On the angular-spectrum representation of multipole wave fields

The closed-form expression of the angular spectrum of multipole fields, both scalar and vectorial, of any order and degree, evaluated across a plane orthogonal to an arbitrary (fixed) direction, is provided. Such a result has been obtained by starting from the Weyl representation of multipole fields and using suitable transformation rules. Moreover, as far as the vectorial case is concerned, knowledge of the (vectorial) transverse angular spectrum allows one to gain some insight into the polarization structure of the multipole fields evaluated across a typical plane. Such information could be useful, for instance, in those problems dealing with the interaction between planar partially reflecting surfaces and waves.     

Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach

We consider the coherent reflection and transmission of electromagnetic waves from a slab of a dilute system of randomly located, polarizable, spherical particles. We focus our attention on the case where the size of the spheres is comparable to the wavelength of the incident radiation. First, using wave-scattering and Mie theories, we derive expressions for the coherent fields that are transmitted and reflected by a very thin slab. Then we find the effective-current distribution that would act as a source of these fields. We conclude that if the effective currents were induced in an effective medium, this medium must possess, besides an effective electric permittivity, also an effective magnetic permeability. We find that both of these optical coefficients become functions of the angle of incidence and the polarization of the incident wave. Then we calculate the reflection coefficient of a half-space by considering a semi-infinite pile of thin slabs and compare the result with Fresnel relations. Numerical results are presented for the optical coefficients as well as for the half-space reflectance as a function of several parameters. The reflectance is compared with that obtained without considering the magnetic response. Finally, we discuss the relevance and the physics behind our results and indicate as well the measurements that could be performed to obtain an experimental verification of our theory.     

Light scattering at the boundary between two media

Coefficients of diffuse reflection and transmission of light by smooth Fresnel boundaries of an optically thick layer illuminated by scattered radiation are calculated. Consideration is given to the absorption effect on angular diagrams of light at the boundaries. An analysis is made of asymptotic equations of radiation transfer in a medium with reflecting boundaries, and the range of their applicability is studied. Using methods of geometric optics, coefficients of reflection of directional and diffuse radiation from a rough surface are studied. The results can find use in various areas of science and technology, specifically, in optical diagnostics of biological tissues.     

Two-dimensional multipoles from arbitrary current densities in polygonal domains

A complex analytic multipole decomposition of the magnetic field produced by an arbitrary, continuous current density in a two-dimensional polygonal domain is obtained by series expanding the Green's function of complex magnetic field. The multipole coefficients are given explicitly as functions of the vertex coordinates of the polygon.     

Evanescent waves in the magnetic field of an electric dipole

The magnetic field of radiation emitted by an electric dipole contains travelling and evanescent waves when represented as an angular spectrum. The evanescent waves decay exponentially away from the xy-plane, and will therefore not contribute to the detectable radiation in the far field, in general. It is well known, however, that in a small region around the z-axis the evanescent waves of the electric field do end up in the far zone. We have studied the corresponding magnetic evanescent waves, and we have found that the evanescent waves of the magnetic field do not contribute to the far zone in the neighbourhood of the z-axis. When considering the neighbourhood of the xy-plane, it appears that both the electric and magnetic evanescent waves end up in the far field, and the travelling and evanescent waves contribute equally to the radiation in the far zone. Close to the dipole the radiation field diverges, and we have shown that this is entirely due to the evanescent waves.     

Coupled Dielectric Nanoparticles Manipulating Metamaterials Optical Characteristics

In this paper, we investigate the concept and theory of all-dielectric metapatterned structures that manipulate electric and magnetic optical characteristics. A 3-D array of dielectric particles is designed, where the spheres operate in their magnetic modes and their couplings offer electric modes. An analytical solution for the problem of plane wave scattering by 3-D array of dielectric nanospheres is presented. FW multipole expansion method is applied to express the optical fields in terms of the electric and magnetic dipole modes and the higher order moments. By enforcing the boundary conditions at the surface of each sphere, with the use of the translational addition theorem for vector spherical wave functions, required equations to determine the scattering coefficients are obtained. Novel materials features in optics are demonstrated. Electric and magnetic scattering coefficient resonances around the same frequency band are obtained. It is highlighted how a metapatterned structure constructed from dielectric nanosphere unit cells can provide electric and magnetic modes resulting in backward wave phenomenon. A comprehensive circuit model based on the RLC (resistor, inductor, and capacitor) realization is presented to successfully analyze the scattering performance of a dielectric nanosphere. To better understand the physics of an array of spheres, circuit models for the interactions, and couplings between spheres are also accomplished. The engineered dispersion diagram for a 3-D array of identical highly coupled nanospheres is scrutinized, verifying that the high couplings between spheres can offer the backward wave characteristics.     

