AFRL-AFOSR-VA-TR-2016-0129 ANISOTROPIC GRID GENERATION | Deliverables

During this program we have had several major accomplishments. These include finalizing our prior work on simple anisotropic surfaces consisting of discrete regions of homogeneous impedance values, and demonstrating them in the form of several useful structures. Examples include beam shifting structures, and scattering control surfaces. We have also developed a new method for patterning anisotropic surfaces based on defining a set of points which are shifted according to the desired impedance, and then used to define a lattice of cells. The goal of this work is to create smoothly varying inhomogeneous anisotropic impedance surfaces with arbitrary and well-defined impedance profiles that can perform useful functions. We have demonstrated this method in the form of a planar Luneburg lens, and an improved beam shifting structure. We have also developed a method for validating that the pattern of unit cells accurately reproduces the desired impedance function, although this last task is currently still in progress. Our next work is to develop a way to automatically define the starting function for the cell generation algorithm. At that point we will have a full procedure for starting with a desired impedance profile, and validating that the final output produces the intended profile. Introduction The interaction between electromagnetic waves and objects can be defined entirely by the surface impedance of those objects. This controls the scattering behavior and thus the radar cross-section, and it also controls surface wave propagation which determines antenna coupling parameters, interference between co-located electronic systems, and all other aspects of electromagnetic interaction. Thus, defining the surface impedance is important for controlling how such systems behave. This has traditionally been accomplished with layered materials, resistance cards, magnetic radar absorbing materials, and other such treatments. It has also been accomplished with periodic structures such as frequency selective surfaces. For the past several years, the field of meta-surfaces has been continually evolving. Beginning with the high impedance surface in 1999, the field has expanded to include holographic surfaces, which have been used to create conformal antennas and cloaking structures. These provide a much simpler approach than other work in metamaterials, because they are built using an electrically thin structure which can be fabricated using printed circuit technology. It is now recognized that anisotropy can provide even greater control over the propagation of surface waves, and the scattering of incoming plane waves. A classic example is the soft and hard surfaces that were studied several decades ago, which can be used to enhance or suppress TM or TE surface waves depending on the direction of propagation. Such structures can also be implemented as artificial impedance surfaces, whereby they can be much thinner and simpler DISTRIBUTION A: Distribution approved for public release. to fabricate. Several simple examples of applications for anisotropic surfaces will be described below. The difficulty with creating arbitrary anisotropic surfaces is that they require elongated unit cells to create high anisotropy. Because such cells do not fit into a regular square or hexagonal grid, regions with different primary directions of anisotropy cannot be smoothly or easily connected, as shown in figure 1. As a result, all of the initial work with such patterns involved discrete regions of homogeneous impedance. We have now developed a new technique for producing arbitrary and isotropic impedance services, which is the primary topic of this report. We have demonstrated that such structures can be useful for performing certain electromagnetic functions, and we have fabricated and tested several examples. Our present work is on validating that the patterns generated by this technique produce the intended impedance profile. Figure 1. An example of a simple pattern to produce an anisotropic impedance surface, which can be described by an impedance tensor. The impedance is largely controlled by the length of the cells along each direction. The difficulty identified on the center panel is that highly anisotropic regions with different primary directions cannot be smoothly or easily connected. The goal of this work is to produce the electromagnetic equivalent of snake skin, pictured at right, with smoothly varying cells of different sizes and orientations. Background and Applications A variety of anisotropic impedance surface structures have been studied in the past, and several examples are shown in figure 2. These include the original holographic anisotropic surface which was studied by the author, as well as similar structures that have been studied by other groups. The common theme of these structures is that the individual unit cells have some kind of anisotropy, either in the form of slices with varying angles, or having different capacitances in different directions. Regardless of the approach, the result is the same and the impedance along a given direction is a result of the sheet capacitance in that direction, which generally relates to the length of the unit cell and the density of gaps in that direction. The limitation of these approaches is that the cells must have an aspect ratio close to one, such as squares, circles, or hexagons. To create highly anisotropic impedance surfaces, highly elongated cells are needed. However, as discussed above, these are difficult to form into arbitrary patterns because they cannot be arranged on a simple grid that still allows for arbitrary and varying angles. DISTRIBUTION A: Distribution approved for public release. Figure 2. Examples of previous anisotropic surfaces include the original holographic tensor impedance surface created by the author (left), a similar structure studied by Stefano Maci (center), and another variant studied by Tony Grbic (right). As one approach to creating anisotropic unit cells, we have explored a variation on the classic mushroom shape, which is shown in figure 3. Adding a conductive via increases the available impedance range significantly. However, it also substantially reduces the bandwidth. The structure shown in figure 3 is a compromise, where the via is present but capacitively connected to the patch. The patch is also elongated to produce an anisotropic surface impedance. The result is that this structure can have both broad bandwidth and also a wide range of impedance values. The drawback of the structure is that the basic unit cell is still a square or rectangle, and thus it can only be arranged on a regular grid, forbidding the potential of smoothly varying arbitrary patterns. Figure 3. A broadband anisotropic cell design consists of an elongated patch and a capacitively coupled via. The capacitive coupling allows the surface to retain the wide impedance range, while increasing the bandwidth. Nonetheless, this unit cell type has proven the potential of highly anisotropic unit cells for practical applications. One example is shown in figure 4. This is a small section of the interface between two different regions of anisotropic impedance surface based on the unit cell type shown in figure 3. The entire structure was much larger than this small section, roughly 12 x 18". This sample allowed us to test refraction at a boundary between two anisotropic impedance surfaces, and also to demonstrate the beam shifting approach, and techniques for guiding surface waves around obstacles. As shown in the figure, a surface wave will refract both upon entering the surface, and upon passing into a second impedance surface with a different primary direction. When the interface between the two surfaces is illuminated directly, the incoming wave is split into two beams, and can thus avoid a scattering object that would otherwise be in the way. This can be used for example to reduce scattering by holes or apertures in the skin of an aircraft, or to control the direction of propagation of waves along the metal body. 200 300 400 500 600 700 800 5 10 15 20 25 k (m-1) Fr eq ue nc y (G Hz ) Rot 0 Rot30 Rot 60 Rot 90 Light 8 10 12 14 16 18 0 200 400 600 80