Efficiency of high frequency surface wave radars may be improved by inserting a metamaterial in the vicinity of transmitting antennas that will reinforce the propagation of surface waves. This paper deals with the first and second order derivations of the surface impedance boundary conditions (IBC) applied to model such a metamaterial, which is equivalent to a bounded ground with a low negative permittivity. The goal of this paper is to extend an approach previously based on the classical Leontovich IBC which is usually restrained to high permittivity grounds. As shown here, a simplification in the expression of the surface impedance is possible in the case of a planar and homogeneous surface. That allows to have a first order impedance boundary condition substituted for the required second order impedance boundary condition.
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