Recent efforts by several researchers around the world to combine fractal geometry with electromagnetic theory have led to a plethora of new and innovative antenna designs. In ttlis report, we provide a comprehensive overview of recent developments in t h e rapidly growing field of fractal antenna engineering. Fractal antenna engineering research h a s been primarily focused in two a r e a s : the first deals with the analysis and design of fractal antenna elements, and the second concerns the application of fractal concepts to the design of antenna arrays. Frilctals have no characteristic size, a n d are generally composed of many copies of themselves at different scales. T h e s e uniqile properties of fractals have b e e n exploited in order to develop a new class of antenna-element designs that are multi-band and/or compact in size. On the other hand, fractal arrays are a subset of thinned arrays, and have been shown to p o s s e s s several highly desirable properties, including multi-band performance. low sidelobe levels, and the ability to develop rapid beamforming algorithms based on the recursive nature of fractals. Fractal elements a n d arrays are also ideal candidates for use in reconfigurable systems. Finally, we will provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.

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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.

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