Related papers: Eigenmodes of index-modulated layers with lateral …
This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric…
This article presents a mathematical framework for solving Maxwell's equations in cylindrical and spherical geometries with continuous angular indices. We extend beyond standard discrete harmonic decomposition to a continuous spectral…
We present an easy-to-implement numerical method for analyzing electromagnetic wave propagation in dielectric rings. Our approach employs a finite-difference-based solver in cylindrical coordinates, solving a mixed electric-magnetic field…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…
In this paper, we present the stability analysis of the perfectly matched layer (PML) in two-space dimensional layered elastic media. Using normal mode analysis we prove that all interface wave modes present at a planar interface of…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
The initial-boundary value problem (IBVP) for the Maxwell-Bloch equations with an arbitrary inhomogeneous broadening and periodic boundary condition is studied. This IBVP describes the propagation of an electromagnetic wave generated by…
Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
From a three-dimensional boundary value problem for the time harmonic classical Maxwell equations, we derive the dispersion relation for a surface wave, the edge plasmon-polariton (EP), that is localized near and propagates along the…
This paper considers the scattering of a time-harmonic acoustic plane wave by an elastic body with an unbounded periodic surface. The original problem can be confined to the analysis of the fields in one periodic cell. With the help of the…