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Brain aggregates of β amyloid (βA) protein plaques have been widely recognized as associated with many neurodegenerative diseases, and their identification can assist in the early diagnosis of Alzheimer's disease. We investigate the feasibility of using a spectral x-ray coherent scatter system with a silicon strip photon-counting detector for identifying brain βA protein plaques. This approach is based on differences in the structure of amyloid, white and grey matter in the brain. We simulated an energy- and angular-dispersive X-ray diffraction system with an x-ray pencil beam and Silicon strip sensor, energy-resolving detectors. The polychromatic beam is geometrically focused toward a region of interest in the brain. First, the open-source MC-GPU code for Monte Carlo transport was modified to accommodate the detector model. Second, brain phantoms with and without βA were simulated to assess the method and determine the radiation dose required to obtain acceptable statistical power. For βA targets of 3, 4 and 5 mm sizes in a 15-cm brain model, the required incident exposure was about 0.44 mR from a 60 kVp tungsten spectrum and 3.5 mm of added aluminum filtration. The results suggest that the proposed x-ray coherent scatter technique enables the use of high energy x-ray spectra and therefore has the potential to be used for accurate in vivo detection and quantification of βA in the brain within acceptable radiation dose levels.

A rigorous, simple and efficient approach is derived in this paper for multipole expansion of a circularly symmetric Bessel beam. Different from the existing rigorous methods which are based on the plane wave spectrum of a Bessel beam, a straight-forward integral procedure is presented in a traditional way to obtain the analytical expressions of the expansion coefficients, also called beam shape coefficients (BSCs). The convergence and correctness of the BSCs are verified numerically in detail for both on-axis and off-axis cases. The results in this paper are useful in various analytical scattering theories, such as the generalized Lorenz-Mie theory and the Null-field method, when a Bessel beam is considered.

A new approach to the scattering problem of waves by junctions is developed with the aid of the modified theory of physical optics (MTPO). The relation between the fundamental MTPO integral and the Fresnel function is given as a theorem with its proof. Then the integrals relation with the geometrical optics (GO) and diffracted waves is put forth with a theorem on the uniform asymptotic evaluation of scattering integrals. A new definition is introduced for the scattering process and it is shown that the solutions of some problems, related with material half-planes and junctions can be obtained easily by only evaluating the GO fields according to the new definition of the scattering phenomenon. The scattered and diffracted fields can be derived directly in terms of the MTPO integrals as a result of the relation between the GO and scattered waves. The resultant diffracted field expressions are investigated numerically.

Despite the recent extensive study of the nonradiating (anapole) mode in the resonant light scattering by nanoparticles, the key questions, about the dynamics of its excitation at the leading front of the incident pulse and collapse behind the trailing edge, still remain open. We answer the questions, first, by direct numerical integration of the complete set of the Maxwell equations, describing the scattering of a rectangular laser pulse by a dielectric cylinder. The simulation shows that while the excitation and the collapse periods, both have the same characteristic time-scale, the dynamics of these processes are qualitatively different. The relaxation to the steady-state scattering at the leading front is accompanied by high-amplitude oscillatory modulations of the envelope of the basic electromagnetic oscillations, while behind the trailing edge the decay of the envelope is monotonic. Then, we present the general arguments showing that this is the case for the anapole excited in any classical system. Next, we introduce a simple, exactly integrable yet accurate, physically transparent model describing the dynamics of the anapole. The model admits generalization to a broad class of resonant phenomena and may be regarded as a compliment to the commonly used Temporal Coupled-Mode Theory.

We provide a simple semi-classical formalism to describe the coupling between one or several quantum emitters and a structured environment. Describing the emitter by an electric polarizability, and the surrounding medium by a Green function, we show that an intuitive scattering picture allows one to derive a coupling equation from which the eigenfrequencies of the coupled system can be extracted. The model covers a variety of regimes observed in light-matter interaction, including weak and strong coupling, coherent collective interactions, and incoherent energy transfer. It provides a unified description of many processes, showing that different interaction regimes are actually rooted on the same ground. It can also serve as a basis for the development of more refined models in a full quantum electrodynamics framework.

