A co‐axial waveguide is filled with an anisotropic hyperbolic medium that has a radial negative component of the tensorial permittivity and permeability. This waveguide has no cutoff frequency for propagating transverse electric and transverse magnetic modes. These modes of propagation are described by Bessel functions of first and second kinds (Neumann function) with an imaginary order. This feature of below cutoff propagation is useful for miniaturizing the size of the waveguide. Further, the double negative character of the radial components of the permittivity and permeability also occasion a better impedance match of the waveguide to free space. Such waveguide can be projected to be useful as miniaturized efficient coupler and imaging probes.

中文翻译：

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波在充满双曲负折射率介质的圆柱波导中的传播

同轴波导管填充有各向异性双曲线介质，该介质的张量电容率和磁导率在径向上为负。该波导不具有用于传播横向电和横向磁模式的截止频率。这些传播模式由第一类和第二类贝塞尔函数（诺依曼函数）以虚序描述。截止传播以下的特征对于使波导的尺寸最小化是有用的。此外，介电常数和磁导率的径向分量的双重负特性也使波导与自由空间的阻抗匹配更好。可以将这种波导投影为有用的小型化高效耦合器和成像探头。