Polarization-independent characteristics of the metasurfaces with the symmetrical axis's orientation angle of 45° or 135°

A series of symmetrical nanoantennas with a symmetrical axis orientation angle of 45° or 135°, which are suitable for both X/Y linear and circular polarizations incidences simultaneously, have been designed and investigated in detail. We have deduced the transmitted matrix of the metasurface structure by rigorous mathematical theory, and found that the essential reason for the polarization-independence characteristics is that there are the same transmitted amplitudes and phases under the incidences of X/Y linear and circular polarization lights due to metasurface structure with the symmetrical axis's orientation angles of 45° or 135°. Based on the V-shaped, C-shaped, U-shaped and elliptical slit nanoantennas, we have verified the proposed theory fully by numerical simulations. The independence of the incident polarizations is very important for the practical applications and developments of the metasurfaces.