Experimental study of anti-resonant behavior of material parameters in periodic and aperiodic composite materials

Abstract

In the literature on composite materials with extreme or unusual electromagnetic properties (so-called metamaterials), it is common to retrieve the effective material parameters from the scattering parameters (complex reflection and transmission coefficients) of the metamaterial layer. Most often, this retrieval is done by using the well-known Nicolson-Ross-Weir method or its modifications. It is commonly known that one of the two effective parameters of many metamaterials retrieved in this way (either effective permittivity or permeability) exhibits the so-called anti-resonance, which is a nonphysical feature. This effect has been understood as a manifestation of spatial dispersion in the sample. Many previous works have either claimed or assumed that the anti-resonance is an effect caused by the periodicity of the composite material. To our knowledge, this claim was never supported by comparisons of periodical and random samples. In some other works, it has been theoretically shown that the anti-resonance of the retrieved material parameters can be avoided, e.g., by the introduction of additional surface parameters into the retrieval procedure. If it is so, the anti-resonance has nothing to do with the internal periodicity of the bulk medium. In the present work, we numerically and experimentally investigate the question if the internal periodicity of metamaterial layers is essential for the appearance of anti-resonances in extracted material parameters. We show that it is not so. Therefore, our result is in favor of the theory which treats the anti-resonance as a deficiency of the Nicolson-Ross-Weir retrieval procedure applied to spatially dispersive media.