Propagation in waveguide filled with anisotropic MNG metamaterial with hyperbolic dispersion - Rigorous analysis and physical interpretation

Propagation of plane waves in an infinite anisotropic Mu-Negative (MNG) metamaterial with hyperbolic dispersion curve is analyzed rigorously. It is shown that anisotropic MNG metamaterial supports inhomogeneous type of plane wave, a wavelength of which may become infinitesimally short for some special directions of propagation. It is also shown that shortening of a wavelength is actually a consequence of different signs of permeability in transversal and longitudinal directions (i.e. a consequence of the hyperbolic shape of a dispersion curve). This huge shortening is possible even for a permeability whose absolute value is equal to one. A field distribution inside a waveguide filled with anisotropic MNG material can be thought as a superposition of two plane waves, as in the case of ordinary waveguide but a peculiar dependence of a wavelength on direction of propagation enables propagation below a cut-off frequency. These cases, in which a subwavelength propagation is possible are investigated both analytically and experimentally. Finally, it is attempted to give a physical interpretation of peculiar propagation caused by hyperbolic shape of a dispersion curve.