to the discovery of gradient and curl forces, and nontrivial optomechanical manifestations, such as negative and lateral optical forces. Here, we uncover the existence of two fundamental torque components, which originate from the reactive helicity gradient and momentum curl of light, and which represent the rotational analogues to the gradient and curl forces, respectively. Based on the two components, we introduce and demonstrate the concept of lateral optical torques, which act transversely to the spin of illumination. The orbital angular momentum of vortex beams is shown to couple to the curl torque, promising a path to extreme torque enhancement or achieving negative optical torques. These results highlight the intersection between the areas of structured light, Mie-tronics and rotational optomechanics, even inspiring new paths of manipulation in acoustics and hydrodynamics.

Enantioselective Optical Trapping of Multiple Pairs of Enantiomers by Focused Hybrid Polarized Beams

Enantiomers (opposite chiral molecules) usually exhibit different effects when interacting with chiral agents, thus the identification and separation of enantiomers are of importance in pharmaceuticals and agrochemicals. Here an optical approach is proposed to enantioselective trapping of multiple pairs of enantiomers by a focused hybrid polarized beam. Numerical results indicate that such a focused beam shows multiple local optical chirality of opposite signs in the focal plane, and can trap the corresponding enantiomers near the extreme value of optical chirality density according to the handedness of enantiomers. The number and positions of trapped enantiomers can be changed by altering the value and sign of polarization orders of hybrid polarized beams, respectively. The key to realizing enantioselective optical trapping of enantiomers is that the chiral optical force exerted on enantiomers in this focused field is stronger than the achiral optical force. The results provide insight into the optical identification and separation of multiple pairs of enantiomers and will find applications in chiral detection and sensing.

Tailoring nonuniform local orbital angular momentum density

As is well known, a light beam with a helical phase carries an optical orbital angular momentum (OAM), which can cause the orbital motion of trapped microparticles around the beam axis. Usually, the speed of the orbital motion is uniform along the azimuthal direction and depends on the amount of OAM and the light intensity. Here, we present the reverse customized method to tailor the nonuniform local OAM density along the azimuthal direction of the focal field, which has a hybrid polarization distribution and maintains a doughnut-shaped intensity profile. Theoretical analysis and experimental results about the orbital motion of the trapped polystyrene sphere show that the nonuniform local OAM density can be tailored by manipulating the polarization states of the focal field. Our results provide an ingenious way to control the local tangential optical force and the speed of the orbital motion of particles driven by the local OAM density and will promote exciting possibilities for exploring ways to control the mechanical dynamics of microparticles in optical trapping and microfluidics.

Optomechanical effects caused by non-zero field quantities in multiple evanescent waves

Evanescent waves, with their high energy density, intricate local momentum, and spatial distribution of spins, have been the subject of extensive recent study. These waves offer promising applications in near-field particle manipulation. Consequently, it becomes imperative to gain a deeper understanding of the impacts of scattering and gradient forces on particles in evanescent waves to enhance and refine the manipulation capabilities. In this study, we employ the multipole expansion theory to present analytical expressions for the scattering and gradient forces exerted on an isotropic sphere of any size and composition in multiple evanescent waves. The investigation of these forces reveals several unusual optomechanical phenomena. It is well known that the scattering force does not exist in counter-propagating homogeneous plane waves. Surprisingly, in multiple pairs of counter-propagating evanescent waves, the scattering force can arise due to the nonzero orbital momentum (OM) density and/or the curl part of the imaginary Poynting momentum (IPM) density. More importantly, it is found that the optical scattering force can be switched on and off by simply tuning the polarization. Furthermore, optical forces typically vary with spatial position in an interference field. However, in the interference field generated by evanescent waves, the gradient force becomes a spatial constant in the propagating plane as the particle's radius increases. This is attributed to the decisive role of the non-interference term of the electromagnetic energy density gradient. Our study establishes a comprehensive and rigorous theoretical foundation, propelling the advancement and optimization of optical manipulation techniques harnessed through multiple evanescent waves. Specifically, these insights hold promise in elevating trapping efficiency through precise control and manipulation of optical scattering and gradient forces, stimulating further explorations.

