We theoretically investigate the optical force exerted on an isotropic particle illuminated by a superposition of plane waves. We derive explicit analytical expressions for the exerted force up to quadrupolar polarizabilities. Based on these analytical expressions, we demonstrate that an illumination consisting of two tilted plane waves can provide a full control on the optical force. In particular, optical pulling, pushing and lateral forces can be obtained by the proper tuning of illumination parameters. Our findings might unlock multiple applications based on a deterministic control of the spatial motion of small particles.
We consider the lateral optical force between resonator and waveguide, and study the possibility of an equilibrium that occurs solely from the optical force. We prove analytically that a single- resonance system cannot give such an equilibrium in resonator-waveguide force. We then show that two-resonance systems can provide such an equilibrium. We provide an intuitive way to predict the existence of an equilibrium, and give numerical examples.
Here we demonstrate that giant transverse optical forces can be generated in nanoscale slot waveguides of hyperbolic metamaterials, with more than two orders of magnitude stronger compared to the force created in conventional silicon slot waveguides, due to the nanoscale optical field enhancement and the extreme optical energy compression within the air slot region. Both numerical simulation and analytical treatment are carried out to study the dependence of the optical forces on the waveguide geometries and the metamaterial permittivity tensors, including the attractive optical forces for the…
Transverse spin angular momentum (SAM) of light and associated transverse chiral optical forces have received tremendous attention recently as the latter may lead to an optical separation of chiral biomolecules. In this context, the relative magnitude of chiral and non-chiral forces represents a challenge for the implementation of chiral separation schemes. In this work we demonstrate that, by spatially separating the maxima of transverse spin density from the gradient of field intensity, it is possible to dominate chiral-specific components of the force over non-chiral ones. To that end, we s…
We present a multipole expansion theory for optical force exerting on a particle immersed in generic monochromatic free-space optical field. Based on the theory, we have, for the first time, successfully decomposed the optical force on a spherical particle of arbitrary size into a conservative and a nonconservative parts, which are, respectively, written as a gradient of a scalar function and curl of a vector function in an explicit and analytical form. As a result, a scalar potential and a vector potential can be defined, up to gauge freedoms, for the optical force. The decomposition shed lig…
Optical forces have been fruitfully applied in a broad variety of areas that not only span the traditional scientific fields such as physics, chemistry, and biology, but also in more applied fields. It is customary and useful to split the optical force into the (conservative) gradient force and the (non-conservative) scattering and absorption force. These forces are different in attributes. The ability to tailor them will open great potential in fundamental optics and practical applications. Here, we present an analytical and a numerical approach to calculate these forces, and, with these tool…
The downscaling of optical systems to the micro and nano-scale results in very compliant systems with nanogram-scale masses, which renders them susceptible to optical forces. Here we show a specially designed resonant structure for enabling efficient static control of the optical response with relatively weak repulsive and attractive optical forces. Using attractive gradient optical forces we demonstrate a static mechanical deformation of up to 20 nanometers in the resonator structure. This deformation is enough to shift the optical resonances by roughly 80 optical linewidths.
We analyze how chirality can generate pulling optical forces and left-handed torques by cross-coupling linear-to-angular momenta between the light field and the chiral object. In the dipolar regime, we reveal that such effects can emerge from a competition between non-chiral and chiral contributions to dissipative optical forces and torques, a competition balanced by the strength of chirality of the object. We extend the analysis to large chiral spheres where the interplay between chirality and multipolar resonances can give rise to a break of symmetry that flips the signs of both optical forc…
Arthur Ashkin was awarded the 2018 Nobel prize in physics for the invention of optical tweezers. Since the first publication in 1986 Optical Tweezers have been used as a tool to measure forces and rheological properties of microscopic systems. For the calibration of these measurements, the knowledge of the forces is fundamental. However, it is still common to deduce the optical forces from assumptions based on the particle size with respect to the trapping laser wavelength. This show the necessity to develop a complete and accurate electromagnetic model that does not depend on early approximat…
We proposed an optomechanical system to quantify the net force on a strand of cleaved silica optical fiber in situ as the laser light was being guided through it. Four strands of the fiber were bond to both sides of a macroscopic oscillator, whose movements were accurately monitored by a Michelson interferometer. The laser light was propagating with variable optical powers and frequency modulations. Experimentally, we discovered that the driving force for the oscillator consisted of not only the optical force of the light exiting from the cleaved facets but also the tension along the fiber ind…
