Rigorous formulation of surface plasmon-polariton-waves propagation along the direction of periodicity of one-dimensional photonic crystal

A rigorous formulation of the canonical boundary-value problem is presented to find the surface plasmon-polariton waves guided by the interface of a one-dimensional photonic crystal and metal along the direction of the periodicity. The problem is formulated using the rigorous coupled-wave approach and a dispersion equation has been obtained. The Muller's method and Newton--Raphson method were used to obtain illustrative numerical results of the dispersion equation. The solutions were found to converge as the number of Floquet harmonics increased. This formulation does not require the computation of the photonic bandgaps and directly computes the surface-wave modes. This formulation could engender new applications of plasmonics exploiting the neglected interface along the direction of periodicity of the one dimensional photonic crystals.