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Understanding how the structured incident light interacts with the inherent properties of the manipulated particle and governs the optical force/torque exerted is a cornerstone in the design of optical manipulation techniques, apart from its theoretical significance. Based on the Cartesian multipole expansion theory, we establish a framework for optical force/torque exerted on an arbitrary sized bi-isotropic (chiral) spherical particle immersed in generic monochromatic optical fields. Rigorous expressions are thus derived which explicitly bridges such mechanical effects of light with particle-property-dependent coefficients and "force/torque source" quantities that characterize the incident light structures. Such quantities, totalled only 12, are quadratic in terms of electric and magnetic field vectors, among which are linear and angular momenta, gradient of energy density, spin density, and helicity. They are further organized into four categories based on their parity (P) and duality (D) symmetries and shown to couple with a particle with different P and D symmetries to induce optical force/torque. This classification specifies the symmetry-breaking criteria required to induce optical force/torque, offering a promising roadmap for engineering the optical manipulation.

Owing to the ubiquity and easy-to-shape property of optical intensity, the intensity gradient force of light has been most spectacularly exploited in optical manipulation of small particles. Manifesting the intensity gradient as an optical torque to spin particles is of great fascination on both fundamental and practical sides but remains elusive. Here, we uncover the existence of the optical intensity-gradient torque in the interaction of light with chiral particles. Such a new type of torque derives from the interplay between chirality induced multipoles, which switches its direction for particles with opposite chirality. We show that this torque can be directly detected by a simple standing wave field, created with the interference of two counterpropagating plane-like waves. Our work offers a unique route to achieve rotational control of matter by tailoring the field intensity of Maxwell waves. It also establishes a framework that maps a remarkable connection among the optical forces and torques, across chiral to nonchiral.

The exploration of the rich dynamics of electrons is a frontier in fundamental nano-physics. The dynamical behavior of electrons is dominated by random and chaotic thermal motion with ultrafast ($\approx$ ps) and nanoscale scatterings. This generates fluctuating electromagnetic fields in close vicinity of the moving electrons. W studied this fluctuation in small structures and found that its spatial distribution is not uniform, the magnitude of the fluctuation depends on external parameters such as the size ( ~1 $\mu m$) and the shape of the structure and changes can occur by an order of magnitude. Our work opens the possibility of improving the signal to noise ratio in small devices and in manipulating microscopic electron kinematics through nano-optical techniques and to applications in thermal detectors and photothermal photovoltaics.

We study the response of a conical metallic surface to an external electromagnetic (EM) field by representing the fields in basis functions containing integrable singularities at the tip of the cone. A fast analytical solution is obtained by the conformal mapping between the cone and a round disk. We apply our calculation to the scattering- based scanning near-field optical microscope (s-SNOM) and successfully quantify the elastic light scattering from a vibrating metallic tip over a uniform sample. We find that the field-induced charge distribution consists of localized terms at the tip and the base and an extended bulk term along the body of the cone far away from the tip. In recent s-SNOM experiments at the visible-IR range (600nm - 1$\mu m$) the fundamental is found to be much larger than the higher harmonics whereas at THz range ($100 \mu m-3mm$) the fundamental becomes comparable to the higher harmonics. We find that the localized tip charge dominates the contribution to the higher harmonics and becomes bigger for the THz experiments, thus providing an intuitive understanding of the origin of the near-field signals. We demonstrate the application of our method by extracting a two-dimensional effective dielectric constant map from the s-SNOM image of a finite metallic disk, where the variation comes from the charge density induced by the EM field.

It was theoretically proposed and experimentally demonstrated that anti-reflection coating allows one to trap a high dielectric sphere, at the same time enhancing the transverse optical force. Here, by explicitly calculating the gradient force and the scattering force, we rigorously show that these were mainly consequences of the reduction in scattering force due to the suppression of backward scattering, and enhancement in gradient force due to the increased in overall particle size. The reduction of scattering force can be understood within a ray optics theory and also the Mie theory. The coating approach only works for a spherical particle trapped by an aplanatic beam, and it does not work in general., Comment: 10 pages, 5 figures

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 light on the understanding of the optical force and pave a new way to engineer optical force for various purposes such as equilibrium statistical mechanics as well as optical micromanipulation.

