Entropy based designing and analysis of a compact single layer double negative metamaterial with oblique incidents

Abstract The underlying study investigates a novel fuzzy cross entropy based methodology for enhancing the designing and analysis of a compact single layer double negative metamaterial with varying oblique incidents. Materials having a refractive index greater than unity may slow down the propagation of waves in comparison to the vacuum. A material with zero refractive index can boost the speed and wavelength of the wave to infinity. Nevertheless, metamaterials with a negative index of refraction have the necessary capability for controlling the wave velocity, although, mimicking zero index property in materials is quite difficult in real practices. Based on experimental observations and data visualizations, the lower bound of each measured indiscriminative index of refraction is extracted at various oblique incidents and then rehabilitated into the form of normalized and idealized fuzzy index sets (FISs). Thereafter, the proposed fuzzy cross entropy measure is deployed for identifying the most negative indiscriminative refractive index along with the desired wave velocity, intended to obtain the best incident angle and desired transition frequency. The experimental results suggest that the structure is behaving as a double negative metamaterial for all the azimuth angles with transition frequency fluctuating near to 7 GHz with different negative levels. The lowest transition frequency for the designed structure is observed at 0°azimuthal and increases thereafter with augmenting incident angle up to 90°. Although, the observed transition frequency decreases thereafter with further augmentation of incident angle (from 90°to 180°) and exhibits approximate symmetry in terms of transition frequency with the center of symmetry at 90°. Subsequently, the minimum (maximum) fuzzy cross entropy value between normalized and idealized fuzzy index sets is deployed to obtain the highest (lowest) wave velocity, which is observed at 135°(157.5°) azimuthal angle. The underlying fuzzy cross entropy-based methodology is capable of handling double negative metamaterial with oblique incidents and can effectively be applied for achieving the desired wave velocity as well as indiscriminative refractive index, depending upon the application requirements.