Multimodal propagation of the electromagnetic wave on a structured perfect electric conductor (PEC) surface

Spoof surface plasmon (SSP) on structured perfect electric conductor (PEC)–air interface is usually modeled by an effective plasma frequency in the long wavelength limit. In this limit, the effective permittivity model suggests a purely exponential decay of the field profile on both sides of the interface, drawing an analogy with a surface plasmon polariton (SPP)-like single mode (TM) propagation. However, most of the practical applications and experiments involving SSP fall in the regime where the feature-size of the structure is comparable to the wavelength. In this wavelength regime of practical interest, we show that in contrast to surface plasmon polariton (SPP), the propagation of the surface wave is hybrid involving both TM and TE modes. By combining angular spectrum representation and vector nature of the electromagnetic fields, we show that the field profile of SSP on patterned PEC can be described accurately by superposition of multiple evanescent orders caused by the diffraction from sub-wavelength features at the interface. This multimodal nature of the surface wave readily explains the anisotropic propagation observed earlier. Also, inclusion of at least one mode from higher order Brillouin zone is necessary for describing the near-field above the interface with reasonable accuracy.