a Measured values of refractive index (n) and extinction coefficient (k) of a-Si:H; at λ = 632.8 nm, the complex refractive index is 3.25 + 0.047j. b Unit-cell configuration composed of a-Si:H nanoresonators on a SiO2 substrate. The height (H = 400 nm) and period (P = 290 nm) are constant, but the length (L) and width (W) are different for all nanoresonators, depending on the required phase. For the two front nanoresonators, the \(\vec E\) and \(\vec H\) fields under x-polarized light, which are well confined in the nanoresonators, are depicted. c Efficiency of cross-polarization transmission (Tcross) for a range of P and rotation angles (θ) of the a-Si:H unit cell. The white dashed line at P = 290 nm denotes where the average value of Tcross is ~0.97. d Efficiency of cross-polarization transmission (Tcross) for different L and W. Four points are selected such that they have the maximum transmission efficiency (η) along with a mutual 45° phase difference (white dots are marked at the respective positions). e Wavefront of all nanoresonators for cross-polarized transmitted light at a working wavelength of 632.8 nm, obtained from full-wave simulations. 0–2π phase coverage and complete control over the wavefront of the transmitted light are realized.