Extraordinary Directive Emission and Scanning from an Array of Radiation Sources with Hyperuniform Disorder

The main challenge in the antenna or laser array design is to find the element distribution that best meets the optimal performance for broadband emission and large angle beam steering. In the past, the design strategy was restricted to arrays with periodic, aperiodic, and random distributions, which are characterized by several fundamental limitations related to the operating frequency, the power consumption that arises from interelement interference, and the computation time required during the random optimization process. Furthermore, the interelement spacing has a lower or upper bound due to the elements’ physical dimensions and the former prohibits the use of the aforementioned element distributions for small operating wavelengths, whereas the latter induces high-order grating lobes. We prove that hyperuniform disorder is an array element distribution evolving through natural selection processes that warrants a disordered solution to the array design when this is treated as a packing problem. We theoretically and experimentally report that the array with hyperuniform disorder exhibits extraordinary directive emission and scanning features, while being scalable for extra-large arrays without any additional computational effort.

Figure 1

The effect of the stealthiness parameter $(\chi )$ to the resulting real-space element locations (a) and the corresponding reciprocal space structure factor (b) for an array of 225 elements. The real-space computational domain is a rectangle of side lengths $L_x=L_y=1$ m. Both $k_x$ and $k_y$ reciprocal space coordinates span from $-50\pi$ to $+50\pi$. The structure factor is normalized to its maximum value and then plotted on a logarithmic scale.

Figure 2

The lower and upper bounds for the optimal value of the stealthiness parameter for an array with HUD for a varying number of elements. Arrays with $(N,\chi )$ combinations that reside within the shaded area will have good performance in terms of PSLL reduction for a wide operating bandwidth and large beam-steering angles.

Figure 3

The effect of the array element distribution on the radiation pattern. (a) The element distribution of the periodic array, the base Penrose-tiling array, the random array, and the array with hyperuniform disorder $(\chi =0.489)$. (b) The corresponding radiation pattern of the arrays when $f=f_0$ with $f_0$ being the frequency for which the distance between the sources of the periodic array equals one half of the corresponding operating wavelength. (c) The corresponding radiation pattern of the arrays when $f=3f_0$. (d) The top-down view of the corresponding radiation pattern of the arrays when $f=3f_0$. (e) The top-down view of the corresponding radiation pattern of the arrays when $f=3f_0$ and the main beam is steered towards the $\varphi =0^{\circ },\theta ={30}^{\circ }$ direction, measured from the array’s bore sight. In all panels the results from left to right correspond to the periodic array, the base Penrose-tiling array, the random array, and the array with hyperuniform disorder $(\chi =0.489)$. In the polar radiation plots the angular and radial coordinates correspond to the $\varphi$ and $\theta$ angles, respectively.

Figure 4

Radial distribution function $g_2(r)$ for all the array element distributions that are shown in Fig. 3, namely the (a) periodic array, (b) base-Penrose tiling array, (c) random array, and (d) array with HUD and $\chi =0.489$. The distance parameter $r$ is in meters and takes values in the $[0,L/2]$ interval, where $L$ is the side length of the square aperture area.

Figure 5

(a) Radial distribution function $g_2(r)$ for the array with HUD and $\chi =0.489$ that is shown in Fig. 3. The distance parameter $r$ is in meters. (b) The distribution of points in the array with HUD and $\chi =0.489$ that is shown in Fig. 3, with the reference point in the centre. Around the reference point, several rings of different colors are drawn, whose radii are determined by the distance $r$ of the same colored regions in the RDF graph of (a).

Figure 6

Scalability of the array with hyperuniform disorder. (a) Large array element distribution made from the $3\times 3$ arrangement of the subarray with HUD whose element distribution is shown cut off at the bottom left part of the figure for visualization purposes. Radiation pattern cuts of (b) the subarray and (c) the $3\times 3$ large array that is shown in (a) when $f=6f_0$, where $f_0$ is the frequency for which the minimum distance between the radiation sources equals one half of the operating wavelength.

Figure 7

The fabricated $16$-element Vivaldi antenna array with hyperuniform disorder and $\chi =0.438$ and its test environment.

Figure 8

Simulated (black solid line) and measured (red dotted line) radiation pattern results in the azimuth plane $\left(\varphi =0^{\circ }\right)$ when $f=3$ GHz (left) and $f=6$ GHz (right) for (a) the $16$-element Vivaldi antenna array with hyperuniform disorder and (b) the $16$-element Vivaldi periodic antenna array.

Figure 9

Measured radiation pattern results in the azimuth plane $\left(\varphi =0^{\circ }\right)$ when the main lobe is steered towards the $\varphi =0^{\circ },\theta ={20}^{\circ }$ (black solid line) and the $\varphi =0^{\circ },\theta ={40}^{\circ }$ (red dotted line) directions when $f=3$ GHz (left) and $f=6$ GHz (right) for (a) the $16$-element Vivaldi antenna array with hyperuniform disorder and (b) the $16$-element Vivaldi periodic antenna array.

Figure 10

Power pattern results in the azimuth plane $(\varphi =0^{\circ })$ for the large array with hyperuniform disorder made by the $3\times 3$ arrangement of the fabricated subarray with hyperuniform disorder, shown in Fig. 7, when (a) no steering is applied and (b) when steering is applied towards the $\varphi =0^{\circ },\theta ={20}^{\circ }$ (black solid line) and $\varphi =0^{\circ },\theta ={40}^{\circ }$ (red dotted line) directions. The left-hand plots correspond to the case in which $f=3$ GHz, whereas the right-hand plots correspond to the case in which $f=6$ GHz.