Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Pan-Arctic and regional sea ice predictability: initialization month dependence

Seasonal-to-interannual predictions of Arctic sea ice may be important for Arctic communities and industries alike. Previous studies have suggested that Arctic sea ice is potentially predictable but that the skill of predictions of the September extent minimum, initialized in early summer, may be low. The authors demonstrate that a melt season “predictability barrier” and two predictability reemergence mechanisms, suggested by a previous study, are robust features of five global climate models. Analysis of idealized predictions with one of these models [Hadley Centre Global Environment Model, version 1.2 (HadGEM1.2)], initialized in January, May and July, demonstrates that this predictability barrier exists in initialized forecasts as well. As a result, the skill of sea ice extent and volume forecasts are strongly start date dependent and those that are initialized in May lose skill much faster than those initialized in January or July. Thus, in an operational setting, initializing predictions of extent and volume in July has strong advantages for the prediction of the September minimum when compared to predictions initialized in May. Furthermore, a regional analysis of sea ice predictability indicates that extent is predictable for longer in the seasonal ice zones of the North Atlantic and North Pacific than in the regions dominated by perennial ice in the central Arctic and marginal seas. In a number of the Eurasian shelf seas, which are important for Arctic shipping, only the forecasts initialized in July have continuous skill during the first summer. In contrast, predictability of ice volume persists for over 2 yr in the central Arctic but less in other regions.