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To enhance transmission efficiency of Pancharatnam-Berry (PB) phase metasurfaces, multilayer split-ring resonators were proposed to develop encoding sequences. As per the generalized Snell law, the deflection angle of the PB phase encoding metasurfaces depends on the metasurface period size. Therefore, it is impossible to design an infinitesimal metasurface unit.Consequently, the continuous transmission scattering angle cannot be obtained. In digital signal processing, this study introduces the Fourier convolution principle on encoding metasurface sequences to freely control the transmitted scattering angles. Both addition and subtraction operations between two different encoding sequences were then performed to achieve the continuous variation of the scattering angle. Furthermore, we established that the Fourier convolution principle can be applied to the checkerboard coded metasurfaces.

Free control of far-field scattering angle of transmission terahertz wave using multilayer split-ring resonators’ metasurfaces