Nonzeroth-order anomalous optical transparency in modulated metal films owing to excitation of surface plasmon polaritons: An analytic approach

The problem of anomalous light tunneling through periodically modulated metal films is examined in a purely analytical approach. The approach uses large magnitude of the dielectric permittivity of metals in the visible and near-infrared (it is equivalent to that resulting in the Leontovich boundary conditions for semi-infinite problems). It is shown that the anomalous transparency recently discovered experimentally is caused by the excitation of single-or double-boundary surface plasmon polaritons due to film modulation. Dependences of the resonance transparency on parameters of the problem are analyzed in detail, and the optimum parameters (optimal layer thickness and optimal modulation amplitude) corresponding to extreme values of the transmittance of both zero and nonzero diffraction orders have been found. Classifying the possible types of resonances has allowed the identification of special and nontrivial features of the effect. In particular, we predict strong nonzeroth-order anomalous transparency.