Active exterior cloaking and mimicking for the heat equation

Abstract

We present two methods for cloaking objects from thermal measurements that use active sources instead of metamaterials. One method deals with the parabolic heat equation [1], in which case active sources need to completely surround the object to cloak or mimic. Another method [2], for which the sources do not completely surround the object to cloak, relies on the frequency domain formulation of the heat equation as a Helmholtz equation with complex wave numbers. This second method extends the active exterior cloaking for waves modelled with the Helmholtz equation in [3] from positive wavenumbers to complex ones [2]. We point out the second method can be applied to waves in dispersive media.