Differential form approach to the analysis of electromagnetic cloaking and masking

Abstract

We bring attention to the relationship between (1) electromagnetic masking or cloaking of objects produced by some metamaterial blueprints and (2) some invariances of Maxwell equations obviated by means of the differential forms (exterior calculus) framework.

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

“…However, Hodge operators also incorporate all metric information [191]- [195]. In other words, Maxwell equations-written in terms of differential forms-factor out into two parts: one part encoding only metric and material information and the other part encoding only topological information 3 (at the discrete level, topological information corresponds to mesh connectivity information).…”

Parameter design of cylindrical invisible cloak applied nonlinear transformation

“…The desired materials have permittivity and permeability constitutive tensors representing dielectric/magnetic inhomogeneous and anisotropic materials ("blueprints"), which can be very difficult to fabricate. In a theoretical sense, this result has long been known [2][3][4][5] and it is best appreciated using the language of exterior differential forms [6].…”

Transformation Optics, Generalized Cloaking and Superlenses

“…Now, rule (14) may be applied to D 2 containing objects with arbitrary electromagnetic properties so that a region cloaked by this device is still completely hidden but has the appearance of the objects originally in D 2 . We may call this optical effect masking [15] or "polyjuice" effect. Figs.…”