Study on the maximum effective refractive index of single interface surface plasmon-polariton waveguide

The maximum effective refractive index (ERI) and its corresponding material match relationship of planar single interface SPP waveguide are theoretically analyzed and their approximate analytical equations are deduced, taking the loss factor of the metal in consideration. When the match relationship between the metal and insulator permittivity is satisfied, the SPP waveguide is on resonant state and the maximum ERI is obtained. In case of metal Ag, compared with those results obtained from more precise numerical calculation, the errors of the evaluated maximum ERI and its corresponding insulator permittivity are less than 3%. For single interface SPP waveguides, the maximum ERI is approximately proportional to the real part of the metal dielectric constant and inversely proportional to the square root of the imaginary part. By decreasing the loss of metal not only is the propagation distance lengthened but also the maximum ERI increased.