The principle of optical trapping is conventionally based on the interaction of optical fields with linear induced polarizations. However, the optical force originating from the nonlinear polarization becomes significant when nonlinear optical nanoparticles are trapped by ultrafast laser pulses. Herein we establish the time-averaged optical forces on a nonlinear optical nanoparticle using high-repetition-rate ultrafast laser pulses, based on the linear and nonlinear polarization effects. We investigate the dependence of the optical forces on the magnitudes and signs of the refractive nonlinear…
We demonstrate the measurement of laterally induced optical forces using an Atomic Force Microscope (AFM). The lateral electric field distribution between a gold coated AFM probe and a nano-aperture in a gold film is mapped by measuring the lateral optical force between the apex of the AFM probe and the nano-aperture. Torsional eigenmodes of an AFM cantilever probe were used to detect the laterally induced optical forces. We engineered the cantilever shape using a focused ion beam to enhance the torsional eigenmode resonance. The measured lateral optical force agrees well with simulations. Thi…
Optical forces in the near fields have important applications in on-chip optical manipulations of small particles and molecules. Here, we report a study of optical force and torque on small particles induced by the optical polarization singularities of a gold cylinder. We show that the scattering of the cylinder generates both electric and magnetic C lines (i.e., lines of polarization singularities) in the near fields, and the C lines can induce complex force and torque on a dielectric/magnetic particle. The force and torque manifest dramatic spatial variations with interesting symmetry proper…
In several experiments involving material background, it has been observed that the Chu, Einstein-Laub and Ampere formulations of optical force lead to either different optical forces or wrong total optical force. In order to identify the exact reason behind such significant disagreements, we investigate the optical force in a number of tractor beam and lateral force experiments. We demonstrate that the modified Einstein-Laub or modified Chu formulations, obtained from two mathematical consistency conditions of force calculation, give the time-averaged force that agrees with the experiments. W…
We describe a rigidly-mounted optical cavity which is insensitive to inertial forces acting in any direction and to the compressive force used to constrain it. The design is based on a cubic geometry with four supports placed symmetrically about the optical axis in a tetrahedral configuration. To measure the inertial force sensitivity, a laser is locked to the cavity while it is inverted about three orthogonal axes. The maximum acceleration sensitivity is 2.5\times10^-11/g (where g=9.81 ms^-2), the lowest passive sensitivity to be reported for an optical cavity.
We derived an analytical formula for the optical force acting on a small anisotropic chiral particle. The behavior of chiral particles is qualitatively different from achiral particles due to new chirality dependent terms which couple mechanical linear momentum and optical spin angular momentum. Such coupling induced by chirality can serve as a new mechanism to achieve optical pulling force. Our analytical predictions are verified by numerical simulations.
Structural chirality can induce counter-intuitive optical forces due to inherent symmetry properties. While optical forces on a single chiral particle in the Rayleigh regime have been well studied, optical forces in coupled chiral particles remain less explored. By using full-wave numerical simulations and analytical methods of source representation and coupled mode theory, we investigated the optical forces induced by a plane wave on two chiral particles coupling with each other via the evanescent near fields. We found that the induced electric and magnetic dipoles of the chiral particles hav…
Single-layer graphene exhibits exceptional mechanical properties attractive for optomechanics: it combines low mass density, large tensile modulus, and low bending stiffness. However, at visible wavelengths, graphene absorbs weakly and reflects even less, thereby inadequate to generate large optical forces needed in optomechanics. Here, we numerically show that a single-layer graphene sheet is sufficient to produce strong optical forces under terahertz or infrared illumination. For a system as simple as graphene suspended atop a uniform substrate, high reflectivity from the substrate is crucia…
Optical forces allow manipulation of small particles and control of nanophotonic structures with light beams. Here, we describe a counter-intuitive lateral optical force acting on particles placed above a substrate, under uniform plane wave illumination without any field gradients. We show that under circularly-polarized illumination, nanoparticles experience a lateral force as a result of dipolar, spin-sensitive scattering, with a magnitude comparable to other optical forces. To this end, we rigorously calculate the force experienced by a circularly polarized dipole radiating above a surface.…
We reveal that slow-light enhanced optical forces between side-coupled photonic-crystal nanowire waveguides can be flexibly controlled by introducing a relative longitudinal shift. We predict that close to the photonic band-edge, where the group velocity is reduced, the transverse force can be tuned from repulse to attractive, and the force is suppressed for a particular shift value. Additionally the shift leads to symmetry breaking that can facilitate longitudinal forces acting on the waveguides, in contrast to unshifted structures where such forces vanish.
