Effective material properties extraction method for an asymmetric metamaterial with uneven distances to two measurement ports

This paper derives the new equations for the full extraction method in retrieving effective refractive indices, impedances, and material properties, such as permittivity (ε) and permeability (μ), of an asymmetric metamaterial, meaning that the metamaterial slab is asymmetric along the wave propagation direction, or the slab is not mounted exactly in the middle of two measurement ports. Traditionally, the well-known methods proposed by D.R. Smith and Kong assume the equal distances from the measurement ports to the metamaterial slab surfaces. However, it may create problems in real measurements to place the slab exactly in the middle position between two measurement ports. As a result, the retrieved effective material properties may be discontinuous. In this paper, we derive the new equations to solve the problem and successfully retrieve the continuous material properties of the metamaterial slab.