Fractal Superlattice Cover with Variable Lacunarity For Patch Antenna Directivity Enhancement Analysis and Design

The transmission spectrum of fractal polyadic Cantor superlattice exhibits sharp peaks within forbidden frequency gaps. This property has been exploited by placing such self-similar multi-slab structure in the far field radiation region above a radiating element such as a patch antenna to maximize its directivity at the corresponding transmission peak. A patch antenna having directivity of 30 dBi is developed. The design and optimization of the multi-slab structure is achieved using a doubly recursive algorithm. The effect of changing the fractal lacunarity and/or the stage of growth on the transmission characteristics has been studied in both the spectral and spatial domains. Based on accurate analytical expressions for the cover spectral and spatial transmission coefficient, a novel interpretation for the antenna radiation pattern is presented. The antenna including the cover structure is simulated using the moment method-based software tool IE3D. The effect of varying the lacunarity and stage of growth on the spectral and spatial transmission characteristics has been studied analytically using a Matlab program. Key-Words: transmission spectrum, self-similar structures, fractal lacunarity, fractal dimension, stage of growth, antenna directivity, Computer-Aided Design (CAD), radiation pattern.