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.

基础研究调查了一种新的基于模糊交叉熵的方法，用于增强具有不同倾斜事件的紧凑单层双负超材料的设计和分析。与真空相比，折射率大于 1 的材料可能会减慢波的传播。零折射率的材料可以将波的速度和波长提高到无穷大。尽管如此，具有负折射率的超材料具有控制波速的必要能力，尽管在实际实践中模拟材料中的零折射率特性非常困难。基于实验观察和数据可视化，在各种倾斜事件中提取每个测量的无差别折射指数的下限，然后恢复为归一化和理想化模糊指数集 (FIS) 的形式。此后，所提出的模糊交叉熵测量被部署用于识别最负的无差别折射率以及所需的波速，旨在获得最佳的入射角和所需的过渡频率。实验结果表明，该结构对于所有方位角都表现为双负超材料，过渡频率在接近 7 GHz 时具有不同的负电平波动。设计结构的最低过渡频率在 0°方位角处观察到，此后随着入射角增加至 90° 而增加。虽然，此后观察到的跃迁频率随着入射角的进一步增大（从 90° 到 180°）而降低，并且在跃迁频率方面表现出近似对称性，对称中心为 90°。随后，使用归一化和理想化模糊指标集之间的最小（最大）模糊交叉熵值来获得最高（最低）波速，这是在 135°（157.5°）方位角观察到的。基于模糊交叉熵的基础方法能够处理具有倾斜事件的双负超材料，并且可以根据应用要求有效地应用于实现所需的波速和无差别的折射率。