Characteristic Of Surface Plasmon Polaritons In One-dimensional Semi-infinite Metal/Dielectric Photonic Crystals

Owing to the unique optical properties of metal/dielectric photonic crystals(PCs), they have large application value which are widely used in many fields and are worth discussing in theory. These properties mainly originate from the surface plasmon polaritons(SPPs). Hence, it is necessary and significant to study the SPPs in metal/dielectric PCs. In this paper, the SPPs in one-dimensional semi-infinite metal/dielectric PCs, transversely-truncated and obliquely-truncated metal/dielectric PCs have been investigated theoretically by transfer matrix method and effective medium method.Considering the nonlinear relationship between amplitude of the light field and attenuation coefficient, we have made theoretical extension of the SPPs theory in one-dimensional semi-infinite metal/dielectric PCs. Dispersion equations of the SPPs are obtained in different situations. The SPPs dispersion curves in onedimensional semi-infinite silver/air PCs are numerically calculated and we get new SPP modes. The physical origins of new SPP modes are presented by comparing the SPPs in one-dimensional semi-infinite silver/air PCs with the SPPs in the isolated silver film.We present a theoretical method to solve the SPPs in one-dimensional semiinfinite transversely-truncated metal/dielectric PCs. This method combines the concept of effective medium method with the transfer matrix method. The effect of inter-layer interfaces in the metal/dielectric PCs and PC periodicity on the SPP dispersion relation are taken into consideration efficiently. The one-dimensional semi-infinite transversely-truncated silver/Si O2 PCs is regarded as a specific example. We numerically calculated the dispersion spectrum of the SPPs. A series of separated SPP modes are found and highly localized at the surface. These results obviously show the effect of inter-layer interfaces and PC periodicity on the SPPs and the limitation of effective medium method.A one-dimensional semi-infinite obliquely-truncated metal/dielectric PCs is presented. The properties of the SPPs are investigated in a particular propagating geometry with effective medium method and an extraordinary SPP mode is obtained analytically. The dispersion curves of the SPPs in the metal/Si O2 PCs are got in numerical calculation. Our theory point that the parallel component of the wave vector of the SPP mode propagates along the surface of PCs and the vertical component of the wave vector of the SPP mode is a travelling wave, so the propagation direction of the SPP mode seriously deviates from the surface. We discuss the direction of Poynting vector and localization of the SPP mode. Poynting vector of the SPP mode either is parallel to the in-plane wave vector of the SPP mode or it is anti-parallel to the in-plane wave vector of the SPP mode.