The uniqueness of inverse scattering problems, reciprocity principles, and nonradiating sources related to low-signature structures

TL;DR

This work analyzes low-signature PEC structures consisting of two horizontal walls with cavities to achieve negligible scattering of time-harmonic TM plane waves. It employs a high-precision boundary-integral method with RCIP to study direct scattering, the (non)uniqueness of the inverse problem, reciprocity constraints on the far-field, and the existence of nonradiating near-field sources. The authors establish three key results: (i) the inverse scattering problem for a 2D PEC boundary can be non-unique when data are restricted to a single frequency; (ii) a Lorentz reciprocity relation implies $F^{\rm sc}(0)\approx F^{\rm sc}(\pi)\approx0$ for invisible structures under arbitrary TM excitations; (iii) nonradiating sources induced by incident waves can produce large near-fields while radiating negligibly to infinity. These findings have implications for low-observable technologies and cloaking-like devices, demonstrating both broadband and narrowband designs that minimize scattered power and revealing subtle theoretical aspects of scattering, reciprocity, and nonradiating sources.

Abstract

This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects. Theoretical investigations of the properties of the structures combined with accurate numerical computations lead to three key findings: the first concerns the uniqueness of the solution to an inverse scattering problem, the second establishes a reciprocity relation for the far-field scattering amplitude, and the third reveals the existence of non-radiating sources that generate substantial electromagnetic fields near the source region. The results have applications in low-observable technology.

Figures (11)

• Figure 1: The geometric cross section of a broadband low-signature structure with a fusiform cavity with two cusps. The geometry is specified in \ref{['geombroad']}. For the unit of length, see Remark \ref{['rem:length']}.
• Figure 2: The geometric cross section of a narrowband low-signature structure. The cavities are half ellipses with major axis $w$, minor axis $w/2$, and form a finite-periodic pattern with period $d$. The horizontal walls are specified in \ref{['geomnarrow']}. For the unit of length, see Remark \ref{['rem:length']}.
• Figure 3: $\Sigma$ as a function of $k$ for the fusiform cavity in Figure \ref{['combgeom']}. Dashed red line: without horizontal walls. Solid blue line: with horizontal walls. The minimum is at $k=1.505395$.
• Figure 4: The structure in Figure \ref{['combgeom']} illuminated by \ref{['incidentperp']} at $k=1.505395$; (a) $\log_{10}$ of $\vert H^{\rm sc}({\boldsymbol\rho})\vert$; (b) $\log_{10}$ of estimated absolute pointwise error in $H^{\rm sc}({\boldsymbol\rho})$.
• Figure 5: The structure in Figure \ref{['combgeom']} illuminated by \ref{['incidentObl']} at $k=1.505395$. Red line: $\log_{10}$ of $\vert F^{\rm sc}(\theta)\vert$ at oblique incidence with $\alpha=\pi/3$; Blue line: $\log_{10}$ of $\vert F^{\rm sc}(\theta)\vert$ at perpendicular incidence ($\alpha=0$);

Theorems & Definitions (1)

• Remark 1