A numerical analysis of wave scattering by a body of revolution composed of a homogeneous dielectric sphere and an external inhomogeneous dielectric layer with arbitrary generatrix is carried out. A modification of the hybrid projection method developed in the paper includes expansion of the fields in terms of transverse vector spherical functions, projection of the Maxwell’s equations in the inhomogeneous region on the indicated functions, and use of the one-dimensional method of finite elements in projection form over the radial coordinate. Two more modifications correspond to the case of a perfectly conducting internal sphere and for the case of the absence of the internal sphere. The indicated modifications are realized in MATLAB codes for the case of excitation of the body by a circularly polarized plane wave propagating along the axis of revolution. Numerical results presented and discussed in the paper include the cases of wave scattering by a homogeneous sphere displaced from the origin of coordinates, a perfectly conducting sphere placed inside an inhomogeneous spheroidal layer, and a half-spherical Maxwell’s fish-eye lens.

We perform numerical analysis to study the orbits described by subwavelength-size particles interacting with complex structured light beams. Our solution to the particle dynamics considers: (i) the gradient force, (ii) the transverse radiation pressure, and (iii) polarisation-dependent curl force. The last two terms, (ii) and (iii), constitute the scattering forces. Multiples examples are provided to show the polarisation effects in the trajectories. For the single optical vortex case, the particle is always expelled due to the polarisation-dependent terms. Optical forces due to vector beams, such as cylindrical vector beams and full-Poincare beams have been analysed finding closed and open orbits, respectively. Trapping control has been achieved by varying the separation distance in the off-axis superposition of optical vortices.

In this paper, an introduction to electromagnetic scattering is presented. We introduce the basic concepts needed to face a scattering problem, including the scattering, absorption, and extinction cross sections. We define the vector harmonics and we present some of their properties. Finally, we tackle the two canonical problems of the scattering by an infinitely long circular cylinder, and by a sphere, showing that the introduction of the vector wave function makes the imposition and solution of the boundary conditions particularly simple.

We propose an extensive discussion on the homogenization and scattering analysis of the second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) that are used to model the electromagnetic responses of nonlinear metasurfaces. The GSTCs are solved both in the frequency domain, assuming an undepleted pump regime, and in the time domain, assuming dispersionless material properties but a possible depleted pump regime. Based on these two modeling approaches, we derive the general second-harmonic reflectionless and transmissionless conditions as well as the conditions of asymmetric reflection and transmission. We also discuss and clarify the concept of nonreciprocal scattering pertaining to nonlinear metasurfaces.

In an effective medium description of acoustic metamaterials, the Willis coupling plays the same role as the bianisotropy in electromagnetism. Willis media can be described by a constitutive matrix composed of the classical effective bulk modulus and density and additional cross-coupling terms defining the acoustic bianisotropy. Based on a unifying theoretical model, we unite the properties of acoustic Willis coupling with PT-symmetric systems under the same umbrella and show in either case that an exceptional point hosts a remarkably pronounced scattering asymmetry that is accompanied by one-way zero reflection for sound waves. The analytical treatment is backed up by experimental input in asymmetrically side-loaded waveguides showing how gauge transformations and loss biasing can embrace both Willis materials and non-Hermitian physics to tailor unidirectional reflectionless acoustics, which is appealing for purposeful sound insulation and steering. J.C. acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramon y Cajal grant (Grant No. RYC-2015-17156). J.-P.G. and V.R.G. gratefully acknowledge the support from the ANR Project METAUDIBLE No. ANR-13-BS09-0003 cofounded by ANR and FRAE and the support from the RFI Le Mans Acoustique (Region Pays de la Loire) PavNat project. This article is based upon work from COST Action DENORMS CA15125, supported by COST (European Cooperation in Science and Technology). J.L. would like to acknowledge support from Research Grants Council of Hong Kong (Project No. 16302218).

The propagation of light in foams creates patterns which are explained by the Geometrical Theory of Diffraction, and some of these patterns are known as Parhelic-like circle or Parlaseric circle. We also present the analogy between the atmospheric phenomena known as Parhelic circle, Sun dogs and Sun pillars and the patterns obtained from light scattering in foams. Keywords: Parlaseric circle, Parhelic circle, Plateau borders, Geometrical Theory of Diffraction. 1 Introduction Scattering problems are at very heart of Physics, from Celestial to Quantum Mechanics, with particles or waves, we are always looking for a target. In our experiment, we are observing the light scattering in foams, and the results can be applied in Acoustics, Optics and Spectroscopy. Light through foams presents a complex behavior, for example, though the laws of ray reflection and refraction are simple, the boundary conditions for the light scattering are very difficult to be determined precisely due to many awkward technical aspects, such as nonlinearities, or if the thickness of the liquid films is sufficiently close to the wave length of visible light, there is light interference and thus produce the iridescent colors of soap bubbles. In this paper we discuss the chaotic scattering, diffusion and some aspects of the interface between wave and geometric optics. We have observed that the light scattering dynamics in foams can present two main process: a diffusive one related to Gaussian process and another one related to chaotic dynamics, similar to those observed in chaotic saddles, with some rays of light bouncing back and forth for a certain time, and leaving it through one of several exits. In addition to those behaviors, between geometrics and wave optics, we also have observed the phenomena of the theory of geometrical refraction, with the parlaseric circle.

