Fig. 2. Design of a broadband achromatic metalens.
a Sketch map of the phases of a broadband achromatic lens in the r-ω space with a fixed focal length f. The coordinates of the original point (r, ω, φ) are set as (0, 0, β). Three-phase profiles at 430, 530, and 630 nm are plotted. The value of α is set as 1.45 μm, and β is −1.25 rad. For a given radius of the metalens r, the achromatic phase φ should be linearly associated with the frequency ω, indicating that the effective refractive index neff is independent of the frequency via the relationship between the slant angle θ(r) and neff. b Effective optical path difference (OPD) d∆neff in the f−r space. Several values of the effective OPD are plotted as white curves (Unit, μm). Note that a broadband achromatic metalens with a large radius and short focal length needs a large effective OPD d∆neff, e.g., the red color in the upper-left corner. c Transmission (blue) and phase (red) of a silicon nitride grating. The inset shows the geometry of the nanoposts, where the diameter of the circular hole is 60 nm. The hexagonal lattice constant and the thickness are 320 nm and 400 nm, respectively. A high transmission and a near-linear phase as a function of the angular frequency are achieved in the entire visible region. A pair of parameters (neff, β) is then retrieved from the linear fitting of the phase (black), where neff = c/d·tan(θ) and β is the crossing point at zero frequency. d Calculated (neff, β) results for all considered silicon nitride gratings. Each blue point represents a different grating. Red dashed lines indicate the air and silicon nitride materials; the results show that the neff values of all considered gratings are mostly located between the background material (air) and the chosen dielectric material (SiN). By selecting the optimal β value to obtain the maximum ∆neff, the gratings at red points can be screened out; finally, ten kinds of gratings (inset) are chosen after the discretization of neff to compose the broadband achromatic metalens