Photo-induced charge density distribution in metal surfaces and its extraction with apertureless near-field optics.

Electromagnetic (EM) waves impinging on finite metallic structures can induce non-uniform electrical currents and create oscillating charge densities. These local charges govern the important physical processes such as plasmonic behavior or enhanced Raman scattering. Yet the quantitative calculation and probing of the spatial distribution of the charge density still remain challenging at the subwavelength scale. This is especially the case if one considers the boundary effect, where the charge density can become divergent and conventional finite element methods fail to obtain accurate information. With an approach we recently developed, we calculate this charge density for subwavelength structures with and without sharp corners: gold disks and equilateral triangles. We also devise an independent way to extract the surface charge density distributions from experiments using scattering-type scanning near-field optical microscope (s-SNOM). We found that the charge density [Formula: see text] is related to the near field signal S n by [Formula: see text] With no adjustable parameters, the extracted surface charge distribution from the experiments matches well with that from the theoretical prediction, both in magnitude and phase. Our work provides a quantitative study of the surface charge distributions and a systematic and rigorous treatment to extract surface charge distributions at the nanoscale, opening opportunities for mining the near-field data from s-SNOM.

Scattering of electromagnetic waves from surfaces with conformal mapping: An example of a triangular plate.

We discuss a way to exploit conformal mapping to study the response of a finite metallic film of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to understand different physics issues and provides insights that include the issue of vorticity and eddy current and the nature of the divergent electric field at the boundaries and at corners. We study an example of an equilateral triangular plate and find good agreement with results obtained with traditional numerical techniques.

Resonances and circuit theory for the interaction of metallic disks and annuli with an electromagnetic field.

To understand the nature of the electromagnetic resonances of finite metallic surfaces, we formulate a rigorous and rapidly convergent circuit theory for the interaction of a metallic disk and a metallic annulus with an electromagnetic field. Expressions for the current induced and the resonance condition are derived. A new understanding of the nature of the resonances is obtained. For half of the resonances we find a divergent electric field at the edge of the disk, even though it is smooth in shape. For the disk, we compare with previous results using vector spheroidal wave functions and found good agreement for the resonance condition. Our approach can be generalized to other finite surfaces.

Entangled transverse optical vortex.

We discuss a new kind of optical vortex with the angular momentum perpendicular to the flow direction and entangled in that it is a coherent combination of different orbital angular momentum states of the same sign. This entangled state exhibits many unexpected physical properties. The transverse optical vortex can be generated from the reflection of an electromagnetic wave off an array of ferrite rods. Its vorticity can be reversed by switching the direction of the magnetization of the rods, which usually takes only a nanosecond.

Multiple flat photonic bands with finite Chern numbers.

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.

Nearly total omnidirectional reflection by a single layer of nanorods.

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.

Optical beam steering based on the symmetry of resonant modes of nanoparticles.

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.

Reflected wave of finite circulation from magnetic photonic crystals.

We study the reflection of electromagnetic waves from a two-dimensional magnetic photonic crystal consisting of a periodic array of magnetic cylinders. At some frequencies the reflected wave is found to exhibit a strong circulation in that, locally, the angular momenta of the components are all of the same sign. As a result of this finite circulation, beams incident from different directions exhibit a dramatic change in their reflected waves. This effect can be used to build subwavelength one way waveguides, nearly perfect beam benders and splitters.

Effective-medium properties of metamaterials: a quasimode theory.

Under the generalized coherent-potential approximation, we established a "quasimode" theory to study the effective-medium properties of electromagnetic metamaterials. With this theory, we calculate the self-energy, density of states (DOS), and mean-free paths for optical modes traveling inside a metamaterial, and then determine the effective permittivity and permeability of the metamaterial by maximizing the DOS function. Compared with the traditional methods for calculating effective-medium parameters, the present approach could provide quantitative judgments on how meaningful are the obtained effective-medium parameters. As illustrations, we employed the theory to study the effective-medium properties of several examples including finite metallic wires and split ring resonators.

Longitudinal elliptically polarized electromagnetic waves in off-diagonal magnetoelectric split-ring composites.

We study the propagation of plane electromagnetic waves through different systems consisting of arrays of split rings of different orientations. Many extraordinary EM phenomena were discovered in such systems, contributed by the off-diagonal magnetoelectric susceptibilities. We find a mode such that the electric field becomes elliptically polarized with a component in the longitudinal direction (i.e. parallel to the wavevector). Even though the group velocity [Formula: see text] and the wavevector k are parallel, in the presence of damping, the Poynting vector does not just get 'broadened', but can possess a component perpendicular to the wavevector. The speed of light can be real even when the product 쵵 is negative. Other novel properties are explored.

Manipulating negative-refractive behavior with a magnetic field.

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.

Focusing the electromagnetic wave with a magnetic field.

We examine manipulating the electromagnetic (EM) wave with an external static magnetic field (ESMF) taking advantage of the versatility of the magnetic photonic crystal (PC). The effect of a nonuniform ESMF on the permeability of the constituent magnetic material in the PC is demonstrated to create a gradient of the effective optical index in the crystal, leading to the focusing of the EM wave, with a magnetically tunable focal length, focused waist radius, and the intensity at the focus.

Long-wavelength behavior of two-dimensional photonic crystals.

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.

Manipulating electromagnetic radiation with magnetic photonic crystals.

We examine manipulating electromagnetic waves in magnetic photonic crystals (MPCs) with external magnetic fields. We predict new giant magnetoreflectivity and giant magnetorefractivity effects: with an external magnetic field of a magnitude much smaller than the anisotropy field of the ferromagnet, the MPC can be changed from completely reflecting to nonreflecting with corresponding changes in the angle of refraction. Application to the storage of electromagnetic radiation is also discussed.

Probing states with macroscopic circulations in magnetic photonic crystals.

We predict that when light is reflected off a magnetic photonic crystal (MPC) there is a grazing component that is parallel to the surface; the magnitude of this component can be changed by an external field. The direction of this parallel component is reversed as the direction of the magnetization is reversed. This provides a way to probe states with macroscopic circulations inside the MPC.

Modulational instability criteria for coupled nonlinear transmission lines with dispersive elements.

We investigate the modulational instability of Stokes wave solutions on a system of coupled nonlinear electrical transmission lines with dispersive elements. In the continuum limit, and in suitable scaled coordinates, the voltage on the system is described by the two-dimensional coupled nonlinear Schrödinger equations. The set of coupled nonlinear Schrödinger equations obtained is analyzed via a perturbation approach. No assumption is made on the signs of the relevant coefficients such as the coefficients of nonlinearity and the coupling coefficients. A set of explicit criteria of modulational stability and modulational instability is derived and analyzed. It is numerically shown that the effect of the dispersive elements in the line is to decrease the instability region and the instability growth rate.

Multilayer structures as negative refractive and left-handed materials.

We examine multilayer structures as negative refractive index and left-handed materials, and find that for one polarization there is a wide range (≈90°) of incident angle within which negative refraction will occur. This comes about because the group velocity and the Poynting vector have a large component parallel to the layers, no matter what the angle of incidence of the incoming radiation is. This behaviour in turn comes from the large anisotropy of the phase velocities. If one of the components is a ferromagnetic metal, the system can be a left-handed material above the ferromagnetic resonance frequency.

Radiation torque on a birefringent sphere caused by an electromagnetic wave.

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.

Electromagnetic scattering by optically anisotropic magnetic particle.

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.

Electromagnetic scattering by spherical negative-refractive-index particles: Low-frequency resonance and localization parameters.

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.