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antenna. In this limit β and a/β tend to zero, and we can write 

<img src='content_image/361429.jpg'>

The effective electric and magnetic dipoles are linked by M$_{eff}$ = 2 e$_{z}$ × P$_{eff}$ and by the generalized Bethe relation P$_{eff}$ ∝ a $^{3}$E$_{inc}$ where E$_{inc}$ denotes the incident light polarization. Also, the factor of 2 reappears which is common to all cases of diffraction by a subwavelength aperture as precedently explained. The two-dipole model has another significance because the general expression Eq. 4 converges to Eq. 5 for small azimuthal angles θ . As a direct consequence the phenomenological Oberm¨ uller-Karrai’s model is justified and constitute a good approximation valid for small azimuthal angles. 

Results and discussion - The following Figs. 2,3 show experimental data for both S- and P-polarization and compare them with the calculated profiles of our model. Also shown are the curves for the simpler two-dipole model which is a good approximation only for smaller angles. There are no adjustable parameters in both models. 

As shown in Fig. 2 (S-polarization), our model and the Oberm¨ uller-Karrai model are equivalent for the experimentally accessible angles. They follow the experimental data for all recorded angles. This behavior is different for the P-polarization as shown in Fig. 3. Our model predicts an important “backscattering” in good agreement with the experiment. The two-dipole model does not correctly predict this effect. Qualitatively, the difference between both polarisations can be understood by realising that the Poynting lines in the P-polarisation are tangential to the metal surface, and are consequently very sensitive to boundary conditions on this surface, while in the other polarisation, Poynting lines tend to avoid the metal surface because both the electric and magnetic fields vanish there. The quasi-multipole model is nevertheless in disagreement with the measured data for extreme θ values. We believe that this discrepancy is due to several effects. First, there are strong near-field effects on the surface of the metallic cone which are not accounted for in the model. They appear in higher order terms in the quasi-multipole expansion (these terms are not considered here). Additionally, incoherent scattering due to surface roughness reduces the collected light for large angles which could explain the discrepancy. 

Conclusion - In summary, we have developed an analytical model for the far-field trans- mission pattern of conical, metal-coated fiber tips with a small, subwavelength aperture. It 

