###### Abstract
firstly proposed two kinds of phase-engineered metalens [17], by introducing the phase profiles of focus and Bessel beams into the Pancharatnam-Berry (P-B) based metasurfaces; converging and non-diffraction vortex beams with small converging angles are achieved, respectively. In order to reduce the design complexity of the metasurface, they also proposed a 1-bit non-diffractive microwave vortex beam generator [18], which greatly reduced the types of desired phase units. Based on geometric optics and projection methodologies, two kinds of 3-D printed terahertz discrete dielectric lenses [19] were proposed by [PERSON] et al. to produce non-diffractive high-order vortex beams in the terahertz regime, offering a new approach for the THz ultra-high-speed communications. [PERSON] et al. proposed a reflective metasurface launching multiple pseudo-Bessel beams with high efficiency [20], by which the energy of the beams was preserved as almost constant along the propagation axes. The non-diffractive vortex-wave metasurfaces mentioned above provided profound insights into the generation methodologies; however, they were excited by the externally spatial feeding sources, which occupied large spaces and caused the spatial feed error. To improve these issues, a tensor impedance modulation-based metasurface integrated with a feeding source was proposed by [PERSON] et al. [21], which reduced the space-occupied volume greatly and provided efficient control for the high-order Bessel vortex beams. However, due to the requirement of different rotation angles and the size of the gap in each unit, it was challenging to realize a reconfigurable metasurface which could dynamically steer the non-diffractive waves in the future. [PERSON] et al. proposed a waveguide-fed structure-based holography [22] to construct metasurfaces, which manipulated the radiated beams flexibly by the interference between the surface wave and the predesigned interferogram. Only by changing the on/off states of unit cells that coupled to the continuous guide-mode of magnetic components, could the interferogram with different features be created and the metasurface radiate an expected object wave. This phase-keying holographic method has potential advantages in dynamically reconfigurable metasurfaces and intelligent sensors. It has been applied to the realization of polarized waves [23], multi-beam [24], focus [25],imaging [26] and intelligent sensing [27]. However, the manipulation of the circularly polarized non-diffractive vortex waves carrying OAM has not been researched before. In this work, we propose an innovative methodology for generating a CP quasi-non-diffractive vortex wave with the desired OAM mode by combining non-diffracting theory and the principle of waveguide-fed-based holography. The general forms of the designing formulas were derived to validate our proposal. A metasurface generating an LHCP quasi-diffraction-free vortex wave carrying an \(l=-1\) OAM mode was constructed, simulated and analyzed in the electromagnetic software. The numerical simulations demonstrated that the LHCP quasi-non-diffractive vortex wave possessed an almost constant divergence radius and electric field strength in the 9 times wavelength range compared with a conventional vortex wave. It provided a new way to generate and steer the CP quasi-non-diffractive vortex wave in medium-distance without using an external excitation, which held enormous potential for the miniaturization devices applied in wireless energy transmission and high-capacity communication.