Approximation of the effective refractive index of surface plasmons propagating along micron-sized gold wires in photonic crystal fibers

Since the first presentation of selectively metal filled photonic crystal fibers (PCFs) in 2008, a lot of work and effort has been put in the understanding of propagation characteristics of such fibers which can be utilized as filters or polarizers. A semi-analytical model for the implicit description of the effective refractive index of surface plasmon polaritons propagating (SPPs) along the metal wires has been developed and coupling of fiber core modes to such surface modes has been confirmed experimentally. In this work we will present a method for the fabrication of selectively metal filled photonic crystal fibers and derive the dispersion equation for micron sized wires in silica. We will present a ray-optical approximation of SPPs based on the dispersion of a planar dielectric-gold interface which leads to a full-analytical equation for the prediction of cutoff wavelengths of the SPPs.