We report quantitative experimental measurements of the Abraham force associated with a propagating optical wave. We isolate this force using a guided light wave undergoing an adiabatic mode transformation (AMT) along a liquid-filled hollow optical fiber (HOF). Utilizing this light intensity distribution within the liquid, we were able to generate a time-averaged non-vanishing Abraham force density, while simultaneously suppressing the Abraham-Minkowski force density. The incident laser field induced a linear axial displacement of the air-liquid interface inside the HOF, which provided a direc…
We experimentally studied whispering-gallery modes(WGMs) and demonstrated resonance enhancement of optical forces evanescently exerted on dielectric microspheres. We showed that the resonant light pressure can be used for optical sorting of microparticles with extraordinary uniform resonant properties that is unachievable by conventional sorting techniques.
Like many other physical quantities, the optical force can be expanded using multipole expansion, which has been done in [Nat. Photon. 5, 531], up to electric octupole order. However, in that study, the existence of radiation multipoles were pre-assumed, and the role of the fundamental building units, charges, are not evident. Here, we derive the same multipolar expression of optical force by treating the particles as a collection of point charges or point dipoles, which results in more transparent physics and mathematics.
We demonstrate tunable pulling and pushing optical forces on plasmonic nanostructures around Fano resonance. The plasmonic nanostructure containing a spherical core with optical gain and a metallic shell shows much larger optical pulling force than a pure gain sphere. One can obtain large field enhancement and giant pulling force at the emerged quadrupole mode. The introduction of optical pump compensate the dissipative loss from metal shell, thus enable the strong coupling between a narrow quadrupole mode and a board dipole mode, giving rise to Fano resonance. The giant negative forces origin…
In vectorial diffraction theory, tight focusing of a linearly polarized laser beam produces an anisotropic field distribution around the focal plane. We present a numerical investigation of the electromagnetic field distribution of a focused beam in terms of the input beam polarization state and the associated effects on the trap stiffness asymmetry of optical tweezers. We also explore the symmetry change of a polarization-dependent optical force due to the electromagnetic field redistribution by the presence of dielectric spheres of selected diameters ranging from the Rayleigh scattering regi…
We propose an optomechanical structure consisting of a photonic-crystal (holey) membrane suspended above a layered silicon-on-insulator substrate in which resonant bonding/antibonding optical forces created by externally incident light from above enable all-optical control and actuation of stiction effects induced by the Casimir force. In this way, one can control how the Casimir force is expressed in the mechanical dynamics of the membrane, not by changing the Casimir force directly but by optically modifying the geometry and counteracting the mechanical spring constant to bring the system in…
We theoretically investigate the emergence of lateral (recoil) forces acting on generic dipole-type emitters in the vicinity of a reciprocal translation-invariant substrate. Surprisingly, we find that for linearly-polarized electric dipoles the lateral force invariably vanishes, independent of the anisotropy (e.g., tilted optical axes) or chirality of the substrate. We identify a novel opportunity to have a recoil force relying on a superposition of two linearly-polarized and collinear electric and magnetic dipoles. Counterintuitively, it is shown that when such an emitter stands above a uniax…
We put forward a theory on the optical force exerted upon a dipolar particle by a stationary and ergodic partially coherent light field. We show through a rigorous analysis that the ensemble averaged electromagnetic force is given in terms of a partial gradient of the space variable diagonal elements of the coherence tensor. Further, by following this result we characterize the conservative and non-conservative components of this force. In addition, we establish the propagation law for the optical force in terms of the coherence function of light at a diffraction plane. This permits us to eval…
The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a direction in which there is neither a field gradient nor wave propagation. As their direction and strength depends on the chiral polarizability of the particle, they act as chirality-sorting and may offer a mechanism for passive chirality spectroscopy. The absolute strength of the forces also substantially exceeds that of other recently predicted sideways optical forces, such that they may more readily offer an experi…
