Optimizing performance of metamaterial wormhole superabsorbers

Transmission line-based metamaterials are used to realize and model the conjugate-impedance matched superabsorbers. Here, we formulate an analytical-numerical approach for maximizing the effective absorption cross section of the metamaterial wormhole superabsorber, under the goal of minimizing the complexity of the structure. Analytical expressions for the gradient of the absorption cross section as a function of the structural parameters are derived. Numerical results showing enhanced absorption are obtained under three different optimization strategies: a ring-by-ring approach, a gradient-based optimization, and a mixed algorithm. The best results are achieved with the mixed algorithm, with which it is demonstrated that the optimal wormhole superabsorber significantly outperforms a black body-type absorber of a similar size. This study is of a particular interest for applications of the conjugate-impedance-matched superabsorbers as efficient harvesters of electromagnetic radiation.

Figure 1

Top: The geometry of the superabsorbing metamaterial wormhole object. The structure is formed by meshes of transmission lines: A mesh with double-positive (DPS) and a mesh with double-negative (DNG) effective material parameters. The wormhole object with radius $R_{\mathrm{obj}}$ in the middle of the structure is composed of the DNG mesh. The DPS mesh is electrically connected to the DNG mesh that continues through the wormhole. In this figure, one quarter of the DPS mesh is made semi-transparent in order to make the underlying structure visible. The structure of the DPS and DNG unit cells [16] is also shown. Bottom: Equivalent circuit of the DNG unit cell (a) and a zoom-in picture showing the connections between the unit cells in the top and the bottom planes in the wormhole region (b), as in Ref. [16].

Figure 2

Distribution of the nodal voltage $|U_n|$, $n=120\left[(y/d)+(x/d)\right]+1$, $0\le x/d<120$, $0\le y/d<60$, for the wormhole structure under the plane wave incidence of unitary amplitude, in both the DPS (top) and the DNG (bottom) domains as functions of the normalized coordinates $x/d$ and $y/d$. The radius of the wormhole is $R_{\mathrm{wh}}=20d$. The fixed parameters of the DPS cells are ${\beta }_{0}d=0.315$, $Z_0=1$, $\alpha ={10}^{-4}$. The initial optimization parameters are set based on an optimization attempt with a lower number of the DNG rings.

Figure 3

Distribution of the nodal voltage $|U_n|$, for the wormhole with radius $R_{\mathrm{wh}}=25d$. Here, the initial optimization parameters are set randomly. The other parameters are as in Fig. 2. The resulting beam in the DNG plane is faint and most energy is reflected off the wormhole, seen as the interference pattern in the DPS plane.

Figure 4

The maximum obtained ${\sigma }_{\mathrm{norm}}$ as a function of the total number of rings $N_{\mathrm{rings}}=(R_{\mathrm{obj}}-R_{\mathrm{wh}})/h$. The optimization parameter values have been determined by the optimization algorithms presented in this work. The results of the gradient descent methods with and without the momentum are presented twice: First, using random starting parameters and, second, using the optimized solution for the system composed of $(N_{\mathrm{rings}}-1)$ rings [marked with “(p)”].

Figure 5

Distribution of nodal voltage $|U_n|$ in the structure with the parameters (listed in Table 1) that result in the maximum ${\sigma }_{\mathrm{norm}}$ value achieved in this work. The wormhole radius is $R_{\mathrm{wh}}=23d$, and there are seven rings in the wormhole object.