Fig. 1. Schematic diagram of the transversal and longitudinal displacement measurement by two identical metasurfaces. The double arrow represents linear polarization, and the arrowed circles represent the right-handed circular polarization and left-handed circular polarization.

Fig. 2. The design of the displacement measurement metasurface. (a) The perspective view of the unit cell consists of the Si elliptical cylinder located on the quartz. (b) The top view of the nanopillar. (c), (d) The amplitude transmittance t_o and phase delay φ_o for incidence along o axis as a function of D_o and D_e. t_e and φ_e also can be obtained by exchanging D_o and D_e. (e) The maximum interference intensity |η₁|²|η₂|² as a function of D_o and D_e. The region marked by the red dashed ellipse indicates the area with higher intensity and good tolerance for the size of structure. (f) The simulated farfield intensity distribution of a 30 µm × 30 µm metasurface. The bottom is the normalized intensity distribution along α_y = 0°.

Fig. 3. The displacement measurement properties of the designed metasurface. (a) Schematic illustration of the measurement setup. The inset is the SEM image of the sample. Scale bar, 2 µm. (b), (c) The normalized interference intensity for −1st and +1st order output light as a function of the transversal displacement Δx and the longitudinal displacement Δz. (d) The intensity profiles for −1st and +1st order output light along the white dashed line in (b) and (c). (e) The intensity profiles for −1st and +1st order output light along the black dashed line in (b) and (c).

Fig. 4. The sensitivity and resolution of transversal and longitudinal displacement measurement. The linear regions of the (a) transversal and (b) longitudinal displacement measurement.