Optical waveguides have been a subject of an intensive theoretical research, resulting in applications in several fields, and stimulated research in integrated optics. Homogeneous dielectric waveguides and their properties are covered in detail in many articles and textbooks. However, in waveguides loaded with arbitrary inhomogeneous dielectrics, analytical solutions are possible only for a limited number of permittivity profiles in simple geometries. The analysis of longitudinally inhomogeneous waveguides has been already proposed, but the main drawback of this approach is that it requires cumbersome and time-consuming integration. We therefore suggest to take this a step further by applying our new original analytical approach that does not require integration. The aim of this work is to establish a different method that is generally applicable to any vectorial time-dependent, anisotropic, non-linear, inhomogeneous, dissipative and dispersive media to analyze the field distribution of inhomogeneous 1-D and 2-D waveguides with symmetric and asymmetric permittivity profiles. Our initial consideration of slab problems with arbitrary profiles by means of analytical method shows a great deal of potential for use in applications in fields such as physics, and engineering.
Spoof plasmons are bound electromagnetic waves (EM) at frequencies outside the plasmonic range mimicking (“spoofing”) surface plasmons (SPs), which propagate on periodically corrugated metal surfaces. In recent years, electromagnetic waves propagating at an interface between a metal and dielectric have been of significant interest. Although most plasmonic research so far has focused on the near-infrared and optical ranges of the electromagnetic spectrum (where noble metals support highly confined surface waves), there exists an increasing interest in transferring SPs-based photonics to lower frequencies. However, in these spectral ranges, noble metals behave like perfect electric conductors, whose surface charges are able to screen any external EM excitation with extreme efficiency, preventing the formation of a tightly bound SP. It has been shown that the binding of EM fields to a metal surface can be increased by its corrugation. A surface of a metal perforated with a one-dimensional periodic array of rectangular grooves has already been considered. The question that remains open is the calculation of the effective permittivities for arbitrary grooves. The number of works describing the calculation of the effective dielectric constants for the grooved surfaces is limited. Here we have obtained an analytical dispersion relation of spoof plasmons on an arbitrary perforated surface of a real metal. We have derived analytical expressions for calculation of the permittivities of arbitrary grooves. Based on those results we have determined the minimum spot size for a triangular groove structure.