Optical transmission through metal films with a subwavelength hole array in the presence of a magnetic field

Abstract

In a recent paper Ebbesen et al. ͓Nature ͑London͒ 391, 667 ͑1998͔͒ reported on extraordinary optical transmission through periodic hole arrays in metallic films. They explain this by the coupling of light with surface plasmons. Continuing this idea, we have studied such systems in the presence of a static magnetic field. The problem is treated in the quasistatic limit, i.e., when the wavelength is larger than the hole sizes and the array period. We find that the frequency of the transmission peak depends strongly on both the magnitude and the direction of the applied in-plane magnetic field. The directional sensitivity results in a magneto-induced anisotropy of the optical properties of such systems, even for hole arrays with square or triangular symmetry. ͓S0163-1829͑99͒51120-X͔Recently it was reported that arrays of submicrometer cylindrical cavities in metal films display highly unusual transmission spectra at wavelengths larger than the array period, when no wavelength sensitive interference should occur. 1,2 These unusual optical properties are apparently due to the coupling of light with plasmons on the surface of the periodically patterned metal film. 1-3 Continuing this idea, we have studied such systems in the presence of a static, inplane magnetic field B 0 . We find that the precise frequencies of the sharp peaks in the transmission spectra depend strongly on the magnitude of B 0 , as well as on its direction. The directional sensitivity results in a strong magnetoinduced anisotropy of the optical properties. This is similar to the anisotropic magnetoresistance recently found in periodic conducting composites 4-7 and also to the anisotropic macroscopic dielectric properties recently predicted to appear in metal/dielectric composites in the vicinity of a sharp quasistatic resonance. 8 The present discussion is also based upon the quasistatic approximation. In that respect it differs significantly from photonic band discussions of metal/ dielectric composites like, e.g., Ref. 9.Let us consider a geometry which corresponds to the above-mentioned experiment: 1,2 A metal film, with a square array of identical perpendicular cylindrical holes, is placed in a static, in-plane magnetic field B 0 directed along the principal axis z. A monochromatic light beam, of angular frequency , impinges upon this film along the perpendicular axis y, with linear polarization along the principal axis x of the array-see Fig. 1͑a͒. The local a.c. permittivity tensor of the metal can be written as 8where 0 is the scalar dielectric constant of the background ionic lattice, Î is the unit tensor, and where we used the free-electron Drude approximation for the conductivity tensor with B 0 ʈz. The magnetic field enters only through the Hall-to-Ohmic resistivity ratio Hϵ H /ϭ xy / xx ϭ͉B 0 ͉ ϭ c , where c ϭeB/mc is the cyclotron frequency, is the conductivity relaxation time, p ϭ(4e 2 N 0 /m) 1/2 is the plasma frequency, N 0 is the charge carrier concentration, is the Hall mobility.Treating the cylindrical holes as dielectric inclusio...

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