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We present a fully three-dimensional theoretical study of the extraordinary transmission of light through subwavelength hole arrays in optically thick metal films. Good agreement is obtained with experimental data. An analytical minimal model is also developed, which conclusively shows that the enhancement of transmission is due to tunneling through surface plasmons formed on each metaldielectric interfaces. Different regimes of tunneling (resonant through a "surface plasmon molecule", or sequential through two isolated surface plasmons) are found depending on the geometrical parameters defining the system. PACS numbers: 78.66. Bz, 73.20.Mf, 42.79.Dj, 71.36.+c In the last few years, and mainly due to advances in nanotechnology, there has been a renewed interest in exploiting the dielectric response of metals to make photonic materials [1][2][3]. For instance, the photonic insulating properties of metals can be used to trap incident radiation, focusing light in very small volumes [4][5][6]. Very recently [7], another interesting effect of light interacting with structured metals has been discovered: the transmission of light through subwavelength hole arrays made in a metal film can be orders of magnitude larger than expected from standard aperture theory [9]. Apart from its fundamental interest, this extraordinary transmission effect has potential applications [10,11] in subwavelength photolithography, near-field microscopy, wavelength-tunable filters, optical modulators, and flatpanel displays, amongst others. While the wavelength at which some transmission features appeared suggested [7,8] that surface plasmons (SP) [12] were involved in the process, the physical mechanism for the huge enhancement has not yet been elucidated. Some calculations have been performed for a simpler geometry: an array of slits [13][14][15], where high transmission was also predicted. However, although interesting in their own right, these results do not apply to the experimental situation.In this letter, we present the first fully threedimensional theoretical study of transmission through hole arrays, obtaining an excellent agreement with experimental data. Moreover, we develop a simplified version of the model that clearly captures the physics involved. Fig. 1 shows the experimental "zero-order" transmittance of light at normal incidence (T 00 ), through an array of holes in a free-standing metal film. The free-standing metal film, of which the fabrication is described elsewhere [8] consisted of a 220nm thick Ni core, perforated with a square array of holes by focused-ion beam milling. The film was subsequently overcoated with 50nm of Ag on both sides by sputter deposition which resulted in a coating of the walls of the holes as well as the in-plane surfaces of the film. The total thickness of the film was h = 320nm and the lattice constant of the hole array was L = 750nm. After coating the holes had an average diameter of 280nm. It has been shown [8] that such a "sandwich" structure has the same transmission properties as an eq...

Optically thick metal films perforated with a periodic array of subwavelength holes show exceptional transmission properties. The zero-order transmission spectra exhibit well-defined maxima and minima of which the positions are determined by the geometry of the hole array. We show that the minima are the collection of loci for Wood's anomaly, which occurs when a diffracted beam becomes tangent to the film, and that the maxima are the result of a resonant excitation of surface plasmons ͑SP's͒. SP's from both surfaces of the metal film are apparent in the dispersion diagram, independent of which side of the film is illuminated, indicating an anomalously strong coupling between the two sides. This leads to wavelength-selective transmission with efficiencies that are about 1000 times higher than that expected for subwavelength holes.

Transmission enhancements of order 1000 have been reported for subwavelength hole arrays in metal films and attributed to surface plasmon (SP) resonance. We show that the properly normalized enhancement factor is consistently less than 7, and that similar enhancements occur in nonmetallic systems that do not support SPs. We present a new model in which the transmission is modulated not by coupling to SPs but by interference of diffracted evanescent waves generated by subwavelength features at the surface, leading to transmission suppression as well as enhancement. This mechanism accounts for the salient optical properties of subwavelength apertures surrounded by periodic surface corrugations.