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Lateral optical forces in a direction perpendicular to light propagation have attracted increasing interest in recent years. Up to now, all lateral forces can be attributed to the symmetry breaking in the lateral directions caused by either the morphology of the scatterer geometry or the optical fields impinging on the scatterer. Here we demonstrate, both numerically and analytically, that when an isotropic scatterer breaks the electric-magnetic symmetry, a new type of anomalous lateral force can be induced along the direction of translational invariance where the illumination striking the scatterer has no propagation, field gradient, or spin density vortex (Belinfante's spin momentum). Our analytical results are rigorous for an arbitrary size scatterer, ensuring the universality of our conclusion. Furthermore, the electric-magnetic symmetry-breaking-induced lateral force is comparable in magnitude to other components of the optical force and reversible in direction for different polarizations of the illuminating light, rendering it capable of practical optical manipulation as well as enriching the understanding of light-matter interaction.

We show both analytically and numerically that there is an infinite number of flat bands with different Chern numbers in a two-dimensional magnetic photonic crystal at nearly the same frequency determined by the condition that the effective magnetic permeability μ_{eff}≈-1. This opens the door to explore the physics involving higher order topological invariants in this system. The frequency of these states can be flexibly tuned by an external magnetic field.

It is shown that a single-layer array of high electric permittivity (high-ε) rods with a radius smaller than λ/10 is capable of reflecting more than 97% of the energy of optical waves with an arbitrary incident angle. Here, λ is the incident wavelength. The occurrence of the phenomenon depends on the construction of two particular grating modes (GMs) in the array which result in two corresponding transmitted wave components that cancel each other. The construction of the dominant GMs in the array benefits from the highly independent manipulability of the angular momenta components with opposite signs in high-ε particles. The effect offers the possibility to improve the optical elements integration level in on-chip optical circuits.

We report a phenomenon that an optical beam transmits in a negative direction when passing through a single array of high-refractive-index dielectric nanorods. The mechanism of the negative directional transmission is believed to be due to the symmetry of resonant modes in the dielectric nanoparticles. It is expected to find applications in designing compact optical components to achieve the on-chip beam steering in photonic circuits.

We present an experimental demonstration of self-guiding electromagnetic edge states existing along the zigzag edge of a honeycomb magnetic photonic crystal. These edge states are shown to possess unidirectional propagation characteristics that are robust against various types of defects and obstacles. In particular, they allow for the unidirectional transport of electromagnetic energy without requiring an ancillary cladding layer.

We propose a theory to explain optical trapping by optical vortices (OVs), which are emerging as important tools to trap mesoscopic particles. The common perception is that the trapping is solely due to the gradient force and that it may be characterized by three real force constants. However, we show that the OV trap can exhibit complex force constants, implying that the trapping must be stabilized by ambient damping. At different damping levels, particles exhibit remarkably different dynamics, such as stable trapping and periodic and aperiodic orbital motions.

We investigate the optical trapping of a Rayleigh particle by a linearly or radially polarized Gaussian beam. The Mie theory is applied to obtain a full solution, with the incident beam being described by the mixed dipole model, which is beyond the paraxial approximation. We then obtain approximate analytical expressions for the optical force, equilibrium position, and trap stiffness for a Rayleigh particle. At equilibrium, the displacement for the particle from the focus scales like a(3) (where a is the radius) for a transparent particle, owing to scattering, whereas for absorptive particles it scales like C+Da(2), owing to absorption. The trap stiffness is found to be proportional to a(3), in agreement with the recent experiment. The radially polarized beam is found to be superior to the linearly polarized beam in the Rayleigh regime in terms of its ability to trap. It is found that the larger the ratio of epsilon(r)/epsilon(i), the closer the equilibrium to the focus, and thus higher stability.

We solve analytically the multiple-scattering equations for two-dimensional photonic crystals in the long-wavelength limit. Different approximations of the electric and magnetic susceptibilities are presented from a unified pseudopotential point of view. The nature of the so-called plasmon-polariton bands is clarified. Its frequency as a function of the wire radius is discussed. The corresponding tunable "magnetic surface plasmon" band is pointed out.

We demonstrated a construction of negative-index material (NIM) with epsilon(eff)=mu(eff)=-1 employing ferrites only, with no metallic components. Our design of the NIM is motivated by recent coherent potential approximation results and corroborated by exact numerical calculation demonstrating the negative refraction of an electromagnetic beam, with equal incident and refraction angles, as well as by the slab imaging phenomena, with the source-image separation twice as the slab thickness. The ferrite only based scheme furnishes the fabricated NIM with magnetically tunable working frequency, less loss and the air-matched wave impedance.

In this paper, the scattering matrix of sphere with dielectric biaxial anisotropy is obtained exactly within the framework of the extended Mie theory. By incorporating the scattering matrix into the multiple scattering method, we study theoretically the photonic band structure of three dimensional photonic crystals consisting of biaxial dielectric spheres. Our results demonstrate that complete photonic bandgaps can be found in both fcc and sc lattice structures, which are absent in photonic crystals composed of isotropic dielectric spheres. Moreover we have compared our results with those coming from the photonic crystals consisting of the uniaxially birefringent dielectric spheres. It is found that because of the enhancement of the anisotropy, the degeneracy is lifted further, resulting in two neighboring photonic bandgaps, the lower one is complete while the upper one is partial existing only in some special regions of the first Brillouin zone.

