engleski

Miniatruization of Rectangular Waveguide using Uniaxial Negative Permeability Material

Recent introduction of artificial materials with simultaneously negative permittivity and permeability has initiated a lot of research activities worldwide. One of the potential important applications of the backward-wave materials could be novel guiding structures. Very recently the propagation below cut-off frequency of a waveguide loaded with split-ring resonators (the resonant inclusions usually used for synthesis of negative permeability) was demonstrated. This phenomenon was interpreted by thinking of the waveguide below cut-off frequency of dominant TE mode as the one-dimensional material with negative effective permittivity. Therefore, the waveguide loaded with split-ring resonators was interpreted as a material with both negative permeability and negative permittivity. Although the experimental results show the propagation bellow the cut-off, it was not attempted to verify the existence of the backward waves. In this paper, the original experiment is analyzed and novel physical interpretation is proposed. It is shown that propagation below the cut-off frequency actually occurs due to uniaxial anisotropy of negative permeability of meta-material based on split ring resonators. If one allows usage of anisotropic material for waveguide filling it is not longer necessary to have both permittivity and permeability with same signs. Propagation is also possible if either permeability in transversal direction (for TE modes) or permittivity in transversal direction (for TM modes) has negative sign. In the case of TE modes, the waveguide supports propagation of backward waves below cut-off frequency of an empty waveguide There is no theoretical limit on the lowest frequency of propagation providing that one is able to fabricate uniaxial negative permeability material at given frequency. Thus, it becomes possible to fabricate the waveguide with transversal dimension smaller than half of the wavelength. The simple explanation this peculiar phenomenon is given by analysis of transmission line model of the waveguide. The series inductance per unit length and shunt inductance per unit length have the same sign if the waveguide is filled with isotropic magnetic material (either double positive material or double negative material). On contrary, if the waveguide is filled with uniaxial material with negative permeability in transversal direction, the series inductance will be negative. At one fixed frequency, one can think of negative series inductance as the ordinary capacitance. If the operating frequency is located below cut-off, the equivalent circuit now comprises series capacitance and shunt inductance similar to the left-handed transmission line introduced in. Therefore, the propagation in the form of backward waves becomes possible below the cut-off frequency. Two experimental rectangular waveguides loaded with split-ring resonators in 10 GHz frequency band have been designed, fabricated and tested. The measured results revealed backward-wave pass-band located below the cut off frequency. It was also shown that the increase of physical length of the waveguide caused the decrease of the electrical length. This is the direct proof of backward-wave propagation since the phase of backward wave increases along the waveguide.

backward wave; meta-material; waveguide; miniaturization; anizotropy

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