Fig. 1. Schematic of the transmitted metasurface cloak. The transmitted metasurface cloak consists of two planar metasurfaces, labelled as layer 1 and layer 2, to hide an object inside, such as a cat. Each metasurface is composed of eight subwavelength metasurface elements, each of which provides a local transmitted spectrum shift. To prevent EM waves from scattering in other directions, two PEC blocks are arranged to form a closed rectangular box. Here, we consider both near-field distribution (the out-of-plane magnetic field inside the rectangular region enclosed by the green dashed line) and far-field radar cross section to characterize the cloaking performance. Ideally, after passing through the two-layer metasurfaces, the forward and backward scattering of the incident wave shall be very small, as though the rectangular box were transparent.

Fig. 2. Nonuniqueness issue addressed by a T-NN in the inverse design. (a) Different metasurface arrangements induce exactly the same near field and far field, called the nonuniqueness issue. This nonuniqueness issue will make the deep neural network difficult to converge. (b) Schematic of a T-NN, consisting of an inverse deep neural network (NN1) and a forward deep neural network (NN2). The NN1 has the input of near-/far-field response and the output of metasurface arrangement (nonuniqueness). In contrast, the NN2 has the input of metasurface arrangement and the output of near-/far-field response (uniqueness). In the training procedure of the T-NN, the NN2 is pretrained and fixed, and only the NN1 is updated to reduce the loss function, that is, the difference between the target field response F and the output F′. Therefore, the metasurface arrangement S can be extracted from the intermediate layer.

Fig. 3. Training results of the forward deep neural network (NN2). (a) Learning curve of the NN2 for the far field, with an accuracy of 85.7%; (b) learning curve of the NN2 for the near field, with an accuracy of 89.0%; (c) three metasurface arrangement samples, taken from the test set, to illustrate the performance of the NN2; (d) normalized RCS predicted by the NN2 and the simulated one obtained by importing the above three samples into the commercial numerical software COMSOL; (e) near-field distributions predicted by the NN2, and the simulated one obtained by numerical simulation.

Fig. 4. Training results of the T-NN. (a) Learning curve of the T-NN for the far field, with an accuracy of 93.2%. To intuitively demonstrate the T-NN performance, we blindly select three RCS curves in the test set as the inputs [red curve in (c)], and output the metasurface arrangements from the intermediate layer, as shown in (b). In (c), we also plot the output of the T-NN (green curve), and the simulation result (purple curve) of the samples in (b). (d) Learning curve of the T-NN for the near field, with an accuracy of 92.4%; similar to the RCS above, we also blindly select three samples [upper part of (f)] as the inputs, and output the metasurface arrangements from the intermediate layer, as shown in (e). In (f), the output of the T-NN [middle part of (f)] and the simulation results [lower part of (f)] are also plotted. Obviously, these three in (f), as well as those in (c), are highly consistent with each other.

Fig. 5. Transparent invisibility cloak enabled by the pretrained T-NN. In an ideal case, the scattering of the transparent invisibility cloak should be zero, which is fed into the pretrained T-NN as the input. As such, we obtain the metasurface arrangements in (a). Based on (a), we obtain the normalized RCS of the dielectric cat with/without the cloak, as shown in (b). (c) and (d) are the simulated magnetic fields without/with the cloak, respectively, where the incident plane wave propagates from bottom to top. In (d), the field keeps almost flat after passing though the cloaking device, in stark contrast to that in (c).

Fig. 6. Other functionalities enabled by T-NN. (a) Normalized RCS of a dielectric pigeon and a dielectric cat surrounded by a bilayer metasurface; (b), (c) simulated magnetic field distribution of (b) the pigeon and (c) the cat with a bilayer metasurface; (d) normalized RCS of a dielectric seahorse and a dielectric cat with a bilayer metasurface; (e), (f) simulated magnetic field distribution of (e) the seahorse and (f) the cat with a bilayer metasurface.