Realization of Generalized Soft-and-Hard Boundary

Abstract

The classical soft-and-hard surface boundary conditions have previously been generalized to the form a • E = 0 and b • H = 0 where a and b are two complex vectors tangential to the boundary. A realization for such a boundary is studied in terms of a slab of special wave-guiding anisotropic material. It is shown that analytic expressions can be found for the material parameters and thickness of the slab as functions of the complex vectors a and b. Application of a generalized soft-and-hard boundary as a polarization transformer is studied in detail.

Electromagnetic Wormholes and Virtual Magnetic Monopoles from Metamaterials

“…In the above construction, we removed a one-dimensional curve from the manifold M. Removing is analogous to making a one-dimensional crack that does not affect the EM fields. A careful analysis shows that the physically relevant class of waves, namely those that are locally finite energy and distributional solutions to Maxwell's equations on (M; ", ) and (N;",), correspond perfectly under the transformation F. To guarantee that the fields in N with singular material parameters" and are finite energy solutions and do not blow up near , one must impose at the appropriate boundary condition, namely, the Soft-and-Hard (SH) condition, (see [18,19])…”

“…In addition, one should impose the SH boundary condition on , which may be realized by making the obstacle K from a perfectly conducting material with parallel corrugations on its surface [18,19].…”

Electromagnetic Wormholes via Handlebody Constructions

“…First, to guarantee that the fields in N are finite energy solutions and do not blow up near Σ, we have to impose at Σ the appropriate boundary condition, namely, the Soft-and-Hard (SH) condition, see [8,11], e θ · E| Σ = 0, e θ · H| Σ = 0, where e θ is the angular direction. Secondly, the map F can be considered as a smooth coordinate transformation on M \ γ; thus, the finite energy solutions on M \ γ transform under F into the finite energy solutions on N \ Σ, and vice versa.…”

“…We form the wormhole device around an obstacle K ⊂ R 3 as follows. First, one surrounds K with metamaterials, corresponding to a specification of EM parameters ε and µ. Secondly, one lines the surface of K with material implementing the Soft-and-Hard (SH) boundary condition from antenna theory [8,10,11]; this condition arose previously [3] in the context of cloaking an infinite cylinder. The EM parameters, which become singular as one approaches K, are given as the pushforwards of nonsingular parameters ε and µ on an abstract three-manifold M, described in Sec.…”

Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

“…In classical terms, an SHS condition on a surface Σ [40,47] is η · E| Σ = 0 and η · H| Σ = 0, where η = η(x) is some tangential vector field on Σ, that is, η · ν = 0. In other words, the part of the tangential component of the electric field E that is parallel to η vanishes, and the same is true for the magnetic field H. This was originally introduced in antenna design and can be physically realized by having a surface with thin parallel gratings filled with dielectric material [47,48,67,40]. Here, we consider this boundary condition when η is the vector field η = ∂ θ , that is, the angular vector field that is tangential to Σ.…”