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aperture radius that is negligible compared to the wavelength of the incident light, is able to reproduce the radiation pattern of small apertures over a large angular range. Remaining discrepancies at the largest radiation angles can be accounted for by the boundary condi- tions in the metallic coating. The above-mentioned empirical radiation dipole approach is formally justified for small radiation angles. In addition, it is shown that the angular power spectrum does not critically depend on the exact tip geometry. Especially the dependence on the taper angle is found to be very weak. 

Scatterring and general properties - In order to illustrate the main physical effects of small apertures in metallic surfaces, it is worthwhile to look at similar problems that have been treated historically. As already mentionned in the introduction, Rayleigh[1] and Bethe[2] (see also Ref. [3]) have studied the light diffraction by a subwavelength aperture in infinite, perfectly conducting screen. They have demonstrated that, in the far field, the diffracted electromagnetic field can be described by a combination of effective dipoles which depend on the local incident field ( E$_{inc}$ , B$_{inc}$ ) and on the hole size a : 

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The symbols ⊥ and ‖ refer to the perpendicular and tangential components of fields, respec- tively. These dipole terms are very similar to the induced dipole terms which appear in the well established Rayleigh-Mie theory of diffraction by a small perfectly conducting sphere: P$_{induced}$ = a $^{3}$E$_{inc}$ , M$_{induced}$ = − a 3 $_{2}$B$_{inc}$ . The principal difference arises in the substitution 2 → 1 2 between the magnetic and electric dipole. Strong analogies exist between the theory of diffraction by small hole and the theory of diffraction by small particles. We can under- stand the physical origin of these similitudes using the Clausius Mossoti formula. Indeed, following these formula, 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$_{0}$ is defined by: 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. In the opposite case, namely if ϵ/ϵ$_{0}$, µ$_{0}$/µ ≫ 1, we obtain the Rayleigh-Mie’s solution. 

The diffraction of light by a small aperture in a perfectly conducting plane can be qualita- tively regarded as the complementary case to the scattering of a wave by a small conducting 