We present an exact ab initio calculation of the optical torque on a spherical uniaxially birefringent particle of arbitrary size illuminated by plane electromagnetic wave of arbitrary polarization mode and direction of propagation. The calculation is based on the extended Mie theory and the Maxwell stress tensor formalism. The expression for evaluating radiation torque is derived for arbitrary (absorbing and lossless) isotropic surrounding medium. The dependence of the optical torque on the incident angle, the polarization mode, the material birefringence, as well as the particle size, has been systematically investigated. For normal illumination, namely, with the incident wave vector perpendicular to the extraordinary axis (EA) of the particle, the optical torque caused by a linearly polarized (LP) incident wave always shows the angle dependence . Here, is the angle between the EA and the incident electric field, whereas may take positive or negative values, dependent on , and the particle size. In the small particle limit, versus particle radius displays different power law behaviors, and , for LP and circularly polarized (CP) incident waves, respectively, while for small material birefringence , linear and square laws, and , are found for the LP and the CP incident modes, respectively.

The Mie theory for electromagnetic scattering by spherical particle is extended to the case of magnetic particle with gyromagnetic type of permeability. Specifically, we first construct for the magnetic induction B(I) inside the particle a new set of vector basis functions, which are the solution of the wave equation for B(I) and expanded in terms of the usual vector spherical wave functions (VSWF's) with different values of wave vector k(l). The relationship between k(l) and the frequency is obtained as the eigenvalues of an eigensystem determined by the permeability tensor. The incident and scattered fields are expanded as usual in terms of the VSWF's. By matching the boundary conditions, a linear set of coupled equations for the expansion coefficients are obtained and then solved for the solution to the scattering problem. Preliminary numerical results are presented for the case in which the scattering is due solely to the optical anisotropy within the particle. The scattering efficiency is found to exhibit miscellaneous dependence on the incident angle, the polarization, the degree of anisotropy, as well as the size parameter. In addition, the possibility of the photonic Hall effect for one Mie scatterer is confirmed.

The technique of lattice Boltzmann simulation has been applied to the study of two-dimensional particle suspensions through a modeled arterial stenosis. The stenosis model consists of two-side symmetric semicirculars in a planar channel with the width of the stenosis throat larger than d and less than 2d, where d is the diameter of the particles. When only one particle is positioned off-centerline initially, the particle migrates off-centerline after passing the stenosis and the velocity at the stenosis throat is much larger than that in a flat tube. Only when two particles are positioned symmetrically to the centerline to a very high accuracy can the flow be blocked by two particles completely. A very small asymmetry will be amplified proximal to the stenosis throat in that one of the particles goes back to leave space to let the other particle passing the stenosis first so that the particles cannot be blocked. An evidence of attractive interactions between the particles as well as a particle and a proximal protuberance is observed when the asymmetry is very small and the width at the stenosis throat is between two critical values. The hematocrit distribution of the particles is studied by simulating multiparticle suspensions. It is found that the width of the stenosis throat has a significant influence on the hematocrit distribution of the particles in the flat tubes far from the stenosis.

The Mie scattering of electromagnetic waves of wave vector k by spherical negative-refractive-index particles of radius a exhibits an unusual resonance at ka-->0. The scattering enhancement from the ka-->0 resonance is insensitive to the size of scatterers, distinct from the Mie scattering resonances from positive-refractive-index particles. For media consisting of a collection of the negative-refractive-index particles, the unusual resonance results in a significant reduction of the localization parameter, providing a possibility to reach the light localization transition by reducing the wave vector k, in analogy to electronic systems.

The lattice Boltzmann method is used to study the sedimentaion of a single charged circular cylinder in a two-dimensional channel in a Newtonian fluid. When the dielectric constant of the liquid is smaller than that of the walls, there are attractive forces between the particle and the walls. The hydrodynamic force pushes the particle towards the centerline at low Reynolds numbers. Due to the competition between the Coulomb force and the hydrodynamic force in opposite directions, there is a critical linear charge density q(c) at which the particle will fall vertically off centerline, which is a metastable state in addition to the stable state on centerline, for any initial position of the particle sufficiently far from the proximal wall. It is found that the rotation of the particle plays an important role in the stability of such metastable states. The particle hits on the wall or falls on the centerline when the linear charge density on the particle is greater or less than q(c). The simulation method and the new phenomena are also helpful in the study of charged multiparticle suspensions.

An efficient technique for computing photonic band structure and defect modes is proposed based on the lattice Boltzmann model. Physically, it is a scheme based on the kinetics of the virtual microscopic process, rather than a solution of the macroscopic Maxwell equations. The method has significant advantages of being naturally suited for massively parallel machine, as well as speed and convenience, providing another methodology for photonic band gap materials and, also, for general electromagnetic scattering problems in open region when incorporated with the perfectly matched layer technique.

A lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries. The mass conservation for the boundary condition is tested in detail. The viscous flow in elastic vessels is simulated with a pressure-radius relationship similar to that of the pulmonary blood vessels. The numerical results for steady flow agree with the analytical prediction to very high accuracy, and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally. The model is expected to find many applications for studying blood flows in large distensible arteries, especially in those suffering from atherosclerosis, stenosis, aneurysm, etc.