Supernumerary arcs on rainbows are historically important because in the early 1800s they provided evidence in favor of the wave theory of light. The success of Airy's rainbow integral has overshadowed the earlier contribution from Young, who proposed that supernumerary arcs were caused by interference between two geometrical rays that emerge from the raindrop at the same scattering angle. Airy dismissed Young's idea as "the imperfect theory of interference" because it predicted supernumerary arcs at the wrong angles. Young was unaware that a light ray encountering a focal line can suffer a phase shift of 90°. If these phase shifts are taken into account, the theory of interference becomes surprisingly accurate.

We propose a discussion on the synthesis and scattering analysis of nonlinear metasurfaces. For simplicity, we investigate the case of a second-order nonlinear isotropic metasurface possessing both electric and magnetic linear and nonlinear susceptibility components. We next find the synthesis expressions relating the susceptibilities to the specified fields, which leads to the definition of the nonlinear metasurface conditions for no reflection, themselves revealing the nonreciprocal nature of such structures. Finally, we provide the approximate expressions of the scattered fields based on perturbation theory and compare the corresponding results to finite-difference time-domain simulations.

Two-dimensional (2D) and three-dimensional (3D) diffraction theories form the underlying basis of quantitative phase imaging. This paper reviews how 2D and 3D diffraction theories are developed based on thin and thick object requirements. However, some previously reported work has mixed 2D and 3D theories. This discussion shows that it is possible to enable consistent mixed use of 2D and 3D theories by applying appropriate obliquity factor (OF) modifications. The discussion is concluded with an overall unifying representation for the usage of the OF modifications in 2D and 3D diffraction theories as applied to both thin and thick objects.

Wormlike or threadlike structures with local cylindrical geometry are abundantly found in nature and technical products. A thorough structural characterization in the bulk for a whole ensemble, however, is difficult. The inherent semiordered nature of the tortuous large-scale structure and especially the quantification of branching renders an assessment difficult. In the present work we introduce a hybrid function expressing the scattering intensities for X-rays, neutrons, or light in the small-angle regime for this system. The function is termed "hybrid" because it employs terms from different approaches. The large-scale structure is described via a Guinier term as well as a concomitant power-law expression in momentum transfer q taken from the so-called unified function. The local cylindrical shape, however, is taken into account through a form factor for cylinders from rigid-body modeling. In principle, the latter form factor can be replaced by an expression for any other regular body so that the new hybrid function is a versatile tool for studying hierarchical structures assembled from uniform subunits. The appropriateness and capability of the new function for cylindrical structures is exemplified using the example of a wormlike micellar system.

Canonical solutions to frequency domain Maxwell’s equations, in the spherical coordinate system, have found extensive use as is evident from citations in the scientific literature. What is conspicuous by its absence is lack of such expressions for transient Maxwell systems. The existence of such expressions or approximations, provide the means to glean interesting physics in a variety of applications as well as validate existing numerical fullwave solvers. However, developing these expressions is beset with challenges; direct inverse Fourier transforms of frequency domain expressions are unstable. Successful approaches that ameliorate this instability are more recent endeavor. In this paper, we generalize our earlier contribution to this effort by exploiting a novel representation of the retarded potential to derive expressions for scattering from a dielectric sphere. Several results are provided that demonstrate the stability and accuracy of the method.

Research on light scattering from a large chiral sphere shows that the rainbow phenomenon is different from that of an isotropic sphere. A chiral sphere with certain chirality generates three first-order rainbows. In this Letter, we present a geometric optics interpretation for the phenomenon and make a calculation of the rainbow angles. The ray traces inside the sphere are determined by the reflection and refraction laws of light at the achiral–chiral interface and the chiral–achiral interface. The calculated rainbow angles achieve good agreements with those obtained by the analytical solutions. The effects of chirality and the refractive index of the sphere on rainbow angles are analyzed.

