The diaphanous wedge

Abstract

Complete solutions for the diaphanous wedge, meaning a wedge with identical wavenumbers inside and outside the wedge, are presented. The results are obtained from an integral equation for the fields on the wedge, which is solved by the Mellin and Kantorovich-Lebedev transforms in the static and dynamic cases, respectively. Pertinent formulations of Gegenbauer's addition theorems play an important part in the derivation of the results, which are presented in closed form.

Time-domain three-dimensional diffraction by the isorefractive wedge

“…The perfectly conducting wedge Manuscript can be recovered as a special case. As indicated in [1] and recognized by [8] and [9], the main value of the isovelocity solution is its service, in principle, as the zeroth-order iterate for a wedge of relatively small velocity contrast. However, the envisaged perturbative adjustment (i.e., Neumann series) cannot be constructed in the time domain because an upper bound must be imposed on the frequency.…”

“…1). The constitutive parameters of the lossless external and internal media satisfy the requirement that the intrinsic wave speed remains invariant (1) The name "diaphanous" refers to similar wave speeds in [13], but is adopted by [8] for this isovelocity or isorefractive wedge, with intrinsic impedance , which clearly differs, in general, from the external impedance . This is exactly analogous to the archetypal scattering problem of the density contrast wedge [1].…”

Rotating Waves in the Laplace Domain for Angular Regions

“…For instance, it has been used for the diffraction by an isorefractive wedge [9]. However, sometimes this transform does not exist.…”

“…The importance of this problem is due to the fact that it constitutes a dynamical penetrable wedge problem that we can solve in closed form. The solution of isorefractive wedges has been accomplished in the past by using the Kontorovich-Lebedev transform [9] in the frequency domain and the Green function in the time domain [10]. Wiener-Hopf solutions for the right wedge are also available [11].…”

Isorefractive wedge

“…[3] The solution obtained by Osipov [1993] and by Knockaert et al [1997] is in the spectral domain of KL transforms. In order to express the electromagnetic field in the physical domain, an inverse KL transform resulting in integrals that are difficult to evaluate by saddle point must be performed.…”