  Vortex beams carrying orbital angular momentum (OAM) have been widely applied
in various electromagnetic, optical, and quantum systems. A tailored OAM
spectrum composed of several specific modes as expected holds a promise for
expanding the degrees of freedom of the systems. However, such a broadband
high-purity tailored spectrum is difficult to be achieved by the present
devices, where the broadband amplitude manipulation has not been explored yet.
In this work, inspired by the envelope-modulation theory, an elegant and
universal way to manipulate the OAM spectrum in wide bandwidth is proposed by
using a shape-tailored metasurface. Firstly, the rotating meta-atoms on a
triangular lattice are proved to have smaller coupling distortion than that on
a square lattice, and this behavior is critical for high-purity vortex spectrum
generation by the Pancharatnam-Berry-based metasurfaces. Secondly, a universal
modulation relation is established between the spatial arrangement of
metasurfaces and the generated vortex beams. Finally, the broadband modulated
OAM spectra and the comb-like OAM spectra are theoretically and experimentally
demonstrated by the shape-tailored metasurfaces. The proposed
amplitude-modulation scheme offers a novel concept and engineering route to
manipulate the OAM spectrum in wide bandwidth, which could promote the
development of OAM-based applications.
