In this paper, we propose a novel study of zero-index materials (ZIM) based on lumped element circuits using a wave concept iterative method (WCIP). This method is well used to demonstrate the behavior of zero-index-based microwave applications. This type of metamaterial can maintain the amplitude and the phase of an electromagnetic wave to be constant through the ZIM region, which is an important property to design an in-phase power divider-combiner, enhance the directivity of an embedded source, channel electromagnetic waves without reflection at the interface between waveguides with different cross-sections, and control the transmission of electromagnetic wave by the adjustment of the permittivity of a dielectric defect coated by zero-index metamaterial. The numerical simulations using the WCIP method match the literature and commercial software simulator results.

In this paper, a developed theory of a novel approach of the wave concept iterative process (WCIP) method is presented. This method is well used to demonstrate many attractive properties of metamaterials and to analyze metamaterial-based negative refractive index lenses by easy and speedy computation of the electromagnetic field distribution. These metamaterial-based circuits are established by using periodic L–C and C–L networks. The results of simulation using the proposed method are justified theoretically.

A new study of right-handed and composite right/left-handed metamaterial transmission lines (TL) using their equivalent circuits and a new approach of the wave concept iterative process method is presented. This approach has the advantage of simulating all the periodic structures by only simulating one basic cell thanks to the surrounding periodic walls. A suitable choice of the cell length is necessary to work with the current as well as voltage and to approach the real behavior of the TL. The simulation results of these circuits, such as the calculation of current, voltage and the parameters S, helped to validate all the theoretical study.

This paper proposes an efficient and fast analysis of substrate integrated waveguide (SIW) components using a new approach of the iterative method called WCIP, i.e. “Wave Concept Iterative Process”. This method is based on the iterative resolution of waves between two domains. The first is the spectral domain. We use the Floquet–Bloch decomposition to describe all modes in the spectral domain. The second describes the configuration of the circuit in the spatial domain. It allows taking the exact structure according to the appropriate boundary conditions. This method permits to reduce numerical complexity. The convergence of this approach is always guaranteed. The theoretical suggested study is validated by the simulation of two different examples of SIW circuits. The obtained results are in good agreement with those of measurement and with software HFSS simulations, which prove the advantage of this method.