Passbands of bianisotropic and waveguide bianisotropic metamaterials based on planar double split rings

The transmission properties of a bianisotropic composite material based on regular gratings of planar double split rings (PDSRs) and a waveguide bianisotropic composite material of waveguide structures loaded with such gratings are studied theoretically and experimentally. The tensors of effective permittivity, permeability, and chirality of the PDSR medium are calculated with allowance for the diagonality of the tensors relating the local-average field differences to the PDSR dipole moments, and the dispersion equation is solved. Frequency dependences of the effective refractive indexes of both composite materials are studied. Their pass-bands are determined, the conditions for the existence of forward and backward waves are formulated, and the respective regions of existence (left and right passbands) are found. It is shown that a medium containing only similarly oriented PDSRs at a low concentration has a frequency band in which the permittivity and permeability are both negative, but the squared refractive index is negative there as well and, hence, the waves do not propagate. The positional relationship between the overforbidden bands and passbands of the waveguide bianisotropic material with PDSRs is studied theoretically and experimentally for different excitation conditions of the PDSR system.