Ultraviolet light scattering by a silicon Bethe hole.

Bethe's theory predicts that scattering by a small hole on a thin perfect electric conductor (PEC) is presented as radiation by an in-plane magnetic dipole of the incident magnetic field direction. Even in the near-infrared range where metals are no more PEC, the magnetic dipole radiation of Bethe holes has been demonstrated. However, such Bethe holes' nature has not been addressed yet in the ultraviolet (UV) range where conductivity of metals becomes severely deteriorated. Meanwhile, UV plasmonics has been elevating its importance in spectroscopy and photochemistry, recognizing silicon (Si) as an alternative plasmonic metal featuring the interband transition in the UV range. In this work, we expanded the Bethe's theory's prediction to the UV range by investigating Si Bethe holes theoretically and experimentally in terms of the scattering pattern and polarization. Simulation results showed that the scattered field distribution resembles that of an in-plane magnetic dipole, and the dipole direction at oblique incidence is roughly given as the incident magnetic field direction with a deviation angle which can be predicted from the Fresnel equations. Simulation with various diameters showed that the magnetic dipole nature maintains with a diameter less than the quarter-wavelength and multipoles becomes noticeable for diameters larger than the half-wavelength. We performed scattering polarization measurement at 69-degree incidence, which confirms the theoretical analysis. The features of Si Bethe holes demonstrated here will be useful for designing UV plasmonic metasurfaces.