Multiplexed vortex beam-based optical tweezers generated with spiral phase mask

The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezers setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges and without amplitude modulation. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling nearly independent orbiting dynamics around the optical axis within each vortex. The angular velocity of the confined particles versus the optical power in the focal region is also discussed for different combinations of topological charges.

Creating tunable lateral optical forces through multipolar interplay in single nanowires

The concept of lateral optical force (LOF) is of general interest in optical manipulation as it releases the constraint of intensity gradient in tightly focused light, yet such a force is normally limited to exotic materials and/or complex light fields. Here, we report a general and controllable LOF in a nonchiral elongated nanoparticle illuminated by an obliquely incident plane wave. Through computational analysis, we reveal that the sign and magnitude of LOF can be tuned by multiple parameters of the particle (aspect ratio, material) and light (incident angle, direction of linear polarization, wavelength). The underlying physics is attributed to the multipolar interplay in the particle, leading to a reduction in symmetry. Direct experimental evidence of switchable LOF is captured by polarization-angle-controlled manipulation of single Ag nanowires using holographic optical tweezers. This work provides a minimalist paradigm to achieve interface-free LOF for optomechanical applications, such as optical sorting and light-driven micro/nanomotors.

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.

Structured transverse orbital angular momentum probed by a levitated optomechanical sensor

The momentum carried by structured light fields exhibits a rich array of surprising features. In this work, we generate transverse orbital angular momentum (TOAM) in the interference field of two parallel and counter-propagating linearly-polarised focused beams, synthesising an array of identical handedness vortices carrying intrinsic TOAM. We explore this structured light field using an optomechanical sensor, consisting of an optically levitated silicon nanorod, whose rotation is a probe of the optical angular momentum, which generates an exceptionally large torque. This simple creation and direct observation of TOAM will have applications in studies of fundamental physics, the optical manipulation of matter and quantum optomechanics.

Collecting, transporting and sorting micro-particles via the optical slings generated by a liquid crystal q(φ)-plate

We disclose a transporting/collecting optical sling generated by a liquid crystal geometric phase optical element with spatial variant topological charge, which shows the intriguing repelling/indrawing effect on the micro-particle along the spiral orbit. Two proof-of-concept prototypes, i.e., an optical conveyor and a particle collector, are demonstrated. Based on the distinct dynamic characteristics of the micro-particles in different sizes, we conceptually propose a design for particle sorting. Thus, our proposed method to generate a spiral optical sling with spatial variant orbital angular momentum for on-demand collecting, transporting and sorting micro-particles is substantiated, which can find extensive applications in bio-medicine, micro-biology, etc.

Rotational dynamics of indirect optical bound particle assembly under a single tightly focused laser

The optical binding of many particles has the potential to achieve the wide-area formation of a "crystal" of small materials. Unlike conventional optical binding, where the entire assembly of targeted particles is directly irradiated with light, if remote particles can be indirectly manipulated using a single trapped particle through optical binding, the degrees of freedom to create ordered structures can be enhanced. In this study, we theoretically investigate the dynamics of the assembly of gold nanoparticles that are manipulated using a single trapped particle by a focused laser. We demonstrate the rotational motion of particles through an indirect optical force and analyze it in terms of spin-orbit coupling and the angular momentum generation of light. The rotational direction of bound particles can be switched by the numerical aperture. These results pave the way for creating and manipulating ordered structures with a wide area and controlling local properties using scanning laser beams.

Reversible lateral optical force on phase-gradient metasurfaces for full control of metavehicles

Photonics is currently undergoing an era of miniaturization thanks in part to two-dimensional (2D) optical metasurfaces. Their ability to sculpt and redirect optical momentum can give rise to an optical force, which acts orthogonally to the direction of light propagation. Powered by a single unfocused light beam, these lateral optical forces (LOFs) can be used to drive advanced metavehicles and are controlled via the incident beam's polarization. However, the full control of a metavehicle on a 2D plane (i.e. forward, backward, left, and right) with a sign-switchable LOF remains a challenge. Here we present a phase-gradient metasurface route for achieving such full control while also increasing efficiency. The proposed metasurface is able to deflect a normally incident plane wave in a traverse direction by modulating the plane wave's polarization, and results in a sign-switchable recoil LOF. When applied to a metavehicle, this LOF enables a level of motion control that was previously unobtainable.

