Analysis of Bloch Surface Waves at the Interface Between Two Semi-infinite Rugate Filters with Symmetric Refractive Index Profiles

Surface electromagnetic waves are representation of Maxwell’s frequency domain equations at the interface of two dissimilar materials. In this article, two canonical boundary value problems have been formulated to analyze the multiplicity of electromagnetic surface waves at the interface between two dissimilar materials. In the first problem, interface between two semi-infinite rugate filters having symmetric refractive index profiles is considered and in the second problem, to enhance the multiplicity of surface electromagnetic waves, a homogeneous dielectric slab is included between two semi-infinite symmetric rugate filters. Multiplicity has been observed by varying the size of dielectric material from 0 to 1000 nm. Numerical results show that the number of Tamm waves of different phase speeds, different polarization states, different degrees of localization, and different field profiles that are being propagated at interface between two semi-infinite rugate filters having symmetric refractive profile is almost twice as when asymmetric refractive index profile is used. Having two interfaces when a homogeneous dielectric layer is placed between two semi-infinite rugate filters has increased the multiplicity of electromagnetic surface waves.