Cylindrical Plasmonic Waveguides Cladded by Hyperbolic Metamaterials

　　Conventional dielectric waveguides, such as optical fiber, cannot operate at the nanoscale due to the diffraction limit that light cannot be guided within the subwavelength structures. Plasmonic waveguides (PWs), guiding surface plasmon-polaritons (SPPs)––a form of surface waves which have smaller effective wavelength at the same frequency, make light can propagate in subwavelength dimensions and have been used in photonic integrated circuits. However, the propagation length of SPPs in PWs are limited due to the losses of metal. Hybrid plasmonic waveguides (HPWs) combine the advantages of the dielectric waveguides and the PWs, which have a balanced performance between high confinement and long-range propagation. On the other hand, anisotropic material has been used to control the optical momentum of waves in different directions. In this study, we propose and analyze a new design of cylindrical PWs based on strongly anisotropic media––hyperbolic metamaterial, that is, cylindrical PWs cladded by hyperbolic metamaterials or metal–dielectric–hyperbolic (MDH) cylindrical waveguides. This new type of waveguides has similar function as the HPWs with high field confinement and the long propagation length. 　　We analytically solve the basic properties of the MDH cylindrical waveguides: First, we derive the dispersion equation of three-layer anisotropic cylindrical waveguides based on Maxwell’s equations. Second, the propagation constant, propagation length, mode area and the figure of merit (FOM) of the transverse magnetic modes are obtained from the dispersion relation. Through observing the trend of the FOM, we found the MDH cylindrical waveguides have high field confinement which approximates to the isotropic metal–dielectric–metal (MDM) cylindrical waveguides. Nevertheless, the propagation losses will be sharply reduced, which leads to the longer propagation length. For example, for the case of Ag–ZnO–hyperbolic cylindrical waveguides with the size around 400 nm at wavelength, it perform both extremely small mode area that approximates to the Ag–ZnO–Ag cylindrical waveguides and better propagation length which is almost twice longer than that of the MDM cases.