High-Q electromagnetic filter in the X-Ku band based on a periodic defective structure RHM/ENG

¹ Laboratory of Materials, Waves, Energy and Environment, Team of Waves, Acoustics, Photonics and Materials, Mohamed I University, Oujda, Morocco
² Engineering Sciences Laboratory (LSI), Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, B.P. 1223, Taza Gare, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 24 June 2026

Abstract

In this work, we use the Transfer Matrix Method (TMM) to study a one-dimensional (1D) defective structure composed of N periodic cells. Each cell consists of a right-handed material (RHM) transmission line segment coupled to a transmission line resonator (TLR) made of a metamaterial with negative effective permittivity (ENG, ε₂ (f) < 0). This ENG resonator is modeled by a compact circuit with lumped elements, including a series capacitor (C), a parallel inductor (L), and a resistor (R). A lateral RHM resonator is introduced at the center of the structure to create a defect mode. The perfect structure has an electromagnetic band gap (EBG) whose width strongly depends on the length of the ENG resonators. The introduction of the defect generates a localized mode within this band gap, characterized by a high-quality factor (Q) and unit transmission (T = 1). The frequency of this mode is very sensitive to the length and relative permittivity of the defect. Furthermore, analysis of the transmission spectrum, phase, group delay, and group velocity reveals the existence of a zero-effective-phase (zero – ϕ_eff) gap, whose position and width remain insensitive to the parameters of the defect. These results pave the way for the design of stable and highly selective microwave filters suitable for electronic devices and telecommunications applications in the X-Ku bands.