Douglas H. Werner

An overview of fractal antenna engineering research

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.

Particle swarm optimization versus genetic algorithms for phased array synthesis

Particle swarm optimization is a recently invented high-performance optimizer that is very easy to understand and implement. It is similar in some ways to genetic algorithms or evolutionary algorithms, but requires less computational bookkeeping and generally only a few lines of code. In this paper, a particle swarm optimizer is implemented and compared to a genetic algorithm for phased array synthesis of a far-field sidelobe notch, using amplitude-only, phase-only, and complex tapering. The results show that some optimization scenarios are better suited to one method versus the other (i.e., particle swarm optimization performs better in some cases while genetic algorithms perform better in others), which implies that the two methods traverse the problem hyperspace differently. The particle swarm optimizer shares the ability of the genetic algorithm to handle arbitrary nonlinear cost functions, but with a much simpler implementation it clearly demonstrates good possibilities for widespread use in electromagnetic optimization.

Genetic Algorithms in Electromagnetics

Preface. Acknowledgments. 1. Introduction to Optimization in Electromagnetics. 1.1 Optimizing a Function of One Variable. 1.1.1 Exhaustive Search. 1.1.2 Random Search. 1.1.3 Golden Search. 1.1.4 Newtons Method. 1.1.5 Quadratic Interpolation. 1.2 Optimizing a Function of Multiple Variables. 1.2.1 Random Search. 1.2.2 Line Search. 1.2.3 Nelder-Mead Downhill Simplex Algorithm. 1.3 Comparing Local Numerical Optimization Algorithms. 1.4 Simulated Annealing. 1.5 Genetic Algorithm. 2. Anatomy of a Genetic Algorithm. 2.1 Creating an Initial Population. 2.2 Evaluating Fitness. 2.3 Natural Selection. 2.4 Mate Selection. 2.4.1 Roulette Wheel Selection. 2.4.2 Tournament Selection. 2.5 Generating Offspring. 2.6 Mutation. 2.7 Terminating the Run. 3. Step-by-Step Examples. 3.1 Placing Nulls. 3.2 Thinned Arrays. 4. Optimizing Antenna Arrays. 4.1 Optimizing Array Amplitude Tapers. 4.2 Optimizing Array Phase Tapers. 4.2.1 Optimum Quantized Low-Sidelobe Phase Tapers. 4.2.2 Phase-Only Array Synthesis Using Adaptive GAs. 4.3 Optimizing Arrays with Complex Weighting. 4.3.1 Shaped-Beam Synthesis. 4.3.2 Creating a Plane Wave in the Near Field. 4.4 Optimizing Array Element Spacing. 4.4.1 Thinned Arrays. 4.4.2 Interleaved Thinned Linear Arrays. 4.4.3 Array Element Perturbation. 4.4.4 Aperiodic Fractile Arrays. 4.4.5 Fractal-Random and Polyfractal Arrays. 4.4.6 Aperiodic Refl ectarrays. 4.5 Optimizing Conformal Arrays. 4.6 Optimizing Reconfi gurable Apertures. 4.6.1 Planar Reconfi gurable Cylindrical Wire Antenna Design. 4.6.2 Planar Reconfi gurable Ribbon Antenna Design. 4.6.3 Design of Volumetric Reconfi gurable Antennas. 4.6.4 Simulation Results-Planar Reconfi gurable Cylindrical Wire Antenna. 4.6.5 Simulation Results-Volumetric Reconfi gurable Cylindrical Wire Antenna. 4.6.6 Simulation Results-Planar Reconfi gurable Ribbon Antenna. 5. Smart Antennas Using a GA. 5.1 Amplitude and Phase Adaptive Nulling. 5.2 Phase-Only Adaptive Nulling. 5.3 Adaptive Reflector. 5.4 Adaptive Crossed Dipoles. 6. Genetic Algorithm Optimization of Wire Antennas. 6.1 Introduction. 6.2 GA Design of Electrically Loaded Wire Antennas. 6.3 GA Design of Three-Dimensional Crooked-Wire Antennas. 6.4 GA Design of Planar Crooked-Wire and Meander-Line Antennas. 6.5 GA Design of Yagi-Uda Antennas. 7. Optimization of Aperture Antennas. 7.1 Refl ector Antennas. 7.2 Horn Antennas. 7.3 Microstrip Antennas. 8. Optimization of Scattering. 8.1 Scattering from an Array of Strips. 8.2 Scattering from Frequency-Selective Surfaces. 8.2.1 Optimization of FSS Filters. 8.2.2 Optimization of Reconfi gurable FSSs. 8.2.3 Optimization of EBGs. 8.3 Scattering from Absorbers. 8.3.1 Conical or Wedge Absorber Optimization. 8.3.2 Multilayer Dielectric Broadband Absorber Optimization. 8.3.3 Ultrathin Narrowband Absorber Optimization. 9. GA Extensions. 9.1 Selecting Population Size and Mutation Rate. 9.2 Particle Swarm Optimization (PSO). 9.3 Multiple-Objective Optimization. 9.3.1 Introduction. 9.3.2 Strength Pareto Evolutionary Algorithm-Strength Value Calculation. 9.3.3 Strength Pareto Evolutionary Algorithm-Pareto Set Clustering. 9.3.4 Strength Pareto Evolutionary Algorithm-Implementation. 9.3.5 SPEA-Optimized Planar Arrays. 9.3.6 SPEA-Optimized Planar Polyfractal Arrays. Appendix: MATLAB(r) Code. Bibliography. Index.

