Fractal antenna engineering: the theory and design of fractal antenna arrays

TLDR

A fractal is a recursively generated object with a fractional dimension, and this property enables the design of antennas and arrays whose fractional dimensions derive from the generating subarray. The article offers a comprehensive overview of recent developments in fractal antenna engineering, focusing on the theory and design of fractal arrays. The authors describe key properties of fractal arrays—frequency‑independent multi‑band behavior, low‑sidelobe design schemes, systematic thinning approaches, and rapid beam‑forming algorithms that exploit fractal recursion. Although still early, the preliminary results are intriguing and suggest potential future practical applications.

Abstract

A fractal is a recursively generated object having a fractional dimension. Many objects, including antennas, can be designed using the recursive nature of a fractal. In this article, we provide a comprehensive overview of recent developments in the field of fractal antenna engineering, with particular emphasis placed on the theory and design of fractal arrays. We introduce some important properties of fractal arrays, including the frequency-independent multi-band characteristics, schemes for realizing low-sidelobe designs, systematic approaches to thinning, and the ability to develop rapid beam-forming algorithms by exploiting the recursive nature of fractals. These arrays have fractional dimensions that are found from the generating subarray used to recursively create the fractal array. Our research is in its infancy, but the results so far are intriguing, and may have future practical applications.