Under certain circumstances, plasmonic coatings could be a solution to the design of stealthy targets over the microwave range. In this communication, Perfectly Electrically Conducting (PEC) spheres with plasmonic coatings are studied in the microwave spectrum. Two main issues are raised. The first one is related to the fact that the exact computation of the Radar Cross Section (RCS) of finely textured targets with overall dimensions greater than the wavelength of interest often leads to problems of hundreds of thousands of unknowns, resulting in high CPU time consumption. The question then arises with respect to the most appropriate effective medium approximation one should use in order to correctly describe the electromagnetic behaviour of the coating. In this context, a relevant diamagnetic homogenization model is proposed. The resulting approximated RCS computations are in good agreement with the exact full wave solution over a broad range of microwave frequencies. Next to this purely numerical approach, the second issue was to design and to manufacture a textured spherical metallic target so as to bring sound experimental evidence to the calculated theoretical microwave response. Relying on computer-aided additive manufacturing, a periodically grooved metallic sphere has been realized successfully. Eventually, as we shall see, experimental RCS measurements of a periodically grooved metal sphere and the corresponding theoretical computations compare fairly well.

The Characteristic Mode Theory is a valuable tool in RCS analysis. Although the mathematical framework is established in the context of PEC objects, we apply the eigenvalue decomposition on Scattering Operators of coated objects, which coating is modeled by an impedance condition on the surface. We show that the computed scattering operators exhibit the mathematical properties indicated by the theory, and exhibit an empirical möbius transform between the value of the impedance coating, and the first eigenvalue of the decomposition of the operator. This could be successfully used as a zero order model for the RCS of the object.

As far as RADAR Cross Section (RCS) computations are concerned, meshing inclusions much smaller than the wavelength of interest λ to model microscopic details often leads to untractable problems when target dimensions are much greater than λ. Consequently equivalent material parameters are necessary, and they can be derived from “effective medium approximations” (EMA). In this work we focus on EMA introduced by Pendry et al. (“Mimicking surface plasmons with structured surfaces”, Science, vol. 305, p. 847, 2004) and further investigated by Garcia-Vidal et al. (“Surfaces with holes in them: new plasmonic metamaterials”, Journal of Optics A, vol. 7, p. S97–S101, 2005) in relation with perfect electrical conductors perforated with grooves. The EMA anisotropic dielectric permittivity can be deduced from extended Bruggeman theory. The EMA magnetic permeability must be modified to correct the effective index: the product εμ is forced to be equal to 1 so as to ensure a correct phase velocity in the grooves.

In anechoic chambers, the quality of RCS measurements is limited by couplings with the walls. In this work new calibration targets are introduced to assess these couplings. The idea is to get null monostatic RADAR Cross Section at some desired frequency by designing suitable plasmonic coatings. Such coatings are obtained on a metallic object by performing periodic grooves. They are thus an interesting alternative to standard RADAR Absorbing Materials whose constitutive parameters are not always well-known. Under a rotational symmetry assumption, very accurate RCS computations are possible up to several tens of GHz.

We review the characteristic current decomposition, first introduced by Garbacz (1968, A generalized expansion for radiated and scattered field. Ph.D. Dissertation, Ohio State University, Columbus) and then by Harrington & Mautz (1971, Theory of characteristic modes for conducting bodies. IEEE Trans. Antennas Propag., AP-19, 622-628). Our approach is based on the study of the scattering operator, or scattering matrix, the unitarity property of which plays a central role. The spectral decomposition of this operator leads to a particular characteristic far fields (or eigenfar-fields), from which a set of characteristic currents can be derived. These currents are those of Garbacz, Harrington and Mautz. They satisfy a generalized eigenequation involving usual integral operators split according to the regular/singular decomposition of the free space Green kernel. We provide proof of existence, denseness and orthogonality for these sets of characteristic modes (both currents and far fields). In addition to its theoretical interest, our analysis is motivated by its application to radar cross-section (RCS) analysis, where this particular decomposition turns out to be a powerful tool, especially for objects of small dimensions compared with the wavelength of the incident wave. Numerical computations are presented for a general three-dimensional object and the electrical field integral equation, including the first characteristic currents and their analyses in terms of their impact on the monostatic RCS.

RCS issues lead to problems of hundreds of thousands of unknowns as soon as the target gets greater than the wavelength. For computational limiting reasons, details of the coating cannot thus be meshed, even if they play a key role like in metamaterial design. Equivalent boundary conditions or effective medium approximation are then necessary. In this paper we consider spheres with plasmonic coatings. Exact and approximated RCS computations are compared over a broad range of RF frequencies.