Evanescent electromagnetic waves possess spin-momentum locking, where the direction of propagation (momentum) is locked to the inherent polarization of the wave (transverse spin). We study the optical forces arising from this universal phenomenon and show that the fundamental origin of recently reported non-trivial optical chiral forces is spin-momentum locking. For evanescent waves, we show that the direction of energy flow, direction of decay, and direction of spin follow a right hand rule for three different cases of total internal reflection, surface plasmon polaritons, and $HE_{11}$ mode …
In this work a method for generating a long-range optical pulling force is presented which is realized by utilizing a vortex beam and a device designed based on transformation optics through conformal mapping. The device works by transforming an input perfect vortex beam into an almost non-paraxial plane wave, and generates a pulling force by maximizing the forward momentum of the beam. A three-dimensional full-wave analysis of the device is performed and the optical force is computed by the Maxwell stress tensor method. The simulation results show a very good agreement with the theoretical ca…
We investigate numerically the modification of surface-plasmon assisted optical force on a gold nanorod pair by incorporating dielectric interlayer. The frequency dependent electromagnetic forces are obtained through full-vectorial solution of Maxwell equations with a finite element solver. We obtain the common and relative electromagnetic force experienced by the nanorods with dielectric interlayers of different permittivity or thickness. In particular, we demonstrate that the use of a liquid crystal interlayer can be utilized as a dynamic tuning mechanism for the reversal of the direction of…
We investigate optical (transverse gradient) forces between two high-index dielectric planar waveguides immersed in low-index dielectric fluid media. Complimentary to previous studies, we extend optical forces calculations, in order to take into account a non-vacuum (and non-air) background medium, by using the Minkowski stress tensor formulation; we derived a very simple set of equations in terms of the effective refractive indexes of the waveguide eigenmodes. We also used a normalized version of the dispersion relation method to calculate the optical forces, in order to validate our results …
A slab with relative permittivity $ε= - 1 + iδ$ and permeability $μ= - 1 + iδ$ has a critical distance away from the slab where a small particle will either be cloaked or imaged depending on whether it is located inside or outside that critical distance. We find that the optical force acting on a small cylinder under plane wave illumination reaches a maximum value at this critical distance. Contrary to the usual observation that superlens systems should be highly loss-sensitive, this maximum optical force remains a constant when loss is changed within a certain range. For a fixed particle-slab…
Optical pulling forces or tractor beams can pull particles against light propagation by redirecting the incident photons forward. This is typically achieved using Bessel beams with very small half-cone angles, which considerably limits its applicability. One can circumvent such issue by using a superposition of plane waves. In order to investigate optical pulling forces exerted by a pair of non-colinear plane waves, we develop a theoretical framework based on Mie theory, Debye potentials and Wigner rotation matrices. We apply this framework to calculate the optical pulling force on metallo-die…
We study the optical forces acting on toroidal nanostructures. A great enhancement of optical force is unambiguously identified as originating from the toroidal dipole resonance based on the source-representation, where the distribution of the induced charges and currents is characterized by the three families of electric, magnetic, and toroidal multipoles. On the other hand, the resonant optical force can also be completely attributed to an electric dipole resonance in the alternative field-representation, where the electromagnetic fields in the source-free region are expressed by two sets of…
Optical forces acting on nano-sized particles are typically too small to be useful for particle manipulation. We theoretically and numerically demonstrate a mechanism that can significantly enhance the optical force acting on a small particle through a special type of resonant particle-substrate coupling. The resonance arises from the singular behavior of the particle's effective polarizablity in the presence of a metal-dielectric-metal multilayer substrate. We show that this phenomenon is closely related to the existence of a flat-band plasmon mode supported by the multilayer substrate.
