A multiphysics theoretical approach for cloaking: Strong and weak solutions

An analytical approach for controlling the zeros of a scattering event (i.e., cloaking) is given, substituting the concept of positive-negative constitutive parameters with a positive-negative contrast formulation. Starting from the zero scattered field condition, a proper manipulation is performed and two different equations are derived: the Contrast-Field-Green Cloaking Equation (CFGCE) and the Contrast Cloaking Equation (CCE). In the present paper, the CCE is deeply analyzed and compared with the existing cloaking approaches in literature. It is shown how Transformation Optics and Scattering Cancellation methods corresponds to the Strong and Weak solutions of the CCE, respectively. This unique equation turns out to be independent from the involved physical events, if the main contrast parameter is properly chosen. Under its main assumptions, the CCE predicts a cloaking effect for arbitrary backgrounds, arbitrary shape objects and arbitrary physics of fields (e.g., magnetic, thermal, acoustic, etc.).