## 1 Introduction  
Electromagnetic waves can realize the wireless transmission of energy and information, which provide an irreplaceable role for the development of society. Meanwhile, the divergence characteristic of an electromagnetic wave limits its application, and the Bessel beam [1] with non-diffracting characteristic shows the potential to solve this problem. Therefore, devices that can generate high-performance Bessel beams have been extensively studied, and a source with limited spatial size can only generate a quasi-Bessel beam, which has the ideal Bessel beam's characteristics over a finite non-diffracting area [2; 3; 4; 5]. As the energy in the non-diffraction area has the characteristics of uniform and high efficiency, it is suitable for Bessel beams to be used in wireless power transfer (WPT) [6; 7; 8] and near-field communication systems [9; 10]. The high-order Bessel beams with the characteristics that vortex beams have also show great potential in the field of high-speed wireless communication and high-resolution imaging [11; 12; 13]. However, most devices can only generate on-axis Bessel beams, and there are few studies on off-axis Bessel beams [14; 15; 16; 17; 18; 19; 20; 21]. So, we studied some methods about steering Bessel beams or focused beams [22; 23; 24; 25; 26; 27; 28; 29], and it is easy to find that, although the Bessel beams have a wider range of energy distribution, there are very few methods to steer them. One method is proposed to steer Bessel beams using computer holograms with the help of amplitude modulation [22]. Another novel method can generate arbitrarily directed Bessel beams using an off-axis multi-focusing antenna [24], and this method is also helpful to improve the design precision of the depth-of-field of the beam. As the beam deflection requires only phase modulation, the lack of amplitude modulation will result in a deflected beam that is not strictly a Bessel beam, and we can call it a pseudo Bessel beam. It is not easy to maintain high efficiency and high directionality when the beam is deflected, and because the performance of the single off-axis pseudo Bessel beam is not satisfactory, multiple pseudo Bessel beams are more difficult to be achieved. This also leads to the fact that the devices generate Bessel beams that are not multifunctional, which makes them unable to give full play to their advantages in wireless transmission systems. In this paper, we propose a method to generate a single off-axis pseudo Bessel beam and multiple pseudo Bessel beams with accurate propagation directions and high efficiency. To modulate electromagnetic waves effectively [30; 31; 32], we firstly use a reflective metasurface that has low loss to generate the off-axis pseudo Bessel beam in any desired direction. As the reflective metasurface is single-layer, it is also low profiled compared with non-planar or multi-layer devices [5; 6]. The unit cell of the metasurface has a periodicity of 8 mm at 10 GHz, and it also has the characteristics of a small size, high efficiency, and insensitive to both polarization and incidence angle. As the method we proposed satisfies the requirement of a transverse wave vector component of the Bessel beam, comparing with existing methods, the generated off-axis pseudo Bessel beam using our method has an accurately controllable propagation direction and high efficiency. Then, according to the proposed method and electromagnetic field superposition principle, a metasurface with \(47\times 47\) unit cells is proposed to generate multiple pseudo Bessel beams simultaneously for the first time. The metasurface is simulated with a standard X-band horn in ANSYS HFSS and the results show that the proposed method can be used to generate dual pseudo Bessel beams. The generated beams have a transmission efficiency of 59.2% at a transmission distance of 400 mm and maintain high efficiency in the non-diffracting area.