Experimental investigation of two-dimensional backward wave meta-material based on parallel-plate waveguide filled with double ring resonators
AbsIracf - Two-dimensional backward-wave meta-material based on evanescent parallel-plate waveguide filled with uniaxial magnetic tilling with negative transversal permeability is investigated experimentally. The prototype comprised a two-dimensional array of the double ring resonators sandwiched between two metallic plates and it was operating in 8 GHz frequency hand. The backward-wave propagation was verified by the measurement of negative lateral displacement of the beam impinging the meta-material slab at several different angles of incidence I. INTRODUCTION A material which supports propagation of the backward waves ('left-handed material' or 'backward-wave material') was predicted theoretically in sixties by Veselago (I) and realized experimentally for the first time by Smith at al. (2) in 2000. The rather simple type of one-dimensional backward-wave meta-material based on an evanescent waveguide loaded with the split ring resonators was presented in (3). Such a waveguide was interpreted as one-dimensional material with both negative permeability and negative permittivity (3). In (4,5), it was shown that the propagation below the cut-off frequency actually occurs due to uniaxial anisotropy of negative permeability of the meta-material based on the split ring resonators. The extension of this basic principle to two dimensions, similarly to the idea introduced in (6), is investigated experimentally in this paper. 11. THEORETICAL RESULTS Let us analyze the structure that comprises a slab of anisotropic uniaxial magnetic materials sandwiched within the two infinite parallel PEC plates (Fig.1). If the optical axis of the uniaxial material is perpendicular to the plates (the transversal direction), it is obvious that this structure is essentially isotropic in two dimensions. Thus, the electromagnetic energy will propagate in any direction parallel to the plates (the longitudinal direction) in the exactly the same way (the propagation for two perpendicular longitudinal directions is sketched in Fig. 5). For any particular longitudinal direction, one may think of this structure as a parallel plate waveguide. In the lossles case, the longitudinal propagation factor of such a waveguide is given by the simple set of equations (4,51: Here, k, stands for longitudinal propagation factor, ko is a free space propagation factor, g is relative permittivity and p,, and pi, stand for relative permeability in transversal and longitudinal directions of the waveguide, respectively. The symbol f stands for a frequency of the signal, whereas Lo and L are the cut-off frequency of an empty parallel-plate waveguide and the parallel-plate waveguide filled with a material, respectively. If the transversal permeability is negative &<0 ) and the longitudinal permeability is positive (ppO), one must choose the negative sign in front of the square root in (I) for frequencies below the cut-off. This yields the peculiar phenomenon of the backward-wave propagation. Hence, the structure actually behaves as two-dimensional backward-wave meta-material provided that the vector of the magnetic field is perpendicular to the walls (TE 01 mode). If one stacks more parallel plate waveguides in the transversal direction, it is possible to manufacture the two-dimensional 'backward-wave' material of arbitrary thickness, as proposed in (6). The backward-wave propagation below the cut-off frequency can he simply explained by two-dimensional transmission line equivalent circuit of the structure (Fig.2). The distributed series impedance (212) is associated with the transversal permeability. The distributed shunt admittance associated with the relative permittivity (Y,) and the admittance associated with the longitudinal permeability (Y,) form the tank circuit. In the case of the uniaxial material with positive permeability, the series admittance will he also positive. Below the cut-off, the tank circuit behaves as an inductance and, for any direction parallel to the plates, the whole structure behaves as a transmission line with the distributed series inductance and the distributed parallel inductance (L-L transmission line), This kind of transmission line does not support the propagating waves. If the transversal
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