Observation of high-order imaginary Poynting momentum optomechanics in structured light

Optical forces on small particles are conventionally produced from the intensity or phase gradient of light. Harnessing the imaginary Poynting momentum (IPM) of light to generate nontrivial forces would unlock the full potential of optical manipulation techniques, but so far, it is demonstrated only for dipolar magnetoelectric particles. Here, we show that the IPM can be coupled to the force via the interplay of multipoles higher than dipoles, giving rise to high-order IPM forces that can be exerted on a large variety of Mie particles. The high-order concept and theory can be extended to the well-known optical gradient force and radiation pressure, and may inspire new insights for studying the interaction of matter with other classic waves, such as acoustics.

The imaginary Poynting momentum (IPM) of light has been captivated as an unusual origin of optical forces. However, the IPM force is predicted only for dipolar magnetoelectric particles that are hardly used in optical manipulation experiments. Here, we report a whole family of high-order IPM forces for not only magnetoelectric but also generic Mie particles, assisted with their excited higher multipoles within. Such optomechanical manifestations derive from a nonlocal contribution of the IPM to the optical force, which can be remarkable even when the incident IPM is small. We observe the high-order optomechanics in a structured light beam, which, despite carrying no angular momentum, is able to set normal microparticles into continuous rotation. Our results provide unambiguous evidence of the ponderomotive nature of the IPM, expand the classification of optical forces, and open new possibilities for levitated optomechanics and micromanipulations.

The complex Maxwell stress tensor theorem: The imaginary stress tensor and the reactive strength of orbital momentum. A novel scenery underlying electromagnetic optical forces

We uncover the existence of a universal phenomenon concerning the electromagnetic optical force exerted by light or other electromagnetic waves on a distribution of charges and currents in general, and of particles in particular. This conveys the appearence of underlying reactive quantities that hinder radiation pressure and currently observed time-averaged forces. This constitutes a novel paradigm of the mechanical efficiency of light on matter, and completes the landscape of the optical, and generally electromagnetic, force in photonics and classical electrodynamics; widening our understanding in the design of both illumination and particles in optical manipulation without the need of increasing the illuminating power, and thus lowering dissipation and heating. We show that this may be accomplished through the minimization of what we establish as the reactive strength of orbital (or canonical) momentum, which plays against the optical force a role analogous to that of the reactive power versus the radiation efficiency of an antenna. This long time overlooked quantity, important for current progress of optical manipulation, and that stems from the complex Maxwell theorem of conservation of complex momentum that we put forward, as well as its alternating flow associated to the imaginary part of the complex Maxwell stress tensor, conform the imaginary Lorentz force that we introduce in this work, and that like the reactive strength of orbital momentum, is antagonistic to the well-known time-averaged force; thus making this reactive Lorentz force indirectly observable near wavelengths at which the time-averaged force is lowered. The Minkowski and Abraham momenta are also addressed.

Nanoneedle formation via doughnut beam-induced Marangoni effects

Recently, nanosecond pulsed optical vortices enables the production of a unique chiral and sharp needle-like nanostructure (nano-needle). However, the formation process of these structures has been unsolved although mass transport by angular momentum would contribute to the chirality. Here, we reveal that another key factor in the formation of a sharp nano-needle is the Marangoni effect during the melting condition at high temperature. Remarkably, the thickness and height of the nano-needle can be precisely controlled within 200 nm, corresponding to 1/25 of beam radius (5 µm) beyond the diffraction limit by ring-shaped inhomogeneous temperature rise. Our finding will facilitate the development of advanced nano-processing with a variety of structured light beams.

The Poynting Vector Field Generic Singularities in Resonant Scattering of Plane Linearly Polarized Electromagnetic Waves by Subwavelength Particles

