Novel analytical method for solving resonant frequency and induced current of four coupled unit cells metasurface

Abstract Metasurfaces are artificially engineered composite structures composed of arrays of sub-wavelength resonators that can exhibit negative values of permeability and permittivity at resonant frequencies. This unique approach to realizing new properties has been explored in the development of highly advanced THz bio-sensors, optical sensing, filters, and intelligent reflecting surfaces for 6G and beyond. Several techniques have been developed to study and characterize metasurfaces. Since analytical methods have not previously been used to characterize and study the resonant frequency of metasurfaces with arrays of unit cells, experimental techniques and 3D full-wave numerical solvers are commonly employed. However, these methods are computationally expensive, requiring significant time, cost, and resources. In contrast, analytical methods provide closed-form solutions with reduced computational complexities. This paper presents a novel analytical technique for analyzing metasurfaces consisting of four circular doubly split double-ring unit cells, which have not been previously studied analytically. A lumped-element equivalent circuit for the metasurface was developed, and the induced current equation was derived using mesh current analysis. The resonant frequency and peak induced current were analyzed by varying the mean radius and inter-ring distance. Results show that increasing the inter-ring distance from 1.1 mm to 1.3 mm increases the resonant frequency by 3%, while increasing the mean radius decreases the resonant frequency by 6%. The metasurface exhibits a 2.6 GHz bandwidth and a Q-factor of 2.17 at a resonant frequency of 5.63 GHz. Comparisons with 3D numerical solvers demonstrate the performance and validation of the analytical method, with an average error of 10%. The average time for the 3D numerical solver to compute the resonant frequency and other parameters was 68.55 s, while the analytical method calculates the resonant frequency in 2.2751 s, providing a strong impetus for developing efficient analytical models for metasurfaces.