The Role of Surface Plasmon Resonance in Enhanced Transmission Through Metallic Gratings

Abstract

We investigate the physical origin of enhanced transmission features of one-dimensional (1D) metal gratings and identify two different surface plasmon resonances which influence the transmission of electromagnetic wave through a perforated metallic slab (Ebbesen et al., Nature 391:667–669, 1998). Theoretical analysis, similar to Roszkiewicz and Nasalski (J Phys B At Mol Opt Phys 46(2):025401, 2013), is confirmed by numerical simulations of transmission spectra of various metallic gratings. Our structure is shown in Fig. 26.1. The metallic 1D grating is periodic in the x-direction with period p and uniformly extended along the y-direction. Relative metallic permittivity $\varepsilon _{m}(f) = 1 - f_{p}^{2}/(f^{2} + if\gamma )$ with f _p  = 2, 147 THz and γ = 5 THz. We argue that enhanced transmission can be explained as an effect of two types of plasmon resonances (Figs. 26.1 and 26.2): Lengthwise plasmon resonance – LPR (symmetric and antisymmetric) propagating along the two interfaces of the metal slab (Fig. 26.1). This resonance appears as a sharp maximum (or two maxima, respectively) and a sharp minimum (Cao and Lalanne, Phys Rev Lett 88:057403, 2002). LPR is excited when the wave vector of the plasmon resonance coincides with $k\sin \varphi + m(2\pi /p)$ ($m = \pm 1,\pm 2\ldots$). Crosswise plasmon resonance – CPR is excited in air gaps. The incident wave is guided through the grating if its frequency equals the CPR’s resonant frequency. Consequently, the CPR appears as a Fabry-Perot spectral resonance in the transmission spectrum when its wavelength λ corresponds to m(d∕2). Both plasmonic resonances could be represented by surface waves propagating along homogeneous slabs. Using this approximation, dispersion relations could be calculated as in Markoš and Soukoulis (Wave propagation: from electrons to photonic crystals and left-handed materials (Google eBook). Princeton University Press, Princeton, 2008). Results are shown in Fig. 26.2. The transmission spectrum was calculated numerically by our own numerical program based on the rigorous coupled-wave analysis – RCWA