The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic device design, it is unclear whether the performance of resulting designs is close to that of the best possible design. This question remains unsettled for absorptionless electromagnetic devices since the absence of material loss makes it difficult to provide provable bounds on their scattering properties. We resolve this problem by providing non-trivial lower bounds on performance metrics that are convex functions of the scattered fields. Our bounding procedure relies on accounting for a constraint on the electric fields inside the device, which can be provably constructed for devices with small footprints or low dielectric constrast. We illustrate our bounding procedure by studying limits on the scattering cross-sections of dielectric and metallic particles in the absence of material losses.
Deep Learning-Enabled Invisible Electromagnetic Scattering Amplifier
Key Lab of Advanced Transducers and Intelligent Control System, Ministry of Education and Shanxi Province, College of Physics and Optoelectronic Engineering, Taiyuan University of Technology（先进换能器与智能控制系统重点实验室（教育部和山西省），物理与光电工程学院，太原理工大学）
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $γ$. Closed-form expressions were derived for the expansion coefficients of the scattered field phasors in terms of those of the incident field phasors. These expansion coefficients were used to obtain analytical expressions for the total scattering, extinction, forward scattering, and backscattering efficiencies of the sphere. Resonances exist for relatively low values of $γ$,…
Optical properties of nonmagnetic structures that support artificial optically-induced magnetic responses have recently attracted surging interest. Here we conduct symmetry-dictated investigations into scattering properties of nonmagnetic particles from perspectives of electromagnetic duality with discrete geometric rotations. For arbitrary scattering configurations, we reveal that far-field scattering patterns are invariant under duality transformations, which in particular means that scattering patterns of self-dual clusters with random particle distributions are polarization independent. Ba…
We demonstrate that directional electromagnetic scattering can be realized from a artificial Mie resonant strcuture which supports electric and magnetic dipole modes simultaneously. The directivity of the far-field radiation pattern can be switched by changing the incident light wavelength as well as tailoring the geometric parameters of the structure. Particularly, the electric quadrupole at higher frequency contribute significantly to the scattered fields, leading to enhancement of the directionality. In addition, we further design a quasiperiodic spoof Mie resonant structure by alternately …
In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our resul…
Metasurfaces have attracted significant research interest owing to their unprecedented control over the spatial distributions of electromagnetic fields. Herein we propose the concept of metasurface tessellation to achieve reconfigurable scattering functions. Square meta-tiles, composed of identical structures, are arranged to fill a surface. The electromagnetic scattering of the tiled surface is determined by the orientation distribution of the meta-tiles. We present three typical cases of meta-tiles consisting of binary elements to realize several distinct scattering patterns. This study prov…
Pseudo-spectral frequency-domain method with background field decomposition and Green's function preconditioner for electromagnetic scattering problem in EUV lithography
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is de…
A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A matrix formulation of the Maxwell equations, using the Riemann-Silberstein-Weber vectors, forms a basis for the QLA and a possible unitary representation. The electromagnetic fields are discretized using a 16-qubit representation at each grid point. The discretized QLA equations reproduce Maxwell equations to second order in an appropriate expansion parameter…
Under conditions of strong scattering, a dilemma often arises regarding the best numerical method to use. Main competitors are the Born series, the Beam Propagation Method, and direct solution of the Lippmann-Schwinger equation. However, analytical relationships between the three methods have not yet, to our knowledge, been explicitly stated. Here, we bridge this gap in the literature. In addition to overall insight about aspects of optical scattering that are best numerically captured by each method, our approach allows us to derive approximate error bounds to be expected under various scatte…
We perform quantitative spectral analysis on the Born equation, an integral equation for electromagnetic scattering that descends from the Maxwell equations. We establish norm bounds for the Green operator associated with the Born equation, thereby providing numerical tools for error estimates of the Born approximation to light scattering problems.
This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole structures, which are able to induce resonant scattering of electromagnetic wave and the so-called extraordinary optical transmission. We develop a multiscale framework for the underlying scattering problem based upon a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the tiny hole. The matching of the electrom…
We carry out quantitative studies on the Green operator $ \hat{\mathscr G}$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup $\{\exp(-iτ\hat{\mathscr G})|τ\geq0\} $ on polynomial compactness and the Arendt-Batty-Lyubich-Vũ theorem. The strongly-stable evolution semigroup inspires our proposal of a non-perturbative method to solve the light scattering problem and improve the Born approximation.
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator polynomials are constructed from the Green operator of electromagnetic scattering on scatterers with smooth boundaries. As a consequence, it is shown that the strongly singular Born equation has a discrete spectrum, and that the spectral series $ \sum_λ|λ|^2|1+2λ|^4$ is convergent, counting multiplicities of the eigenvalues $ λ$. This reveals a shape-independent opti…
This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the inclusions are allowed to be negative-valued. Using layer potential techniques for the full Maxwell system, the scattering problem is reformulated into a system of integral equations. We derive the complete eigensystem of the involved matrix-valued integral operator within spherical geometry. As applications, we construct two types of plasmonic structures s…
A boundary integral formulation of electromagnetics that involves only the components of $\boldsymbol{E}$ and $\boldsymbol{H}$ is derived without the use of surface currents that appear in the classical PMCHWT formulation. The kernels of the boundary integral equations for $\boldsymbol{E}$ and $\boldsymbol{H}$ are non-singular so that all field quantities at the surface can be determined to high precision and also geometries with closely spaced surfaces present no numerical difficulties. Quadratic elements can readily be used to represent the surfaces so that the surface integrals can be calcu…