We present the results of a study of the Poynting vector field generic singularities at the resonant light scattering of a plane monochromatic linearly polarized electromagnetic wave by a subwavelength particle. We reveal the impact of the problem symmetry, the spatial dimension, and the energy conservation law on the properties of the singularities. We show that, in the cases when the problem symmetry results in the existence of an invariant plane for the Poynting vector field lines, a formation of a standing wave in the immediate vicinity of a singularity gives rise to a saddle-type singular point. All other types of singularities are associated with vanishing at the singular points, either (i) magnetic field, for the polarization plane parallel to the invariant plane, or (ii) electric field, at the perpendicular orientation of the polarization plane. We also show that in the case of two-dimensional problems (scattering by a cylinder), the energy conservation law restricts the types of possible singularities only to saddles and centers in the non-dissipative media and to saddles, foci, and nodes in dissipative. Finally, we show that dissipation affects the (i)-type singularities much stronger than the (ii)-type. The same conclusions are valid for the imaginary part of the Poynting vector in problems where the latter is regarded as a complex quantity. The singular points associated with the formation of standing waves are different for real and imaginary parts of this complex vector field, while all other singularities are common. We illustrate the general discussion by analyzing singularities at light scattering by a subwavelength Germanium cylinder with the actual dispersion of its refractive index.

Inversion method of particle size distribution of milk fat based on improved MPGA

Milk fat’s particle size and distribution not only affect product quality, but also have great impacts on food safety in the economy and society. Based on total light scattering method, this paper has studied the inversion method of particle size distribution under dependent mode condition by combining multi-population genetic algorithm (MPGA) with Tikhonov smooth function. It has minimized the influence from light-absorb medium to improve the inversion accuracy. The approach introduces Tikhonov smooth function and apparent optical parameters to build an objective fitness function and weaken the ill condition of the particle size inversion equation. It also introduces multi-population genetic algorithm to solve the premature convergence of genetic algorithms. The results show that the relative error of the milk fat simulation solution with a nominal diameter is -3.52%, which meets the national standard of ±8% and better than the relative error of -5.01% of the standard genetic algorithm. Thus, the improved MPGA can reconstruct particle size distribution, with a good reliability and stability.

Inverse Optical Torques on Dielectric Nanoparticles in Elliptically Polarized Light Waves

Elliptically polarized light waves carry the spin angular momentum (SAM), so they can exert optical torques on nanoparticles. Usually, the rotation follows the same direction as the SAM due to momentum conservation. It is counterintuitive to observe the reversal of optical torque acting on an ordinary dielectric nanoparticle illuminated by an elliptically or circularly polarized light wave. Here, we demonstrate that negative optical torques, which are opposite to the direction of SAM, can ubiquitously emerge when elliptically polarized light waves are impinged on dielectric nanoparticles obliquely. Intriguingly, the rotation can be switched between clockwise and counterclockwise directions by controlling the incident angle of light. Our study suggests a new playground to harness polarization-dependent optical force and torque for advancing optical manipulations.

Scanning force sensing at micrometer distances from a conductive surface with nanospheres in an optical lattice

The center-of-mass motion of optically trapped dielectric nanoparticles in a vacuum is extremely well decoupled from its environment, making a powerful tool for measurements of feeble subattonewton forces. We demonstrate a method to trap and maneuver nanoparticles in an optical standing wave potential formed by retroreflecting a laser beam from a metallic mirror surface. We can reliably position a ∼170nm diameter silica nanoparticle at distances of a few hundred nanometers to tens of micrometers from the surface of a gold-coated silicon mirror by transferring it from a single-beam tweezer trap into the standing wave potential. We can further measure forces experienced by the particle while scanning the two-dimensional space parallel to the mirror surface, and we find no significant excess force noise in the vicinity of the surface. This method may enable three-dimensional scanning force sensing near surfaces using optically trapped nanoparticles, promising for high-sensitivity scanning force microscopy, tests of the Casimir effect, and tests of the gravitational inverse square law at micrometer scales.

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.

Tailoring of Inverse Energy Flow Profiles with Vector Lissajous Beams

In recent years, structured laser beams for shaping inverse energy flow regions: regions with a direction of energy flow opposite to the propagation direction of a laser beam, have been actively studied. Unfortunately, many structured laser beams generate inverse energy flow regions with dimensions of the order of the wavelength. Moreover, there are significant limitations to the location of these regions. Here, we investigate the possibility of controlling inverse energy flow distributions by using the generalization of well-known cylindrical vector beams with special polarization symmetry—vector Lissajous beams (VLBs)—defined by two polarization orders (p, q). We derive the conditions for the indices (p, q) in order, not only to shape separate isolated regions with a reverse energy flow, but also regions that are infinitely extended along a certain direction in the focal plane. In addition, we show that the maximum intensity curves of the studied VLBs are useful for predicting the properties of focused beams.