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 establish universal relationships between optical force/torque on a general particle and different parts of linear and angular momentum (AM) of generic monochromatic optical field. It is rigorously proved that the optical force comes about by the transfer of orbital (canonical) optical momentum from light to matter, while the other part of optical momentum, known as spin momentum, does not generate optical force on matter but, instead, stays conserved even when the translational invariance is broken by putting particles into the optical fields. On the other hand, based on a generic multipole theory of optical torque, we demonstrate that the optical torque stems from the transfer of the total optical AM, including both orbital and spin AM, clarifying in generic case the long-standing confusion about whether the orbital AM can induce a spinning torque on a general particle in generic optical fields., Comment: 24 pages

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 electric and magnetic multipole fields based on symmetry. The confusion is resolved by conceptually introducing the irreducible electric dipole, toroidal dipole, and renormalized electric dipole. We demonstrate that the optical force is a powerful tool to identify toroidal response even when its scattering intensity is dwarfed by the conventional electric and magnetic multipoles., Comment: 25 pages, 7 figures

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 tools, we create a fairly general class of 2D conservative optical force field. In general, particles immersed in an optical force do not obey equilibrium statistical mechanics, making the analysis complicated. With conservative forces, these issues are resolved., Comment: 16 pages, 4 figures

Maxwell noted that light carries angular momentum, and as such it can exert torques on material objects. This was subsequently proved by Beth in 1936. Applications of these opto-mechanical effects were limited initially due to their smallness in magnitude, but later enabled by the invention of laser. Novel and practical approaches for harvesting light for particle rotation have been demonstrated, where the structure is subjected to a positive optical torque along a certain axis21 if the incident angular momentum has a positive projection on the same axis. We report here a counter-intuitive phenomenon of negative optical torque, meaning that incoming photons carrying angular momentum rotate an object in the opposite sense. Surprisingly this can be realized quite straightforwardly in simple planar structures. Field retardation is a necessary condition. The optimal conditions are explored and explained., Comment: 15 pages, 3 figures

A photon carries a momentum of, so one may anticipate light to "push" on any object standing in its path via the scattering force. In the absence of intensity gradient, using a light beam to pull a particle backwards is counter intuitive. Here, we show that it is possible to realize a backward scattering force which pulls a particle all the way towards the source without an equilibrium point. The underlining physics is the maximization of forward scattering via interference of the radiation multipoles. We show explicitly that the necessary condition to realize a negative (pulling) optical force is the simultaneous excitation of multipoles in the particle and if the projection of the total photon momentum along the propagation direction is small (as in some propagation invariant beams), attractive optical force is possible. This possibility adds "pulling" as an additional degree of freedom to optical micromanipulation., Comment: 11 pages, 4 figures

We study the properties of an artificial electromagnetic black hole for transverse magnetic modes rigorously. A multi-layered structure of such a black hole is then proposed as a reduced variety for easy experimental realizations. An actual design of composite materials based on the effective medium theory is given eventually with only five kinds of real isotropic materials. The finite element method confirms the functionality of such a simple design.

We propose a rigorous theory for the optical trapping by optical vortices, which is emerging as an important tool to trap mesoscopic particles. The common perception is that the trapping is solely due to the gradient force, and may be characterized by three real force constants. However, we show that the optical vortex trap can exhibit complex force constants, implying that the trapping must be stabilized by ambient damping. At different damping levels, particle shows remarkably different dynamics, such as stable trapping, periodic and aperiodic orbital motions.

When an oscillating line source is placed in front of a special mirror consisting of an array of flat uniformly spaced ferrite rods, half of the image disappeared at some frequency. We believe that this comes from the coupling to photonic states of the magnetic surface plasmon band. These states exhibit giant circulations that only go in one direction due to time reversal symmetry breaking. Possible applications of this "rectifying" reflection include a robust one-way waveguide, a 90 degree beam bender and a beam splitter, which are shown to work even in the deep subwavelength scale.

Transformation optics is used to design a gateway that can block electromagnetic waves but allows the passage of other entities. Our conceptual device has the advantage that it can be realized with simple materials and structural parameters and can have a reasonably wide bandwidth. In particular, we show that our system can be implemented by using a magnetic photonic crystal structure that employs a square ray of ferrite rods, and as the field response of ferrites can be tuned by external magnetic fields, we end up with an electromagnetic gateway that can be open or shut using external fields. The functionality is also robust against the positional disorder of the rods that made up the photonic crystal., Comment: 14 pages, 8 figures

We identify different types of the photonic band gaps (PBGs) of two dimensional magnetic photonic crystals (MPCs) consisting of arrays of magnetic cylinders and study the different tunability (by an external static magnetic field) of these PBGs. One type of the band gaps comes from infinitely degenerate flat bands and is closely related to those in the study of plasmonics. In addition, such PBGs are magnetically tunable and robust against position disorder. We calcualte the transmission of the PBG's and found excellent agreement with the results of the photonic band structure calculation. Positional disorder of the lattice structure affects the different types of PBGs differently., Comment: 4 pages, 5 figures

We consider the resonant optical force acting on a pair of transparent microspheres by the excitation of the Morphology Dependent Resonance (MDR). The bonding and anti-bonding modes of the MDR correspond to strong attractions and repulsions respectively. The dependence of the force on separation and the role of absorption are discussed. At resonance, the force can be enhanced by orders of magnitude so that it will dominate over other relevant forces. We find that a stable binding configuration can be induced by the resonant optical force., Comment: 4 pages, 4 figures

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation., Comment: 4 pages, 3 figures