Effective Medium Theory of Left-Handed Materials

TLDR

The study focuses on metamaterials composed of periodic arrays of wires, cut wires, split‑ring resonators, closed SRRs, and combinations thereof. The authors employ transfer‑matrix calculations and analytical expressions to extract effective permittivity and permeability of finite‑length metamaterials, thereby explaining their transmission characteristics. They demonstrate that SRRs exhibit a strong electric response comparable to cut wires, dominating left‑handed material behavior, and introduce a criterion to distinguish left‑handed from right‑handed transmission peaks, supported by analytical expressions for effective parameters.

Abstract

We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity $ϵ$ and permeability $\ensuremath{\mu}$. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut wires, split ring resonators (SRRs), closed SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left or right handed.