Highly sensitive permittivity sensor using an Inhomogeneous Metamaterial Cylindrical Waveguide

Cylindrical waveguides filled with anisotropic metamaterials enable novel wave propagation phenomena. A nanoporous alumina microtube is a manifestation of such an anisotropic waveguide with an effective permittivity tensor ( $\varepsilon _{r} \neq \varepsilon _\phi = \varepsilon _{z}$ ). The metamaterial would be considered to be filled homogeneously or inhomogeneously depending on the variation of the size of the nanopores and density of the nanopores. The electromagnetic fields in such metamaterial waveguide are highly sensitive to the refractive index of the material embedded in the nanopores and the variation of the density of the inclusion in the radial direction due to the modal field distributions. We show that there is a large variation in the reflection coefficient ( $S_{11}$ ) of the inhomogeneously filled nanoporous waveguide with an embedded liquid with small variations in the material properties of the liquid. This variation in the $S_{11}$ parameter can use to determine the purity of liquid. Our results show that the permittivity variations of the inclusion material can be monitored up to the sixth decimal places theoretically. The analysis also indicates that the inhomogeneous metamaterial waveguide is more sensitive compared to both the homogeneously filled metamaterial waveguide and an isotropic waveguide covered with metamaterial clad. This waveguide has potential applications in biomedical and chemical sensing applications.