Fig. 1. Schematic diagram of the virtual metasurface compared with the conventional one.

Fig. 2. Structure and network design: (a) geometrical parameter of unit in front view and side view; (b) phase response when the length changes from 0.9 to 3.7 mm, and the step length is 0.4 mm; (c) phase response after rotating the unit 90 deg; (d) amplitude of cross-polarized wave when the length changes from 0.9 to 3.7 mm, and the step length is 0.4 mm; (e) amplitude response after rotating the unit 90 deg.

Fig. 3. Design of focusing metasurfaces and generation of virtual meta-atoms: (a), (b) two phase profiles of metasurface with a 180 deg phase difference; (c), (d) generated focusing metasurfaces filled according to the phase profiles in (a) and (b); (e), (h) distributions of electric fields Ex on the XOZ plane; (f), (i) electric field intensity distribution on the XOY plane when Z=30  mm; (g), (j) phase distribution on the XOY plane when Z=30  mm.

Fig. 4. Virtual metasurface design and verification: (a) focusing metasurfaces are spliced together according to the chessboard arrangement; (b) the intensity distribution of Ex on the focusing plane in chessboard arrangement; (c) the phase distribution of Ex on the focusing plane in chessboard arrangement; (d) the 3D far-field scattering beam of metasurface in chessboard arrangement.

Fig. 5. Verification that the far-field scattering modulation is realized by the VM rather than the entity metasurface: (a) virtual metasurface is aligned with the obstacle (a metal plate with spaced apertures); (b) the phase profile of entity metasurface; (c) the intensity distribution of Ex on the focusing plane in chessboard arrangement with the obstacle; (d) the phase distribution of Ex on the focusing plane in chessboard arrangement with the obstacle; (e) the 3D far-field scattering beam of metasurface in chessboard arrangement with the obstacle; (f) the 3D far-field scattering beam of entity metasurface; (g) the 3D far-field scattering beam of entity metasurface with obstacle.

Fig. 6. Sample fabrication and performance verification: (a) the photographs of TFMTs; (b) the photographs of spliced TFMTs according to checkerboard configuration and the samples with obstacle; (c) near-field measurement environment; (d) far-field measurement environment; (e), (f) the electric field distributions in XOZ cross sections of the 0 and 1 focusing metasurfaces; (g) the electric field distributions in XOY cross sections of the virtual metasurface with checkerboard configuration; (h) the measured far-field radiation patterns under the chessboard arrangement when φ=45° and φ=−45° on orthogonal diagonal lines; (i) the measured far-field radiation patterns under the chessboard arrangement with obstacle when φ=45° and φ=−45° on orthogonal diagonal lines.

Fig. 7. Fitting performance of neural network.

Fig. 8. Theoretical formation path of focus and more aperture sizes: (a) theoretical formation path of focus; (b) 3D far-field result with obstacle when HR=20  mm and Rhole=19  mm; (c) 3D far-field result with obstacle when HR=25  mm and Rhole=16  mm; (d) 3D far-field result with obstacle when HR=30  mm and Rhole=13  mm.

Fig. 9. Cross profile comparison between the existence of obstacles and the absence of obstacles: (a) comparison of entity metasurface; (b) comparison of VM.