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Propagation of wave in a cylindrical waveguide filled with hyperbolic negative index medium

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.