The monostatic theorem of Weston states that a null radar cross section (RCS) will be observed for objects with rotational symmetry that are impedance matched to their host medium, i.e., that have their material parameters ε r =u r . A study of the generalization of this result applied to heterogeneous magnetodielectric (MD) scatterers is presented. The entire object of interest is divided into a set of small cubical unit cells in a three-dimensional checkerboard format, i.e., two different materials are distributed alternately in lego-like designs. Numerical computations are presented to compare the RCS levels of perfectly impedance-matched scatterers and their lego-based equivalents. The degree of homogenization that can be attributed to these heterogeneous scatterers for a variety of double positive material choices, including extreme values, is addressed specifically in relation to their satisfaction of Weston's theorem.

This work deals with the modeling of embedded antennas on aircrafts. A standard GPS patch antenna is chosen as a reference case to illustrate a comprehensive work from design to evaluation. To fit the topic of the special session, we focus on the disturbances on both impedance matching and radiation patterns induced by embedding in a cavity. Finally we explain how to adapt the antenna definition in order to compensate the coupling with its environment.

This work deals with electromagnetic modeling, RCS analysis and classification in the Low Frequency domain, that is to say for objects whose dimensions are close to the wavelength of the incident wave. More precisely a method for characterizing RADAR signatures using eigenvectors of the scattering matrix is developed. Indeed the spectral decomposition of this operator leads to particular characteristic far fields (or eigenmodes), from which a set of characteristic currents can also be derived. Numerical computations are presented for 3-D objects and the Electrical Field Integral Equation (EFIE), including the first characteristic currents and their analysis in terms of their impact on both the monostatic and the bistatic RCS. Use of these modes in RCS analysis and classification seems to be worth being considered.

The monostatic theorem of Weston states that a null RCS is observed for matched ε = μ objects with rotational symmetry. In this work we study a generalization of this result applied to heterogeneous magnetodielectric scatterers. The whole object of interest or the coating surrounding it is divided into a set of small cubical unit cells that are alternatively either purely dielectric or purely magnetic, i.e., the two materials are distributed in a lego format. Numerical computations are presented to compare the RCS levels of the original perfectly and the lego-based roughly impedance-matched scatterers.

In this paper we consider Maxwell's equations together with a dissipative non-linear magnetic law, the Landau-Lifchitz-Gilbert equation, and we study long time asymptotics of solutions in the 1D case in an innnite domain of propagation. We prove long-time convergence to zero of the electromagnetic eld in a Fr echet topology deened by local energy seminorms: this corresponds to the local decay of energy. We then introduce that the set of stationary states for the Landau-Lifchitz-Gilbert equation and prove that it corresponds to the attractor set for the distribution of magnetization whose presence is one of the characteristics of ferromagnetic media. Keywords: Maxwell's equations-Landau-Lifchitz-Gilbert law-local decay of energy-Liapunov theory-long-time asymptotics. Comportement aux temps longs d'une couche ferromagn etique 1D R esum e : Nous consid erons dans ce rapport les equations de Maxwell coupl ees avec une loi de comportement magn etique dissipative et non lin eaire, la loi de Landau-Lifchitz-Gilbert, et nous nous int eressons dans le cas monodimensionnel au comportement asymptotique des solutions pour les temps longs. Nous montrons la d ecroissance locale vers 0 du champ electromagn etique, r esultat directement li e a la d ecroissance locale de l' energie. Nous introduisons ensuite l'ensemble des etats d' equilibre pour l' equation de Landau-Lifchitz-Gilbert, et nous montrons qu'il s'agit en fait d'un ensemble attracteur pour la distribution d'aimantation. Mots-cl e : Equations de Maxwell-loi de Landau-Lifchitz-Gilbert-d ecroissance locale de l' energie-comportement asymptotique aux temps longs-th eorie de Liapunov.

This paper deals with the dynamic modelling of thin ferromagnetic layers, based on the coupling of Maxwell's equations with the nonlinear Landau-Lifschitz-Gilbert law. A 2-D micromagnetic model is described which involves a FDTD code to determine equilibrium configurations and a finite element method to compute magnetostatic fields. Finally, after linearization, the susceptibility spectra of films supporting a weak-stripe-domain structure are computed and successfully compared to existing measurements without introducing any fitting parameter.

Our goal in this work is to establish the existence and the uniqueness of a smooth solution to what we call in this paper the corner problem, that is to say, the wave equation together with absorbing conditions at two orthogonal boundaries. First we set the existence of a very smooth solution to this initial boundary value problem. Then we show the decay in time of energies of high order-higher than the order of the boundary conditions. This result shows that the corner problem is strongly well-posed in spaces smaller than in the half-plane case. Finally, specific corner conditions are derived to select the smooth solution among less regular solutions. These conditions are required to derive complete numerical schemes.

In this Note, we return to the theory of characteristic modes which was introduced 30 years ago for electromagnetic scattering problems. A simple mathematical framework is proposed and complete definitions are given. The potential interest of this theory in terms of Radar Cross Section (RCS) analysis is then discussed, especially in the low frequency case. Finally, a 3-D example is presented to illustrate the efficiency of this decomposition. (C) 2004 Academie des sciences. Publie par Elsevier SAS. Tons droits reserves.