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 this report, we provide a comprehensive overview of recent developments in the rapidly growing field of fractal antenna engineering. Fractal antenna engineering research has been primarily focused in two areas: 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. Fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These unique properties of fractals have been 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 possess 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 and arrays are also ideal candidates for use in reconfigurable systems. Finally, we provide a brief summary of recent work in the related area of fractal frequency-selective surfaces.

An overview of fractal antenna engineering research

Metasurfaces: From microwaves to visible

The multiband behavior of the fractal Sierpinski (1915) antenna is described. Due to its mainly triangular shape, the antenna is compared to the well-known single-band bow-tie antenna. Both experimental and numerical results show that the self-similarity properties of the fractal shape are translated into its electromagnetic behavior. A deeper physical insight on such a behavior is achieved by means of the computed current densities over the antenna surface, which also display some similarity properties through the bands.

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On the behavior of the Sierpinski multiband fractal antenna

Fractal geometry involves a recursive generating methodology that results in contours with infinitely intricate fine structures. This geometry, which has been used to model complex objects found in nature such as clouds and coastlines, has space-filling properties that can be utilized to miniaturize antennas. These contours are able to add more electrical length in less volume. In this article, we look at miniaturizing wire and patch antennas using fractals. Fractals are profoundly intricate shapes that are easy to define. It is seen that even though the mathematical foundations call for an infinitely complex structure, the complexity that is not discernible for the particular application can be truncated. For antennas, this means that we can reap the rewards of miniaturizing an antenna using fractals without paying the price of having to manufacture an infinitely complex radiator. In fact, it is shown that the required number of generating iterations, each of which adds a layer of intricacy, is only a few. A primer on the mathematical bases of fractal geometry is also given, focusing especially on the mathematical properties that apply to the analysis of antennas. Also presented is an application of these miniaturized antennas to phased arrays. It is shown how these fractal antennas can be used in tightly packed linear arrays, resulting in phased arrays that can scan to wider angles while avoiding grating lobes.

Fractal antennas: a novel antenna miniaturization technique, and applications

Preface 1. Introduction 2. FDTD Method for periodic structure analysis 3. EBG Characterizations and classifications 4. Design and optimizations of EBG structures 5. Patch antennas with EBG structures 6. Low profile wire antennas on EBG surfaces 7. Surface wave antennas Appendix: EBG literature review.

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Electromagnetic Band Gap Structures in Antenna Engineering

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.

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

Planar chiral metamaterials comprising double-layer dielectricmetal- dielectric resonant structures in the shape of a gammadion are presented in the near-infrared regime. The unit cell of the doubly-periodic metamaterial design is optimized using the genetic algorithm for maximum circular dichroism and for maximum optical activity. A circular dichroism value in excess of 50% is predicted for the optimized design. Maximum polarization rotatory powers in terms of the minimum allowed transmittances are also obtained and presented.

http://cearl.ee.psu.edu/Projects/Assets/Project1/Project1_5/4_planar_chiral_metamaterial.pdf

Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation.

Metamaterials are being applied to the development and construction of many new devices throughout the electromagnetic spectrum. Limitations posed by the metamaterial operational bandwidth and losses can be effectively mitigated through the incorporation of tunable elements into the metamaterial devices. There are a wide range of approaches that have been advanced in the literature for adding reconfiguration to metamaterial devices all the way from the RF through the optical regimes, but some techniques are useful only for certain wavelength bands. A range of tuning techniques span from active circuit elements introduced into the resonant conductive metamaterial geometries to constituent materials that change electromagnetic properties under specific environmental stimuli. This paper presents a survey of the development of reconfigurable and tunable metamaterial technology as well as of the applications where such capabilities are valuable.

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Reconfigurable and Tunable Metamaterials: A Review of the Theory and Applications

The transformation optics technique for designing novel electromagnetic and optical devices offers great control over wave behavior, but is difficult to implement primarily due to limitations in current metamaterial design and fabrication techniques. This paper demonstrates that restricting the spatial transformation to a conformal mapping can lead to much simpler material parameters for more practical implementation. As an example, a flat cylindrical-to-plane-wave conversion lens is presented and its performance validated through numerical simulations. It is shown that the lens dimensions and embedded source location can be adjusted to produce one, two, or four highly directive planar beams. Two metamaterial designs for this lens that implement the required effective medium parameters are proposed and their behavior analyzed.

Conformal mappings to achieve simple material parameters for transformation optics devices

An efficient, black-box multiobjective optimization technique is presented, which is capable of simultaneously optimizing designs for performance as well as robustness when input tolerance values are not known a priori . During the optimization process, adaptive statistical surrogate mappings between input variables and output objectives are formulated within a model selection framework. These statistical models can be evaluated in fractions of a second and serve as an efficient surrogate for a more computationally intensive process, such as an electromagnetic simulation. By exploiting the speed offered from surrogate modeling techniques, new, high-performance designs can be quickly identified. In addition, complete tolerance analysis can be conducted within the optimization loop, which provides designers with critical information regarding the robustness of designs. To demonstrate the effectiveness of this approach, it will be applied to the optimization of a capacitively loaded monopole and a wideband Vivaldi antenna.

Pingjuan L. Werner

Papers

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

Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation.

Reconfigurable and Tunable Metamaterials: A Review of the Theory and Applications

Conformal mappings to achieve simple material parameters for transformation optics devices

Efficient Multiobjective Antenna Optimization With Tolerance Analysis Through the Use of Surrogate Models