We investigate the diffraction of TM mode at an open-ended deeply corrugated cylindrical waveguide. We analyze the case when wavelengths and the waveguide radius are much greater than the corrugation period. In this case, equivalent boundary conditions (EBC) can be used. The approach applied uses the solution of the corresponding Wiener–Hopf–Fock equation. Typical radiation patterns are presented and analyzed.
Far-field asymptotics for the quasi-spherical body waves generated in an arbitrarily anisotropic elastic half-space by a surface source is derived from the Green’s matrix based integral representation for the solution to the corresponding elastodynamic problem. The asymptotics is validated by numerical integration and illustrated with several numerical examples.
In this work, we study dipolar oscillations in infinite and finite one-dimensional arrays of scatterers supporting dipole resonances. We show that the presence of two dipolar responses of different types in a single scatterer can induce a change of the dispersion of an infinite chain from monotonic to non-monotonic one. In turn, the non-monotonic dispersion leads to the interaction between two collective modes in the corresponding finite chain. This results in a strong suppression of the radiative losses of one of the modes for a certain distance between the scatterers. Moreover, by tuning the ratio of the resonant frequencies in a single scatterer the optimal period can be shifted to the values that can be realized in feasible optical designs.
Given a semiclassical distribution f h microlocalized on a Lagrangian manifold Λ 0 , H ∈ C ∞ (T ∗ ℝ n ), and H = E a regular energy surface, we find asymptotic solutions of the PDE (H(x,$\hat p$)−E)u h (x,E) = f h (x) in terms of the Maslov canonical operator, when the Hamilton vector field v H fails to be transverse to Λ 0 at some points.
We deal with the ultrahyperbolic equation in ℝ d × ℝ n . Our goal is to construct its fundamental solutions that satisfy a certain support condition. In the particular case n = 1, they coincide with either the advanced or the retarded fundamental solution of the wave equation. Such fundamental solutions provide Volterra type transformations which can be utilized in the study of perturbed ultrahyperbolic equations.
