Optical antennas are devices that convert freely propagating optical radiation into localized energy, and vice versa. They enable the control and manipulation of optical fields at the nanometre scale, and hold promise for enhancing the performance and efficiency of photodetection, light emission and sensing. Although many of the properties and parameters of optical antennas are similar to their radiowave and microwave counterparts, they have important differences resulting from their small size and the resonant properties of metal nanostructures. This Review summarizes the physical properties of optical antennas, provides a summary of some of the most important recent developments in the field, discusses the potential applications and identifies the future challenges and opportunities.

Antennas for light

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

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

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Fractal design concepts for stretchable electronics

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

Experimental and computed results show a multiband behaviour over five bands for the new fractal Sierpinski antenna. Such a behaviour is based on the self-similarity properties of the antenna's fractal shape, which might open an alternative way for designing new multiband and frequency independent antennas.

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Fractal multiband antenna based on the Sierpinski gasket

A small but long wire fractal antenna based on the Koch curve is presented. Experimental and numerical results show that the antenna improves the features of a common linear monopole. The radiation resistance is increased and the Q is reduced at each fractal iteration, approaching the fundamental limit on small antennas.

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Small but long Koch fractal monopole

Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of "measures". The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way one applies finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented. >

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Measured equation of invariance: a new concept in field computations

Most array factor design techniques are highly dependent on the operating wavelength. In this paper, a novel technique based on fractal structures is described for multiband operation. The analysis is focused in two different approaches: the fractal spatial arrangement of array elements and the fractal design of array factors. Although the patterns of fractal arrays show some interesting similarity properties at several bands, the directivity is not held constant through the bands. Nevertheless, such structures have been shown to be useful for designing low side-lobe arrays with equally weighted current elements. On the other hand, the fractal array factors presented do keep the same shape at several bands because they are designed as selfsimilar curves. The arrays that would synthesize such patterns present a characteristic power-law current distribution analogous to the spectral distribution of the bandlimited fractal Weierstrass function.

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Rafael Pous

Papers

On the behavior of the Sierpinski multiband fractal antenna

Fractal multiband antenna based on the Sierpinski gasket

Small but long Koch fractal monopole

Measured equation of invariance: a new concept in field computations

Fractal design of multiband and low side-lobe arrays