The understanding of the physical principles of light guidance and its interactions with surrounding matter is the main requirement for a detailed study of polymer-optical fibres (POFs). This chapter briefly summarises the physical fundamentals of light and the application of physical laws in optical fibres. Beginning with Maxwell equations and a definition of electromagnetic (EM) waves, interactions in solid matter in the form of polarisation and magnetisation will be discussed. The EM wave equations in vacuum and solid-state media are motivated as fundamental physical law of light's propagation. Scattering phenomena like Mie and Rayleigh scattering occurring in optical fibres are discussed afterward, and their influence onto the fibres' performances is deduced. As it is essential for data transport and signal transmission in optical fibres, boundary phenomena in the form of Snell's law and total reflexions are described by using mathematical and geometrical approaches. Finally, an overview of anisotropic effects like birefringence and the dispersion of light in real media is given in order to finalise the understanding of physical processes in POFs. A summary of the importance of physical effects in optical fibres is made which enables a qualitative understanding of the parameters which determine the efficiency of optical fibres and the currently existing bottlenecks and challenges towards high-performance polymer-optical fibres.

We develop a technique for finding closed-form expressions for electromagnetic fields in radially inhomogeneous bianisotropic media, both the solutions of the Maxwell equations and material tensors being defined by the set of auxiliary two-dimensional matrices. The approach is applied to determine the scattering cross-sections by spherical particles, the fields inside which correspond to the Airy-exponential waves.

Scattering techniques (i.e., static light scattering, small angle neutron scattering,11 or small angle X-ray scattering) are excellent tools to study nanoscopic objects in solution. However, to interpret the experimental data, one needs to use the appropriate form factor. While recent progress has been made in the writing of form factors for complex structures, there is still a need to develop a method to evaluate the form factor of inhomogeneous elongated scatterers. Here, we propose an approach based on the principle of "Russian dolls". Multiblock rods are represented as multi generations of rods (mother, daughter, granddaughter, etc.), where each rod is nested within the rod of the previous generation, like Russian dolls. A shift parameter is used to introduce asymmetry in the rod along its long axis. This approach not only allowed us to write the form factor of multiblock rods, but it also gave us the possibility to account for the polydispersity in length of each block and of the shift parameter. Finally, we applied these equations to the case of a series of solutions of triblock comicelles slightly polydisperse in length.

The results of investigation of the problem of cylindrical wave scattering by infinite and finite Veslago lenses are discussed. The problem is considered in a rigorous electrodynamic formulation. It is shown that the superfocusing effect is impossible in an ideal Veselago lens. It is reported that the near-field structures observed in the case of diffraction of a cylindrical wave by an electrically thick lens and an electrically thin lens are substantially different.

Inspired by a general theorem on non-radiating sources demonstrated by Devaney and Wolf, a unified theory for invisible and cloaking structures is here proposed. By solving Devaney-Wolf theorem in the quasi-static limit, a weak solution is obtained, demonstrating the existence of Anapole modes, Mantle Cloaking and Plasmonic Cloaking. Beyond the quasi-static regime, a strong solution of Devaney-Wolf theorem can be formulated, predicting general non-scattering devices based on directional invisibility, Transformation Optics, neutral inclusions and refractive index continuity. Both weak and strong solutions are analytically demonstrated to depend on the concept of contrast, mathematically defined as a normalized difference between constitutive parameters (or wave-impedance property) of a material and its surrounding background.

Researchers experimentally investigate the superluminal kinematics of scattering light sources through ultrafast time-resolved imaging., The invariance of the speed of light is one of the foundational pillars of our current understanding of the universe. It implies a series of consequences related to our perception of simultaneity and, ultimately, of time itself. Whereas these consequences are experimentally well studied in the case of subluminal motion, the kinematics of superluminal motion lack direct evidence or even a clear experimental approach. We investigate kinematic effects associated with the superluminal motion of a light source. By using high-temporal-resolution imaging techniques, we directly demonstrate that if the source approaches an observer at superluminal speeds, the temporal ordering of events is inverted and its image appears to propagate backward. Moreover, for a source changing its speed and crossing the interface between subluminal and superluminal propagation regions, we observe image pair annihilation and creation, depending on the crossing direction. These results are very general and show that, regardless of the emitter speed, it is not possible to unambiguously determine the kinematics of an event from imaging and time-resolved measurements alone. This has implications not only for light, but also, for example, for sound and other wave phenomena.