Modern optical nano-elements pursue ever-smaller sizes and individualized functionalities. Those elements that can efficiently manipulate the magnetic field of light boast promising future applications with a great challenge: the magnetic near field is irretrievable from conventional optical far-field characterization. Here we propose photoinduced magnetic force microscopy to directly and exclusively sense the magnetic field of light at the nanoscale. The proposed instrument exploits a magnetic nanoprobe with exclusive magnetic excitation under structured light illumination. The magnetic nanop…
Light-actuated motors, vehicles, and even space sails have drawn tremendous attention for basic science and applications in space, biomedical, and sensing domains. Optical bound states in the continuum (BIC) are topological singularities of the scattering matrix, known for their unique light trapping capability and enhanced light-matter interaction. We show that BIC modes enable the generation of enhanced and tunable optical forces and torques. A sharp and controllable lineshape is observed in forces and torques spectra when approaching high-Q resonance BIC modes. Wavelength and polarization t…
Upper bound to optical forces through the multipolar control of optical beams
Centro de Física de Materiales (CFM), CSIC-EHU（材料物理中心）；University of the Basque Country (EHU)（巴斯克大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；LORTEK, Basque Research and Technology Alliance (BRTA)（洛尔特克，巴斯克研究与技术联盟）
Recently the new concepts of transverse spin angular momentum and Belinfante spin momentum of evanescent waves have drawn considerable attention. Here, we investigate these novel physical properties of electromagnetic fields in the context of locally excited surface plasmon polaritons. We demonstrate, both analytically and numerically, that locally excited surface plasmon polaritons possess transverse spin angular momentum and Belinfante momentum with rich and non-trivial characteristics. We also show that the transverse spin angular momentum of locally excited surface plasmon polaritons leads…
The energy-based methods as the Dispersion Relation (DR) and Response Theory of Optical Forces (RTOF) have been largely applied to obtain the optical forces in the nano-optomechanical devices, in contrast to the Maxwell Stress Tensor (MST). In this work, we apply first principles to show explicitly why these methods must agree with the MST formalism in linear lossless systems. We apply the RTOF multi-port, to show that the optical force expression on these devices can be extended to analyze multiple light sources, broadband sources, and multimode devices, with multiple degrees of freedom. We a…
The behavior of Fano resonance and the reversal of near field optical binding force of dimers over different substrates have not been studied so far. In this work, we observe that if the closely located plasmonic cube homodimers over glass or high permittivity dielectric substrate are illuminated with plane wave polarized parallel to dimer axis, no reversal of optical binding force occurs. But if we apply the same set-up over a plasmonic substrate, stable Fano resonance occurs along with the reversal of near field binding force. It is observed that during such Fano resonance stronger coupling …
The recoil optical force that acts on emitters near a surface or waveguide relies on near-field directionality and conservation of momentum. It features desirable properties uncommon in optical forces, such as the ability to produce it via wide-area illumination of vast numbers of particles without the need for focusing, or being dynamically switchable via the polarization of light. Unfortunately, these recoil forces are usually very weak and have not been experimentally observed in small dipolar particles. Some works theoretically demonstrate orders-of-magnitude enhancement of these forces vi…
We discuss optical forces exerted on particles, either dielectric or metallic, near a subwavelength slit illuminated by a photonic nanojet. We compare those cases in which the Mie resonances are or are not excited. The configurations on study are 2D, hence those particles are infinite cylinders and, in order to obtain extraordinary transmission, the illuminating beam is p-polarized. We show the different effects of these particle resonances on the optical forces: while whispering gallery modes under those illumination conditions weaken the force strength, this latter is enhanced by localized p…
We report the first study on the optical force exerted by an evanescent wave on a small sphere with both electric and magnetic response to the incident field, immersed in an arbitrary nondissipative medium. New expressions and effects from their gradient, radiation pressure, and curl components are obtained due to the particle induced electric and magnetic dipoles, as well as to their mutual interaction. We predict possible dramatic changes in the force depending on either the host medium, the polarization and the nature of the surface wave.
From long time transverse and longitudinal optical forces are used for non-contact and noninvasive manipulation of small particle. The following question arises: What is the impact of these forces on the continuous media as air and silica. In this work we obtain analytical expressions for radiation force and radiation potential in dipole approximation of laser pulses propagating in dielectric media. The longitudinal force is proportional to the second time derivative of the intensity profile. At fixed initial energy of a laser pulse, as shorter is the pulse as bigger is the force. It is possib…
We present a position- and time-dependent optical force theory for optomechanics of dispersive 3D photonic materials and devices. The theory applies to media including material interfaces, waveguides, and general photonic crystal structures. The theory enables calculation of the dynamical state of the coupled field-material system and the interference of this state with other excitations of the material, such as surface acoustic waves or phonons. As an example, we present computer simulations of energy and momentum flows through a silicon crystal with anti-reflective structured interfaces. Usi…
Controlling the near field optical binding force can be a key factor for particle clustering, aggregation and localized surface plasmon sensors. So far there is no generic way to reverse the near field optical binding force for plasmonic or dielectric nano-dimers of distinct shapes (cube, cylinder, ring, sphere). In this article, for both plasmonic and dielectric objects, we have demonstrated a general way to control the reversal of near field binding force for different shaped dimer sets. The force reversal is achieved by simple breaking of symmetry, considering the nano particles are half or…
In this work we address, first, the optical force on a magnetodielectric particle on a flat dielectric surface due to an evanescent Bessel beam and, second, the effects on the force of multiple scattering with the substrate. For the first question we find analytical solutions showing that due to the interference of the excited electric and magnetic particle dipoles, the vertical force unusually pushes the object out from the plane. The incident wavelength rules whether the illumination constitutes, or not, an optical trap. As for the second problem, we make a 2D study with a single evanescent …