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

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.

The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces

This paper introduces several different design methodologies for multiband artificial magnetic conducting (AMC) surfaces. The paper begins by investigating the multiband properties exhibited by a conventional electromagnetic bandgap (EBG) AMC that consists of a frequency selective surface (FSS) on top of a thin dielectric substrate with a PEC back plane. The higher-order resonances associated with these surfaces have not been discussed in detail to date, as previous research has been concerned only with exploiting the primary resonant frequency. However, it will be shown that by understanding and making appropriate use of these higher order resonances, it is possible to design multiband AMC surfaces that work for nearly any desired combination of operating frequencies. The first multiband AMC design approach that will be considered is based on the introduction of FSS screens that have fractal or nearly fractal unit cell geometries. This is followed by a more general and robust genetic algorithm (GA) technique for the synthesis of optimal multiband AMC surfaces. In this case, a GA is used to evolve multiband AMC surface designs by simultaneously optimizing the geometry and size of the FSS unit cell as well as the thickness and dielectric constant of the substrate material. Finally, several examples of multiband AMC surfaces are presented, including some practical dual-band and tri-band designs genetically evolved for operation at GPS and cellular frequencies, as well as an example illustrating the success in creating a multiband AMC surface with angular stability.

Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating.

Metamaterials offer a new approach to create surface coatings with highly customizable electromagnetic absorption from the microwave to the optical regimes. Thus far, efficient metamaterial absorbers have been demonstrated at microwave frequencies, with recent efforts aimed at much shorter terahertz and infrared wavelengths. The present infrared absorbers have been constructed from arrays of nanoscale metal resonators with simple circular or cross-shaped geometries, which provide a single band response. In this paper, we demonstrate a conformal metamaterial absorber with a narrow band, polarization-independent absorptivity of >90% over a wide ±50° angular range centered at mid-infrared wavelengths of 3.3 and 3.9 μm. The highly efficient dual-band metamaterial was realized by using a genetic algorithm to identify an array of H-shaped nanoresonators with an effective electric and magnetic response that maximizes absorption in each wavelength band when patterned on a flexible Kapton and Au thin film substrate stack. This conformal metamaterial absorber maintains its absorption properties when integrated onto curved surfaces of arbitrary materials, making it attractive for advanced coatings that suppress the infrared reflection from the protected surface.

