Strong discontinuities in the complex photonic band structure of transmission metallic gratings

Abstract

Complex photonic band structures (CPBS) of transmission metallic gratings with rectangular slits are shown to exhibit strong discontinuities that are not evidenced in the usual energetic band structures. These discontinuities are located on Wood's anomalies and reveal unambiguously two different types of resonances, which are identified as horizontal and vertical surface-plasmon resonances. Spectral position and width of peaks in the transmission spectrum can be directly extracted from CPBS for both kinds of resonances.Recently, metallic films with sub-wavelength apertures became the subject of increasing interest. Experiments show that 2D arrays of sub-wavelength holes in metallic films can lead to extraordinary transmission of light [1][2][3][4][5]. These properties have been attributed to the excitation of coupled surface-plasmons on the upper and lower surfaces of the grating. The ability of these structures to control light has been shown [6,7], and applications have already been proposed in order to exploit these properties in different fields, such as electromagnetic filters or photolithography.Electromagnetic calculations have been carried out by Porto et al.[8] in order to study the mechanisms that enhance the transmission of light through metallic gratings with very narrow slits. They distinguished two different mechanisms, that is the excitation of coupled surface plasmon polaritons on both surfaces of the metallic grating, and the coupling of incident plane waves with waveguide resonances located in the slits. They correspond respectively to surface-plasmon bands and flat bands in the energetic band structure. Similar resonances located in grooves have also been observed experimentally and numerically in the reflected light of metallic gratings [9][10][11].Complex photonic band structures (CPBS) were previously calculated by Kuzmiak et al. for 2D periodic systems with metallic components [12], in order to obtain the attenuation and the lifetime of each mode. CPBS allowed a splitting of the lifetime of degenerate modes at Brillouin-zone boundaries to be observed.In this Letter, we will show that, in the case of rectangular metallic gratings, complex dispersion curves demonstrate the existence of a new kind of discontinuities. Much stronger than for 2D periodic systems, they are located on Wood's anomalies. They correspond to the transition between two different types of resonances, identified as horizontal and vertical surface-plasmon resonances. The first one is a periodic structure resonance, the second one is a FabryPerot like resonance. The discontinuity can be up to four orders of magnitude. Moreover, we will see on zero-order transmission spectra that the calculated complex frequencies are in excellent accordance not only with the spectral position, but also with the width of resonances' peaks. Fig. 1 shows the structure studied in this Letter, which is similar to the one of Porto et al. [8]. In the following, the period of the grating d = 3.5 µm and the width of the slits a = 0.5 µm will be kep...

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