International audience; INTRODUCTION: We aimed to determine the limbal lighting illuminance thresholds (LLITs) required to trigger perception of sclerotic scatter at the opposite non-illuminated limbus (i.e. perception of a light limbal scleral arc) under different levels of ambient lighting illuminance (ALI). MATERIAL AND METHODS: Twenty healthy volunteers were enrolled. The iris shade (light or dark) was graded by retrieving the median value of the pixels of a pre-determined zone of a gray-level iris photograph. Mean keratometry and central corneal pachymetry were recorded. Each subject was asked to lie down, and the ALI at eye level was set to mesopic values (10, 20, 40 lux), then photopic values (60, 80, 100, 150, 200 lux). For each ALI level, a light beam of gradually increasing illuminance was applied to the right temporal limbus until the LLIT was reached, i.e. the level required to produce the faint light arc that is characteristic of sclerotic scatter at the nasal limbus. RESULTS: After log-log transformation, a linear relationship between the logarithm of ALI and the logarithm of the LLIT was found (p\textless0.001), a 10% increase in ALI being associated with an average increase in the LLIT of 28.9%. Higher keratometry values were associated with higher LLIT values (p = 0.008) under low ALI levels, but the coefficient of the interaction was very small, representing a very limited effect. Iris shade and central corneal thickness values were not significantly associated with the LLIT. We also developed a censored linear model for ALI values ≤ 40 lux, showing a linear relationship between ALI and the LLIT, in which the LLIT value was 34.4 times greater than the ALI value. CONCLUSION: Sclerotic scatter is more easily elicited under mesopic conditions than under photopic conditions and requires the LLIT value to be much higher than the ALI value, i.e. it requires extreme contrast

Problems related to propagation of partially coherent fields can be greatly simplified if the correlation function of the field assumes certain specific forms, which allow their representations as incoherent superpositions of fully coherent fields of identical shape. The need for this type of representation is explained and suitable elementary-field decompositions are formulated in spatial, angular, temporal, and spectral domains. Their application to wave propagation in free space and to analysis of light interaction with micro- and nanostructures are discussed, and several illustrative examples are given.

Advances in light shaping techniques are leading to new tools for optical trapping and micromanipulation. For example, optical tweezers made from Laguerre-Gaussian or donut beams display an increased axial trap strength and can impart angular momentum to rotate a specimen. However, the application of donut beam optical tweezers to precision, biophysical measurements remains limited due to a lack of methods for calibrating such devices sufficiently. For instance, one notable complication, not present when trapping with a Gaussian beam, is that the polarization of the trap light can significantly affect the tweezers' strength as well as the location of the trap. In this article, we show how to precisely calibrate the axial trap strength as a function of height above the coverslip surface while accounting for focal shifts in the trap position arising from radiation pressure, mismatches in the index of refraction, and polarization induced intensity variations. This provides a foundation for implementing a donut beam optical tweezers capable of applying precise axial forces.

Light scattering in the Wentzel-Kramers-Brillouin (WKB) approximation is considered from the point of view of stereology. The extinction and absorption cross sections for an ensemble of chaotically oriented particles of arbitrary shape are expressed analytically through the chord length distribution. The analytical approximation for the scattering phase function is proposed. The derived analytical expressions are compared to the calculations with the discrete-dipole-approximation method.

Designs of cloaking devices and more general invisible objects have primarily applied the techniques of transformation optics and scattering cancellation to derive material structures that achieve the desired effects. In this Letter, we note that it is also possible to construct a broader class of invisible objects directly from the defining wave equation. The technique is demonstrated in a scalar formalism with illustrative examples.

Chapter 2 exposes a mathematical model of a waveguide with several cylindrical ends going to infinity, basic notions and mathematical results (with complete proofs) needed in successive chapters: waves, continuous spectrum eigenfunctions, intrinsic radiation principle, and scattering matrices.

A technique for designing localized parity-time (PT) symmetric directionally invisible scatterers and cloaks is introduced and verified by numerical scattering simulations. Implications and generalizations of the method are discussed.

