A Tri-vial Contrast Theory for Electromagnetic Invisibility: Cloaking and Non-radiating Sources

Novel closed-form expressions and general conditions for achieving electromagnetic invisibility are exposed and detailed in terms of a familiar concept in visual and reading contexts: the contrast. Defined as a normalized difference between some property P and the same homogeneous property of the background Pb, the contrast has been used as a parameter in Microwave Imaging problems to detect the presence of buried or unknown scatterers in a given scenario. However, when the contrast is low and it approaches zero, it becomes difficult to reveal the presence of objects in a defined background: such structures appear to be undetectable or invisible. Starting from this observation, all the mathematical conditions for electromagnetic invisibility are reported from two different perspectives: non-radiating sources, when the excitation is internal to the structure itself, and cloaking devices, when the excitation comes from the external world and it is impinging into the device itself. The interests in such invisible structures come from different research areas: optics, for the non-radiating feature of anapole modes, microwave engineering, for surface waves excitation in cloaking devices, and physics, for coordinate transformation in electromagnetics. All these aspects are treated and discussed, with the introduction of two novel concepts for achieving the zeros of the scattered field: the nulling of the average sources in the domain of interest, namely weak solution, and the zeros of the equivalent sources, namely strong solution. The first approach is validated in the quasi-static limit, where closed-form expressions can be written for dielectric-plasmonic systems and for dielectric-metallic patterned particles. In this subwavelength approximation, it turns out that to achieve a non-radiating or cloaking effect, objects can be modeled in terms of lumped elements and the local condition in the domain of interest can be written in the form of the Kirchhoff’s Current Law. The second approach is validated beyond the quasi-static limit and it can be written in the form of a matching problem, where objects can be modeled by lumped admittances and the fields are decomposed in terms of harmonic waves. In order to achieve the non-radiating or cloaking feature, a cancellation effect has to take place for one (or more) harmonic mode(s) and this is performed for dielectric objects by inserting a lumped surface admittance at the object’s contour. Results are shown for single harmonic cancellation, where the surface admittance function Zs appears to be purely reactive and it is computed exploiting the notion of contrast: as a normalized difference between the admittance of the bare object and the admittance of the background region. In this case of single harmonic suppression, the choice is limited to the harmonic mode which is dominant in the scattered field (in the quasi-static limit, n=0) and such dominant scattering contribution changes as the frequency is increased (n ≥ 1 beyond the subwavelength limit). For multi-harmonic cancellation, results indicate that the surface admittance functions Zs appears to be of complex value, with resistive and reactive parts that start oscillating around the azimuthal coordinate, where the admittance mantle cloak is inserted. This oscillating behaviour, especially in the resistive part, is quite sensitive to the changing in the direction of incidence for the incoming wave, but it is able to suppress an arbitrary portion of the harmonic content (n = 0,1, ..,M). Investigations on the effects of the frequency regime and on the change of the direction of incidence are performed for volumetric systems, where the transition from the subwavelength limit to any frequency regime leads to the transition from plasmonics to the use of all-positive dielectric coatings. Exploiting the formulation of an Inverse Scattering Problem, it is possible to manipulate the internal configuration of the electromagnetic fields in many dielectric structures, as a function of the radius of the coating region, in order to synthesize the zeros of the external scattered field in a certain frequency band and for a finite number of direction of arrival for the incoming wave. The arrangement of the dielectric permittivity in the coating layer follows the characteristics of the imposed specifications, especially the number of direction of arrivals (for which the all-dielectric device is cloaked) that ensures the same number of axis of symmetry on the dielectric structure. Concluding remarks and final recap of this PhD study are indicated.