Optical transmission at oblique incidence through a periodic array of sub-wavelength slits in a metallic host

Using the Bloch modes of a periodic, semi-infinite array of slits in a metallic host, we study the transmission of obliquely incident plane-waves through sub-wavelength slits. Matching the tangential E- and H-fields at the entrance facet of the periodic structure yields the complex amplitudes of the various Bloch modes, which exist and propagate within the slit array independently of each other. The computational scheme is robust, convergence is rapid, and a good match at the boundaries is obtained in every case. The regions examined in some detail include the vicinity of the Wood anomaly (where new diffraction orders appear/disappear on the horizon), the neighborhood of a point where surface plasmon polaritons (SPPs) are excited, and an ordinary situation in which the incidence angle is far from the angles that invoke Wood's anomaly or cause the excitation of SPPs. Field distributions and energy flow diagrams in and around the slits reveal the existence of transmission minima (and reflection maxima) at incidence angles associated with the excitation of SPPs.