Partial-wave expansions of angular spectra of plane waves

Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alternate angular spectrum constructed so as to be free of evanescent components contains all partial waves but describes a propagating beam with a small amount of standing-wave component mixed in. A procedure is described for minimizing the standing-wave component so as to more accurately model a purely forward propagating experimental beam.     

Polarization of almost-plane waves

The general polarization behavior of almost-plane waves, in which the electric field varies slowly over a circular pupil, is considered, on the basis of an axial Hertz potential treatment and expansion in Zernike polynomials. The resultant modes of a circular aperture are compared with the well-known waveguide (or optical fiber) modes and Gaussian beam modes. The wave can be decomposed into partial waves of electric and magnetic types. The modes for a square pupil are also considered. The particular application of the effect on polarization of focusing the waves is discussed. Another application discussed is the Fresnel reflection from a dielectric interface, it being shown that the Fresnel reflection alters the relative strength of the electric and magnetic components.     

Asymptotic solutions for optical properties of large particles with strong absorption

The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the TM or the TE wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3 x 2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.     

Computation considerations and fast algorithms for calculating the diffraction integral

Abstract

One of the most basic optical ‘components’ is free-space propagation. A common approximation used when calculating the resultant field distribution after propagation is the Fresnel integral. This integral can be evaluated in two ways: directly or by using the angular spectrum. In this paper, we estimate the regions in which each mode of evaluation is preferable according to computing efficiency and accuracy considerations. A fast numerical algorithm is introduced for each region. The result is relevant also for the evaluation of the Rayleigh-Sommerfeld diffraction formula.     

波数空间中活塞辐射体近场声压分布的计算及测试

在近场范围内,声源在任何平面上的声场都可以通过平面传播波和倏逝波的叠加来得到。以圆形活塞为例,在波数空间中利用角谱法求得其辐射声场的传播波和倏逝波的分布。借助数值分析方法,对圆形活塞声源声轴线上的声压进行计算,得到相应的近场声压分布曲线。由角谱法计算得到的近远场分界点与点源组合法所得结果一致。对不同声源半径时,不同辐射频率下的声压分布曲线进行比较,得出了近场声压的变化规律。阶梯圆盘在辐射理论上应等于对应圆形活塞的辐射。对设计的阶梯圆盘的轴向声压进行了测试,实验测试结果与理论计算结果基本吻合。     

Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwell's electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwell's equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.     

The Effect of a Longitudinal Magnetic Field on the Radiation of Glow Discharge in Helium

The effect of a longitudinal magnetic field on the radiation of a glow discharge in helium is investigated experimentally. It is demonstrated that, with pressures in the discharge chamber below approximately 140 Pa, the intensity of radiation of spectral lines of helium and of continuous spectrum increases by a factor of 200–300 under the effect of a magnetic field. So strong an increase in the radiation of glow discharge in helium is observed in the region where no electric field of discharge is present. An attempt is made at attributing the obtained result to the decrease in the ambipolar diffusion of electrons to the wall; this brings about an increase in the density and temperature of electrons which start exciting metastable states of helium.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 4, 2005, pp. 516–525.Original Russian Text Copyright © 2005 by I. M. Ulanov and A. Yu. Litvintsev.     

Integral equation formulation for reflection by a mirror

When light is incident on a mirror, it induces a current density on its surface. This surface current density emits radiation, which is the observed reflected field. We consider a monochromatic incident field with an arbitrary spatial dependence, and we derive an integral equation for the Fourier-transformed surface current density. This equation contains the incident electric field at the surface as an inhomogeneous term. The incident field, emitted by a source current density in front of the mirror, is then represented by an angular spectrum, and this leads to a solution of the integral equation. From this result we derive a relation between the surface current density and the current density of the source. It is shown with examples that this approach provides a simple method for obtaining the surface current density. It is also shown that with the solution of the integral equation, an image source can be constructed for any current source, and as illustration we construct the images of electric and magnetic dipoles and the mirror image of an electric quadrupole. By applying the general solution for the surface current density, we derive an expression for the reflected field as an integral over the source current distribution, and this may serve as an alternative to the method of images.     

