Fig. 1: Schematic depiction of the generation of an achromatic non-diffracting perfect vortex beam (ANPVB) utilizing a geometric metasurface.

a Broadband light is incident upon the metasurface, which employs precise radial momentum control to generate an ultra-broadband, achromatic, non-diffractive perfect vortex beam. b The metasurface introduces a dominant radial momentum component (|k_r | ≫|k_ϕ|), which governs the transverse momentum distribution (\(|{{{{\mathbf{k}}}}}_{{|}{|}}|=\sqrt{|{{{{\mathbf{k}}}}}_{{r}}{|}^{2}+|{{{{\mathbf{k}}}}}_{{\phi }}{|}^{2}}\approx |{{{{\mathbf{k}}}}}_{{r}}|,{{{{\mathbf{k}}}}}_{{|}{|}}={{{{\mathbf{k}}}}}_{{r}}+{{{{\mathbf{k}}}}}_{{\phi }},{{{{\mathbf{k}}}}}_{{|}{|}}\approx {{{{\mathbf{k}}}}}_{{r}}\)). This design renders changes in azimuthal momentum due to variations in topological charge (\(\Delta |{{{{\mathbf{k}}}}}_{{\phi }}|\propto {l}\)) negligible. The suppression of diffraction is achieved through a nonlinear design of the radial momentum gradient, significantly enhancing the Rayleigh range (z_R).