This PhD tutorial is concerned with a description of the two-dimensional generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method used to compute the interaction of light with arrays of cylindrical scatterers. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. The purpose of this tutorial is to assemble the practical tools necessary to implement the 2D-GLMT method for the computation of scattering by passive scatterers or of resonances in optically active media. The first part contains a derivation of the vector and scalar Helmholtz equations for 2D geometries, starting from Maxwell's equations. Optically active media are included in 2D-GLMT using a recent stationary formulation of the Maxwell-Bloch equations called steady-state ab initio laser theory (SALT), which introduces new classes of solutions useful for resonance computations. Following these preliminaries, a detailed description of 2D-GLMT is presented. The emphasis is placed on the derivation of beam-shape coefficients for scattering computations, as well as the computation of resonant modes using a combination of 2D-GLMT and SALT. The final section contains several numerical examples illustrating the full potential of 2D-GLMT for scattering and resonance computations. These examples, drawn from the literature, include the design of integrated polarization filters and the computation of optical modes of photonic crystal cavities and random lasers., Comment: This is an author-created, un-copyedited version of an article published in Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The T-matrix method, which is also known as the null field method (NFM) or extended boundary condition method (EBCM), has established itself as a well known and highly regarded method for calculating light scattering by non-spherical particles. Its biggest advantage is the possibility to obtain all information about the scattering characteristics of the particle and to store it into one matrix. This enables one to do additional investigations with low efforts. Unfortunately the standard NFM fails to converge for particles with extremely non-spherical particle shapes, like long cylinders or coin-like flat cylinders. In this paper we investigate light scattering by finite particles in the form of an oblate disc sphere, which can be described as flat cylinders with a rounded edge. We use an advanced form of the T-matrix method—the null field method with discrete sources (NFM-DS). By presenting light scattering results we would like to demonstrate the potential this advanced NFM-DS offers. It allows one to ca...

We consider the scattering of a plane wave by a sphere (Lorenz–Mie theory) and the corresponding quantum problem of scattering of an illuminating plane wave beam by a radial potential U ( r ), and demonstrate that cross-sections in both frameworks are amenable to identical expressions, excepted for zero-order phase shift terms which are specific of the quantum framework.

Diffraction from a uniaxial chiral slab with a two-dimensional periodic array of conducting patches is analyzed by the matrix-based approach. Equatorial anisotropy is assumed for the chirality and permittivity whose optical axis is parallel to the plane of incidence. In the analysis, the total fields are given by the superposition of the current-dependent scattering fields, which are expanded in terms of the two-dimensional space harmonics and the incidence fields. The coupled mode equations for the equatorial uniaxial chiral media give the general solutions of fields as superpositions of elliptically polarized eigenmodes. The unknown currents on the patches are determined by applying the method of moments to the boundary conditions of the conducting array. In the numerical computations, the polarization characteristics of diffracted waves are investigated considering the design parameters. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(3): 1–8, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10293

The electromagnetic scattering by a three-dimensional uniaxial anisotropic particle is studied. Electromagnetic fields in a uniaxial medium are expressed in terms of a system of vector functions which are similar to the system of regular spherical vector wave functions. The scattering problem is solved by using the null-field method. Numerical simulations for uniaxial anisotropic ellipsoids are presented.

We consider one-speed transport problems with forward–backward-isotropic scattering in an infinite medium and study its relationship with the diffusion equation. Both time dependent and time independent transport equations are considered. We also obtain the Greens function for this scattering model.

Albert Einstein’s theory of relativity imposes stringent limitations to making macroscopic objects invisible with respect to electromagnetic light waves propagating in vacuum. These limitations are not relevant though for propagation of light in diffusive media like fog or milk because the effective energy speed is significantly lower than in vacuum due to multiple scattering events. Here, by exploiting the close mathematical analogy between the electrostatic or near-field limit of optics on the one hand and light diffusion on the other hand, we design, fabricate, and characterize simple core-shell cloaking structures for diffusive light propagation in cylindrical and spherical geometry.

The scattering of electromagnetic waves from rough surfaces has been actively studied for more than a century now because of its involvement in vast application areas. In the past two decades, great advances have been made by incorporating multiple scattering effects into analytical approaches. However, no model can yet be applied to surfaces with arbitrary roughness. It is also very difficult to study the cross-polarization, shadowing, or multiple scattering effects. In order to study more fundamentally the interaction of polarized light with more general rough surfaces of general media, we have developed a rigorous numerical simulator to calculate the resulting speckle fields. The full Maxwell equations were solved using surface integral equations combined with a boundary element method. The rough surface was discretized by higher order quadrilateral edge elements. The effective tangential electric and magnetic fields in each element in terms of 10 edges were first solved. The scattered electric and magnetic fields everywhere in space were then calculated correspondingly. One of the great advantages of such a simulator is that both the near and far fields can be calculated directly. Preliminary results of different kinds of metallic structures are presented, by which the advantages of the method are demonstrated.