Transformation optical designs for wave collimators, flat lenses and right-angle bends

The transformation optics technique is applied to design three novel devices—a wave collimator, far-zone and near-zone focusing flat optical lenses and a right-angle bend for propagating beam fields. The structures presented in this paper are all two-dimensional (2D), however, the transformation optics design methodologies can be easily extended to develop 3D versions of these optical devices. The required values of the permittivity and the permeability tensors are derived for each of the three devices considered here. Furthermore, the functional performance of each device is verified using full-wave electromagnetic simulations. A wave collimator consists of a 2D rectangular cylinder where the fields (cylindrical waves) radiated by an embedded line source emerge normal to the top and bottom planar interfaces thereby producing highly directive collimated fields. Next, a far-zone focusing lens for a 2D line source is created by transforming the equi-amplitude equi- phase contour to a planar surface. It is also demonstrated that by aligning two far- zone focusing flat lenses in a back-to-back configuration, a near-zone focusing lens is obtained. Finally, a 2D square cylindrical volume is transformed into a cylinder with a fan-shaped cross section to design a right-angle bend device for propagating beam fields.

Frontiers in electromagnetics

“FRONTIERS IN ELECTROMAGNETICS is the first all-in-one resource to bring in-depth original papers on today’s major advances in long-standing electromagnetics problems. Highly regarded editors Douglas H. Werner and Raj Mittra have meticulously selected new contributed papers from preeminent researchers in the field to provide state-of-the-art discussions on emerging areas of electromagnetics. Antenna and microwave engineers and students will find key insights into current trends and techniques of electromagnetics likely to shape future directions of this increasingly important topic. Each chapter includes a comprehensive analysis and ample references on innovative subjects that range from combining electromagnetic theory with mathematical concepts to the most recent techniques in electromagnetic optimization and estimation. The contributors also present the latest developments in analytical and numerical methods for solving electromagnetics problems. With a level of expertise unmatched in the field, FRONTIERS IN ELECTROMAGNETICS provides readers with a solid foundation to understand this rapidly changing area of technology. Topics covering fastdeveloping applications in electromagnetics include: * Fractal electrodynamics, fractal antennas and arrays, and scattering from fractally rough surfaces * Knot electrodynamics * The role of group theory and symmetry * Fractional calculus * Lommel and multiple expansions.

Transformation Electromagnetics: An Overview of the Theory and Applications

The recently introduced transformation-electromagnetics techniques provide a new methodology for designing devices that possess novel wave-material interaction properties. They are based on the form invariance of Maxwells equations under coordinate transformations. These methods provide an extremely versatile set of design tools that employ spatial-coordinate transformations, where the compression and dilation of space in different coordinate directions are interpreted as appropriate scalings of the material parameters. The most famous transformation-optics device is the cloak of invisibility. However, a wide variety of other devices are also possible, such as field concentrators, polarization rotators, beam splitters, beam collimators, and flat lenses. In this paper, an overview of transformation-electromagnetics device design techniques is presented. The paper begins by introducing the underlying design principle behind transformation electromagnetics. Several novel transformation-based device designs are then summarized, starting with electromagnetic cloaks that have spherical shell or cylindrical annular shapes, More general cloaking designs of noncircular annular geometries are treated, and the application of cloaking to RF/microwave antenna shielding is also discussed. Following this, device designs that employ transformations that have discontinuities .on the domain boundary are presented. Unlike those used for cloaks, this type of transformation is capable of modifying the fields outside of the device. Examples of this type of transformation-electromagnetics device are presented, which include flat near-field and far-field focusing lenses, wave collimators for embedded sources (e.g., antennas), polarization splitters and rotators, and right-angle beam benders.

Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning

The scan volume of a thinned periodic linear phased array is proportional to the spacing between array elements. As the spacing between elements increases beyond a half wavelength, the scan range of the array will be significantly reduced due to the appearance of grating lobes. This paper investigates a method of creating thinned aperiodic linear phased arrays through the application of genetic algorithms that will suppress the grating lobes with increased steering angles. In addition, the genetic algorithm will place restrictions on the driving-point impedance of each element so that they are well behaved during scanning. A genetic algorithm approach is also introduced for the purpose of evolving an optimal set of matching networks. Finally, an efficient technique for evaluating the directivity of an aperiodic array of half-wave dipoles is developed for use in conjunction with genetic algorithms.