Related papers: Equilateral triangular waveguides, modal structure…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
This study presents a finite-difference-based numerical solver designed for the electric field formulation of vector wave equations in optically linear, non-magnetic, dielectric waveguides. We construct a generalized eigenvalue problem by…
This paper is devoted to Maxwell modes in three-dimensional bounded electromagnetic cavities that have the form of a product of lower dimensional domains in some system of coordinates. The boundary conditions are those of the perfectly…
This paper concerns the quantitative step of the medical imaging modality Thermo-acoustic Tomography (TAT). We model the radiation propagation by a system of Maxwell's equations. We show that the index of refraction of light and the…
We devise a lucid and straightforward way for explicitly constructing quasi-periodic wave solutions (also called multi-periodic wave solutions) of supersymmetric equations in superspace $\mathbb{R}_\Lambda^{2,1}$ over two-dimensional…
We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…
Topological boundary and interface modes are generated in an acoustic waveguide by simple quasi-periodic patternings of the walls. The procedure opens many topological gaps in the resonant spectrum and qualitative as well as quantitative…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
Resonant three-wave coupling is an important mechanism via which waves interact in a nonlinear medium. When the medium is a magnetized warm-fluid plasma, a previously-unknown formula for the coupling coefficients is derived by solving the…
We consider analytical and numerical solution of NMR relaxation under the condition of surface relaxation in an equilateral triangular geometry. We present an analytical expression for the Green's function in this geometry. We calculate the…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
We consider the waveguiding by thin patterned slabs embedded in a homogeneous medium. In the longwave limit, the wave spectra of slabs are found to be well described by a single frequency-independent parameter, which we call the "guiding…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase…
The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended…
We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…