(which corresponds to r → + ∞ for the static Laplace equation where λ → + ∞ ). In the particular case of an incident plane wave, it reduces to a electromagnetic dipole field (see Fig. 1). The corresponding effective dipoles P eff and M eff depend on the aperture radius and on the incident electromagnetic field E$_{0}$ , B$_{0}$ as given by the formula P eff = ∓ 1 3 $_{π}$a $^{$^{3}$E$_{0}$$_{,}$}$⊥ , M eff = ± 2 3 $_{π}$a $^{$^{3}$B$_{0}$$_{,}$}$‖ . The signs in front of the expressions refer to the “incident + reflected” domain and to the “transmitted” domain, respectively. It is interesting to note that the factor of 2 between M eff and P eff appears in all similar situations as we will see throughout this paper. The physical signification of the Bethe dipoles can be understood using the Clausius Mossoti[16] formula. It describes the polarization produced by a locally constant electromagnetic field E$_{0}$ , B$_{0}$ in a small dielectric sphere of constant permittivities ϵ, µ which is immersed in a homogenous medium with permittivities ϵ$_{0}$, µ$_{0}$ . According to this formula, we have P = ϵ$_{0}$ ϵ/ϵ$_{0}$ − 1 ϵ/ϵ$_{0}$ $_{+2}$a $^{3}$E$_{0}$ , and M = 1 µ$_{0}$ µ/µ$_{0}$ − 1 µ/µ$_{0}$ $_{+2}$a $^{3}$B$_{0}$ . With the condition ϵ/ϵ$_{0}$, µ$_{0}$/µ ≪ 1 for a hole in a perfect metal, we obtain the following two relations: P = − ϵ$_{0}$ 2 a $^{3}$E$_{0}$ , M = 1 $_{µ$_{0}$}$a $^{3}$B$_{0}$ which are related by the same factor of 2 as for the Bethe case. The diffraction of light by a small aperture in a perfectly conducting plane can be regarded as the complementary case to the scattering of a wave by a small conducting particle. This point of view is in agreement with the electromagnetic Babinet[17] theorem which yields this result directly ( see Smythe [9], Landau [18]). Rayleigh has developed the theory of diffrac- tion by small particles and has found that the shape of the particle is not a fundamental parameter if one is interested in the far-field pattern of the scattering wave only. This is due to the fact that the light cannot distinguish the shape of the particle if the wavelength is very large compared to a . Therefore, we anticipate that the existence of two effective dipoles and their far-field behavior is very general and does not depend on the shape of the small hole or the screen geometries. The exact expressions of these dipoles may depend on the hole shape and their directions may differ from the Bethe case, but the factor of two between M and P as well as the presence of the fields and their dependance on the third power of the radius constitute probably a general result. A validity criterion for this statement can be found in the curvature of the surface at the hole location. If the curvature is too strong (i. e. if the curvature radius is too small), the hypothesis cannot be considered as reasonable due to the presence of strong boundary effects at the surface. Therefore, we expect the validity of the dipole model to diminish with the curvature radius. More precisely, the spatial domain in which the dipole model is applicable reduces progressively to a small solid angle around the 4