Towards Printable Natural Dielectric Cloaks via Inverse Scattering Techniques

Abstract

The synthesis of non-magnetic 2D dielectric cloaks as proper solutions of an inverse scattering problem is addressed in this paper. Adopting the relevant integral formulation governing the scattering phenomena, analytic and numerical approaches are exploited to provide new insights on how frequency and direction of arrival of the incoming wave may influence the cloaking mechanism in terms of permittivity distribution within the cover region. In quasi-static (subwavelength) regime a solution is analytically derived in terms of homogeneous artificial dielectric cover with ε < ε ₀, which is found to be a necessary and sufficient condition for achieving omnidirectional cloaking. On the other hand, beyond quasi-static regime, the cloaking problem is addressed as an optimization task looking for only natural dielectric coatings with ε > ε ₀ able to hide the object for a given number of directions of the incident field. Simulated results confirm the validity of both analytic and numerical methodologies and allow to estimate effective bandwidths both in terms of frequency range and direction of arrival of the impinging field.

Figure 1

Geometry of the problem for the synthesis of dielectric cloaking: Ω is the computational domain which includes arbitrarily shaped scattering system Σ (cloaking region) and $\mathrm{\Gamma }=\mathrm{\Omega }/\mathrm{\Sigma }$ (observation region). The Σ region, divided into Σ₁ (bare object) and Σ₂ (cloak cover), is illuminated by an incident field E _i impinging from an angular directions θ _ν. ${\mathrm{\Gamma }}_0$ is a subset of $\mathrm{\Gamma }$ where the scattered field is enforced to be zero in the design procedure based on inverse scattering technique.

Figure 2

(Left) Scattering cancellation with positive (red) and negative (blue) contrast $\chi$ at subwavelength scale $d/\lambda \approx 0$ as necessary and sufficient condition for lumped elements. (Right) Beyond quasi-static regime, complete positive $\chi$ values (e.g., at a distance $D/\lambda \approx 0.5$) can support the same effects on the local scattered field (±|E _s|). When properly designed, all the local distributed natural materials can achieve zero scattered field at any point outside the domain Σ.

Figure 3

Permittivity distribution for synthesized covers to cloak allumina disk: (a) bare object; (b) homogeneous plasmonic cover at subwavelenght regime (f.i., 4 GHz); (c–h) ordinary all dielectric cloaks operating at 25 GHz with different features specified in Table 1.

Figure 4

Real part of the total electric field for the bare and cloaked allumina disk following the order reported in Fig. 3: (a,b) 4 GHz and (c–h) 25 GHz.

Figure 5

SCS calculated at fixed DoA as a function of the frequency for (a) 1λ and (b) 2λ dielectric cloaks and comparison with the bare object and plasmonic cloak: continuous line (bare uncloaked object), dotted line (plasmonic cover), upward-pointing triangle line (2-views dielectric cloak), dash-dot line (4-views dielectric cloak) and dashed line (8-views dielectric cloak); (c,d) SCS calculated at 25 GHz as a function of the DoA, same legend as in (a,b).