International audience; Homogenization of metamaterials based on the analysis of their reflection and transmission spectra often leads to nonphysical values of the effective permittivity and permeability. Here we address this challenge by analyzing the scattering spectra in terms of perfectly emitting and absorbing modes considering nonlocal constitutive relations. The decomposition of the scattering spectra into even and odd modes permits us to quantify the nonlocal contributions and provides explicit formulas for the effective permittivity and permeability which always satisfy the passivity and causality constraints.

Macroscopic electrodynamics with scalar and vector potentials offers a useful paradigm to study the optical properties of conducting materials, forming a non-Cartesian geometrical structure. We elaborate this viewpoint with a new electromagnetic gauge (an extension of the Lorentz gauge) and obtain the equations of motion for the potentials. We next discuss the subtle idea of the Laplace operator on the vector field in an orthogonal curvilinear geometry. Remarkably, the Laplacian on the vector field (as opposed to the scalar one) is not separable in any curvilinear coordinate frame (except the rectangular Cartesian coordinates). This nonseparability of Laplacian, as we show with spherical polar coordinates as an example, does not allow a closed-form, fully analytical, and exact mathematical solution of the field equations. We then introduce the idea of effective field equations for a simplified description of the electromagnetic properties of the material and obtain a closed-form analytical solution for the spherical polar geometry. To account for the electromagnetic responses of the material (isotropic or forming a cubic system), we use linear constitutive relations with wavevector and frequency-dependent response functions (permittivity, permeability, and the conductivity). We use the present formalism to study the scattering of an electromagnetic wave by a spherical grain (finite radius) of a model-conducting material and obtain analytically closed-form expressions for the scattering and absorption cross sections. Present theoretical predictions are consistent with recent optical experiments on metallic nanoparticles and earlier theoretical works on this subject. � 2014 American Chemical Society.

In this paper, we consider the interaction of an electromagnetic field with two eccentric spheres. We propose a quasi-static approach in order to calculate the scattered field and the polarizability and the effective permittivity of the eccentric spheres. We analyze the behavior of the scattering parameters as a function of the dimension and position of the spherical inclusions. Moreover, we consider the case of plasmonic spheres and study the behavior of the plasmon resonances for different reciprocal positions of the two spheres.

A torus is a simple body with cylindrical rotational symmetry. The radius of gyration and scattering function of a torus have been derived in cylindrical coordinates. Some derivatives of a torus (torus with elliptical cross section, tubular torus and two stacked tori) have been treated in the same manner as the torus. The radii of gyration are given by simple formulae and the scattering curves are easily obtained by numerical calculation using a personal computer.

In this paper, we introduce an efficient numerical method to characterize the multiple scattering by random discrete particles illuminated by Bessel beams with arbitrary incidence. Specifically, the vector expressions of Bessel beams that perfectly satisfy Maxwell’s equations in combination with rotation Euler angles are used to represent the arbitrarily incident Bessel beams. A hybrid vector finite element–boundary integral–characteristic-basis function method is utilized to formulate the scattering problems involving multiple discrete particles with a random distribution. Due to the flexibility of the finite element method, the adopted method can conveniently deal with the problems of multiple scattering by randomly distributed homogeneous particles, inhomogeneous particles, and anisotropic particles. Some numerical results are included to illustrate the validity and capability of the proposed method and to show the scattering behaviors of random discrete particles when they are illuminated by Bessel beams.

Interactions between nonlinear media and an object in it are studied theoretically and numerically using dynamical models. The KdV soliton is incidented to the object by numerical simulation and the generation of solitons are detected. The measured amplitudes coincide very well with the theoretical results.

This paper presents an extension of the generalized multipole technique (GMT) for 2D anisotropic scatterers. New expansions similar to the Bessel multipole expansion are derived for arbitrary anisotropic media. Numerical simulations prove the accuracy and the rapid convergence of these expansions. As the results obtained are extremely accurate, this technique is most helpful for the evaluation of reference solutions and for the understanding of the physical interaction of light with arbitrary anisotropic media.