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.

中文翻译：

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使用非均质超材料圆柱波导的高灵敏度介电常数传感器

充满各向异性超材料的圆柱波导可实现新颖的波传播现象。纳米多孔氧化铝微管是具有有效介电常数张量（ $ \ varepsilon _ {r} \ neq \ varepsilon _ \ phi = \ varepsilon _ {z} $ ）。取决于纳米孔的尺寸和纳米孔的密度的变化，将认为超材料被均匀地或不均匀地填充。这种超材料波导中的电磁场对嵌入在纳米孔中的材料的折射率以及由于模态场分布而在径向上包含的密度的变化高度敏感。我们证明反射系数有很大变化（ $ S_ {11} $ 埋入液体的不均匀填充的纳米多孔波导，液体的材料特性变化很小）。这种变化 $ S_ {11} $ 参数可以用来确定液体的纯度。我们的结果表明，夹杂物材料的介电常数变化理论上可以监测到小数点后第六位。分析还表明，与均质填充的超材料波导和覆盖有超材料包覆的各向同性波导相比，非均质的超材料波导更为敏感。该波导在生物医学和化学传感应用中具有潜在的应用。