Optical surface plasmons at a metal-crystal interface with the Drude-Lorentz model for material permittivity

The theory of surface electromagnetic waves (SEMWs) propagating at optical frequencies along the interface of an isotropic noble metal [e.g., gold (Au)] and a uniaxial crystal [e.g., Rutile (TiO$_2$)] is revisited with the Drude-Lorentz (DL) model for the complex dielectric material permittivity $(\epsilon_p)$. The latter accounts for the contributions of both the \textit{intraband} transitions of the free electrons and the multiple \textit{interband} transitions of the bound electrons in metals. The propagation characteristics of the wave vectors and wave frequency of SEMWs, the hybridization factors, i.e., the amplitude ratios between the transverse-electric (TE) and transverse-magnetic (TM) modes in the isotropic metal, and between the ordinary and extraordinary modes in the uniaxial substrate are studied numerically. It is found that the results are significantly modified from those with the Drude model for $\epsilon_p$, especially in the short-wavelength spectra ($\lambda\lesssim500$ nm) and with a small deviation of the orientation of the optical axis. The excitation of such SEMWs can have novel applications in transportation of EM signals in a specified direction at optical frequencies ($\sim$ PHz).