Scattering of a transversely confined Neumann beam by a spherical particle

Various properties of an electromagnetic wave whose spherical multipole expansion contains only Riccati-Neumann functions are examined. In particular, the novel behavior of the beam phase during diffractive spreading is discussed. When a Neumann beam is scattered by a spherical particle, the diffraction and external reflection portions of the scattering amplitude constructively interfere for large partial waves. As a result, a set of rapidly decreasing beam shape coefficients is required to cut off the partial wave sum in the scattering amplitudes. Because of its strong singularity at the origin, a Neumann beam can be produced by a point source of radiation at the center of a spherical cavity in a high conductivity metal, and Neumann beam scattering by a spherical particle can occur for certain partial waves if the sphere is placed at the center of the cavity as well.     

Giant enhancement of dipole-forbidden transitions via lattices of plasmonic nanoparticles

We demonstrate theoretically that electric dipole-forbidden atomic transitions can be excited by the interaction of the quadrupole moment of the transition with the electric near-field in the vicinity of an illuminated periodic array of core–shell metallic nanoparticles via surface-plasmon excitation. The rate of the quadrupole transition is enhanced by nine orders of magnitude relative to the illumination of the atom by a plane wave rendering the transition experimentally observable. At the same time, the enhancement of the quadrupole transition rate means an enhancement of the quadrupole force at the same level, enabling the subwavelength trapping of the atom at the optical near-field landscape. The calculations are based on rigorous electrodynamic calculations based on the layer-multiple-scattering theory for periodic nanostructures of spherical scatterers. The quadrupole transition is studied by means of electromagnetic multipole angular momentum theory which provides a closed formula for the corresponding atomic transition rate.     

Hydrodynamic coefficients for water-wave diffraction by spherical structures

Evaluation of hydrodynamic coefficients and loads on submerged or floating bodies is of great significance in designing these structures. Some special regular-shaped geometries such as those of cylindrical (circular, elliptic) and spherical (hemisphere, sphere, spheroid) structures are usually considered to obtain analytical solutions to wave diffraction and radiation problems. The work presented here is the result of water-wave interaction with submerged spheres. Analytical expressions for various hydrodynamic coefficients and loads due to the diffraction of water waves by a submerged sphere are obtained. The exciting force components due to surge and heave motions are derived by solving the diffraction problem. Theory of multipole expansions is used to express the velocity potentials in terms of an infinite series of associated Legendre polynomials with unknown coefficients and the orthogonality of the polynomials is utilized to simplify the expressions. Since the infinite series appearing in various expressions have excellent truncation properties, they are evaluated by considering only a finite number of terms. Gaussian quadrature is used to evaluate the integrals. Numerical estimates for the analytical expressions for the hydrodynamic coefficients and loads are presented for various depth to radius ratios. Consideration of more values for depth makes it easy to compare the results with those available. The results obtained match closely with those obtained earlier by Wang and Wu and their coworkers     

Neutron angular distribution in a plasma focus obtained using nuclear track detectors

The dense plasma focus (DPF) is a coaxial plasma gun in which a high-density, high-temperature plasma is obtained in a focused column for a few nanoseconds. When the filling gas is deuterium, neutrons can be obtained from fusion reactions. These are partially due to a beam of deuterons which are accelerated against the background hot plasma by large electric fields originating from plasma instabilities. Due to a beam-target effect, the angular distribution of the neutron emission is anisotropic, peaked in the forward direction along the axis of the gun. The purpose of this work is to illustrate the use of CR-39 nuclear track detectors as a diagnostic tool in the determination of the time-integrated neutron angular distribution. For the case studied in this work, neutron emission is found to have a 70% contribution from isotropic radiation and a 30% contribution from anisotropic radiation.     

Electromagnetic synergetic actuators based on polypyrrole/Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> hybrid nanotube arrays

Conducting polymer actuators that can undergo complex and coordinated motions are generally obtained by using complex microfabrication methods to pattern several conducting polymer components. Herein, we describe a facile approach for fabricating electromagnetic synergetic actuators based on polypyrrole/Fe₃O₄ hybrid nanotube arrays. The actuator can perform biomimetic movements like arm-hand coordination. In this case, a magnetic field is used for primary actuation like an arm, i.e., large-scale angular movement, and an electric potential is used for secondary adjustment like a hand, i.e., small-scale angular movement.     

Coupled-wave Analysis of the Bragg Effect Waveguide Coupler

Abstract

A coupled-wave analysis is presented for the Bragg effect waveguide coupler. This device consists of a slanted volume phase grating which is integrated inside the lightguiding layer of an optical waveguide. The wave propagation is described by a set of leaky wave modes. Self-consistency relations are derived to determine the angular mode spectrum and the corresponding radiation loss coefficients. A maximum input coupling efficiency of 80% is predicted for an incident Gaussian beam. The power of a waveguide mode should be emitted into a single output beam reaching an efficiency of almost 100%.