Fig. 2: Mechanism of dynamic spatial frequency modulation.

a Two-dimensional spatial frequency spectrum calculated from the discrete phase distribution profile defined in Eq. (1). The spacing between the optical elements in the neighboring rows and columns are both taken as 300 nm and the operating wavelength is 633 nm. The circle of \(v_x^2 + v_y^2 = \lambda ^{ - 2}\) separates the zones of output propagating (gray) and evanescent (white) waves. Red and blue dots correspond to the low and high frequency components, respectively. b Calculated intensities of the low and high spatial frequency components in dependence on Δφ. The zones of the propagating and evanescent waves are indicated in gray and white, respectively. c Experimental and simulated results of the anomalous reflection intensity modulated by Δφ. Δθ defines the angle difference between the gold nanrods located in the neighboring odd and even columns, respectively. Each gold nanorod has a dimension of 200 nm × 80 nm × 30 nm. They reside on a gold mirror spaced by a SiO₂ layer (100 nm). d Schematic of the reflective metasurface, in which the gold nanorods are embedded in a spacer with a refractive index of 1.5 and thickness of 50 nm. The alternating columns are further covered by two dielectric materials with refractive indices of n_a and n_b, respectively. Δφ contains contributions from both geometric (Δφ_g) and propagation phases (Δφ_p), i.e., Δφ = Δφ_g + Δφ_p. e Simulated intensity of the anomalously reflected light in dependence on n_a and n_b tuning.