## 1 Introduction

[2] The electromagnetic wave scattering from a target in the forward scattering (FS) region (when the target lies in the transmitter-receiver baseline) [*Siegel*, 1958] is a very interesting phenomenon which was first reported by Mie in 1908 when he discovered that the forward scattered energy produced by a sphere was larger than the backscattered energy [*Glaser*, 1985] in a high-frequency domain. This configuration, which corresponds to a bistatic angle near 180°, is a potential solution to detect stealthy targets. Indeed, in a high-frequency domain and in the forward scattering direction, the RCS (radar cross section) is mainly determined by the silhouette of the target seen by the transmitter and is almost unaffected by absorbing coatings or shapings. This phenomenon can be physically explained by the fact that the scattered field in the forward direction represents the perturbation to the incident wave as a blocking effect, which creates a shadowed zone behind the target. In this region, while the total field vanishes, the scattered field tends to the incident field in amplitude but with opposite phase. A simple explanation can be given using the Babinet principle [*Siegel*, 1958] (BP), which states that the diffraction pattern (in the forward direction) of an opaque body is identical to that of a hole (in a perfectly conducting screen) having the same shape as its silhouette.

[3] Nevertheless, the physical optics (PO) approximation is sometimes used instead of the BP [*Glaser*, 1985, 1989; *Kildal et al.*, 1996] and provides good results around the forward direction. *Ufimtsev* [2007, 1990, 1992, 2008, 2009] studied the shadow radiation and demonstrated that the PO approximation can be split up into two components [*Ufimtsev*, 2007, 2008]: one which mainly contributes in the backward direction and thus corresponds to a reflected component, and the other one which mainly contributes in the forward direction and thus corresponds to a shadowed component. This last component corresponds to the radiation of a blackbody. Ufimtsev demonstrated that it can be reduced to a contour integral on its shadow contour by applying integral equations and boundary conditions on two objects having the same shadow contour, the shadow contour being the frontier between the illuminated surface and the shadowed surface of an object. Nevertheless, since he considered blackbodies, *Ufimtsev* [2009] did not study theoretically the behavior of the reflected component in the shadow zone.

[4] By contrast, *Gordon* [1975] did not consider a surface of arbitrary shape like Ufimtsev did with blackbodies but applied the physical optics for calculating the diffraction through apertures: this corresponds to the use of BP. Then, he showed that the surface integral on the flat area of the aperture can be reduced to a line integral on the contour of the aperture and demonstrated that this line integral can be analytically computed if the aperture is a polygon. In a more recent study [*Kubické et al.*, 2011] for the scalar case (2-D problems) it was demonstrated that the shadowed component of PO of an arbitrary-shape object is directly related to BP.

[5] The study is generalized to the vectorial case (3-D problems) for an arbitrary perfectly electric conducting object (not only a blackbody: a perfectly electric conducting (PEC) object being a more general case of the blackbody since the reflection is also considered) in order to obtain a more complete physical insight into the connection between PO and BP. First, a demonstration of the shadow contour theorem, which is different from that of Ufimtsev since an arbitrary perfectly conducting object is considered, is provided. Moreover, the link between the BP and the PO approximations is studied for any object (not only a flat surface as Gordon did): the main conclusion is that BP can be seen as a good approximation of PO in the forward direction. Then, the behavior of the reflected component of PO in the shadow zone is theoretically studied. Last, numerical results compare BP and PO in order to illustrate the theoretical investigations made before. The time convention *e*^{+iωt} is omitted throughout the paper.