  Recently, meta-surface(MS) has emerged as a promising alternative method for
generating vortex waves. At the same time, MS also face the problem of narrow
bandwidth, in order to obtain a board bandwidth, the MS unit cells structure
become more and more complex, which will deduce many inconveniences to the
preparation process of MS device. Therefore, we want to design a simple MS unit
cell with a multi-frequency selection. In this paper, based on the principle of
geometric phase, we design a simple reflective MS unit cell based on metal
double-slit resonant ring. We elaborate on the resonance mechanism of the MS
unit cell. Under the normal incidence of circularly polarized (CP) waves, the
reflection coefficient of the same polarization was greater than 85%. By
rotating the orientation angle of the resonator on the MS unit cell, the
continuous 2pi phase coverage was satisfied in the frequency range of
0.52THz-1.1THz, and the relative bandwidth becomes 71.6%. Based on this, we
construct a vortex generator by using a 15*15 MS unit array. The right-handed
circularly polarized waves (RCP) and left-handed circularly polarized waves
(LCP) are separately incident on MS with topological charges of l=1,2,3 under
multiple resonant frequencies. The generated RCP vortex wave with topological
charges of l=-1,-2,-3 and the generated LCP vortex wave with topological
charges of l=1,2,3. The numerical simulation results exhibit our designed MS
with multiple resonance outcomes can achieve a multi-broadband operation and
generate a wide-band vortex beam. In addition, we also calculate the pattern
purity. Through theoretical analysis and numerical simulation, we prove that
our designed MS can generate a broadband vortex wave.