Formation of Inverse Energy Flux in the Case of Diffraction of Linearly Polarized Radiation by Conventional and Generalized Spiral Phase Plates

Recently, there has been increased interest in the shaping of light fields with an inverse energy flux to guide optically trapped nano- and microparticles towards a radiation source. To generate inverse energy flux, non-uniformly polarized laser beams, especially higher-order cylindrical vector beams, are widely used. Here, we demonstrate the use of conventional and so-called generalized spiral phase plates for the formation of light fields with an inverse energy flux when they are illuminated with linearly polarized radiation. We present an analytical and numerical study of the longitudinal and transverse components of the Poynting vector. The conditions for maximizing the negative value of the real part of the longitudinal component of the Poynting vector are obtained.

Optical forces on a cylinder induced by surface waves and the conservation of the canonical momentum of light

Based on rigorous derivations using the electromagnetic energy-momentum tensor, we established a generic relationship between the longitudinal optical force (along the surface wave propagating direction) on a cylinder induced by surface waves and the energy flux of each surface mode supported on the interface between air and a lossless substrate possessing continuous translational symmetry along the longitudinal direction. The longitudinal optical force is completely attributed to the canonical momentum of light. Our theory is valid for generic types of surface waves and lays the theoretical foundation for the research and applications of optical manipulations by surface waves.

Surface plasmon polaritons of higher-order mode and standing waves in metallic nanowires

The surface plasmon polaritons (SPPs) of higher-order mode propagating along a plasmonic nanowire (NW) or an elongated nanorod (NR) are studied theoretically. The dispersion relations of SPPs in NWs of different radii, obtained from a transcendental equation, show that the propagation lengths of SPPs of mode 1 and 2 at a specific frequency are longer than that of mode 0. For the higher-order mode, the spatial phase of the longitudinal component of electric field at a cross section of a NW exhibits the topological singularity, which indicates the optical vortex. Of importance, the streamlines of Poynting vector of these SPPs exhibit a helical winding along NW, and the azimuthal component of orbital momentum density exists in the nearfield of NW to produce a longitudinal orbital angular momentum (OAM). Two types of standing wave of counter-propagating SPPs of mode 1 and 2 are also studied; they perform as a string of beads or twisted donut depending on whether the handedness of two opposite-direction propagating SPPs is same or opposite. In addition, a SPP of mode 1 propagating along an elongated NR can be generated by means of an end-fire excitation of crossed electric bi-dipole with 90° phase difference. If the criterion of a resonator for a mode-1 standing wave (string of beads) is met, the configuration of a plasmonic NR associated with a pair of bi-dipoles with a phase delay (0° or 180°) at the two ends can be applied as a high-efficiency nanoantenna of transmission. Our results may pave a way to the further study of SPPs of higher-order mode carrying OAM along plasmonic waveguides.

Metalenses for the generation of vector Lissajous beams with a complex Poynting vector density

We propose a method for the design of metalenses generating and focusing so-called vector Lissajous beams (VLBs), a generalization of cylindrical vector beams (CVBs) in the form of vector beams whose polarization vector is defined by two orders (p, q). The designed metalenses consist of subwavelength gratings performing the polarization transformation of the incident linearly polarized laser beams and a sublinearly chirped lens term for the realization of the beam focusing. The possibility of using VLBs for the realization of laser beams with a complex Poynting vector is theoretically shown. The certain choice of orders (p, q) of the generated VLBs makes it possible to control the type of various electromagnetic field components as well as the components of the complex Poynting vector. For example, in contrast to VLBs, the classical types of CVBs cannot provide an imaginary part in the longitudinal component of the Poynting vector. Such light fields are promising for exciting non-standard forces acting on the trapped nano- and microparticles.

Multipole interplay controls optical forces and ultra-directional scattering

We analyze the superposition of Cartesian multipoles to reveal the mechanisms underlying the origin of optical forces. We show that a multipolar decomposition approach significantly simplifies the analysis of this problem and leads to a very intuitive explanation of optical forces based on the interference between multipoles. We provide an in-depth analysis of the radiation coming from the object, starting from low-order multipole interactions up to quadrupolar terms. Interestingly, by varying the phase difference between multipoles, the optical force as well as the total radiation directivity can be well controlled. The theory developed in this paper may also serve as a reference for ultra-directional light steering applications.