Study of cut-off frequency of circular waveguide using metamaterial surface

The objective of this work is to identify an alternative waveguide configuration that allows for the reduction of the cutoff frequency, making integration within the plasma igniter of an electric propulsion (EP) engine possible, where space constraints and performance requirements demand compact and high-efficiency solutions. In this context, the use of a metamaterial surface was analyzed to reduce the cutoff frequency of a circular waveguide, while maintaining its geometric dimensions unaltered, particularly the internal radius and the overall length. The proposed configuration involves the insertion, along the inner wall of the guide, of a series of adhering metal foils arranged on a dielectric layer. Each foil has a length equal to the corresponding circumferential arc (5.24 mm), with a spacing of 0.1 mm between adjacent elements. In numerical simulations, a zero thickness was assumed for both the foils and the external conductive casing, while a cylindrical crown of dielectric material with a relative permittivity of $\epsilon_r = 10$ was inserted between the two parts. The study was conducted using the electromagnetic simulation software CST Studio Suite, following a methodology articulated in three main phases. Firstly, a conventional metallic waveguide was designed and modeled, sized through analytical calculations implemented in a MATLAB environment, to achieve a cutoff frequency for monomodal transmission approximately double that expected for the metamaterial guide (designed to operate in the 1.8–5.6 GHz range). In a second phase, the waveguide with metamaterial coating was constructed, exploring different geometric configurations of the inner surface: foils arranged longitudinally along the axial direction, annular-shaped elements, and square-shaped elements. Among the solutions investigated, the configuration with square elements showed the best performance, ensuring a more uniform and intense electric field distribution within the useful section of the guide. Finally, in the third phase, the metamaterial waveguide was also analyzed in a closed configuration, with the insertion of two coaxial connectors. Their placement was optimized at a distance equal to a quarter of the wavelength, in order to maximize power transfer from the coaxial to the guide. Numerical results showed that the metallic waveguide has a cutoff frequency of 8.9 GHz, while the guide with metasurface reduces this value to 2.2 GHz. The S-parameter and electric field distribution analysis also showed, at the frequency of 2.36 GHz, a transmission coefficient ($S_{21}$) of about -1.812 dB, confirming the effectiveness of the proposed solution. All simulations were conducted assuming vacuum conditions inside the waveguide.