## 1 Introduction  
With the rapid development of modern wireless electronic technology, multiple functions should simultaneously exist in a single device to save resource and space, which raises the demand for multi-functional antennas. Among all these functions, beam steering, focusing and generation of vortex beam are the most popular and related to the phase manipulation of the wavefront. For beam steering, there are two kinds of approaches. One is based on mechanical rotation, such as parabolic reflector [1; 2; 3]. However, these antennas are too bulky and have a slow scanning speed, restricting their practical applications. The other is based on electrical scanning, whose principle is to achieve the angular deflection of the wavefront by electrical engineering the phase distributions. This method is convenient and can be adopted by using various antenna structures, such as resonator cavity [4; 5; 6], reflect array [7; 8; 9; 10], dipole antenna [11; 12], and patch array [13; 14; 15]. In particular, the patch array antenna provides a simple solution with a low profile, compact size, low cost, and ease of integration with planar circuits [16].  
Due to the above characteristics, the patch array can also be applied to beam focusing [17; 18; 19; 20]. One of the most widely used applications of beam focusing is non-contact microwave sensing in which the energy should be confined within a small area [21; 22]. In addition, it is desired to maximize the energy to heat the cancerous tissue without heating the healthy ones adjacent to the tumor [23]. Another function related to wavefront phase manipulation is the generation of orbital angular momentum (OAM) vortex beams [24; 25], which could also be achieved by designing the patch arrays. As we know, the OAM vortex beam can be generated by a circular array of elements with the same amplitude and a continuous phase delay from 0 to \(2l\pi\) after a full turn, where \(l\) is an integer and called the topological charge [26; 27]. Over the past decades, the OAM vortex beam has been widely studied because it can carry infinite and orthogonal OAM which provides a new degree of freedom for coding and modulating in wireless communication [28; 29; 30; 31; 32]. Nevertheless, the above patch arrays are usually organized in low order so that the phase gradient is relatively small, resulting in narrow scanning range and low order topological charge. One method to increase the scanning angle is using expensive materials with special properties [33].  
In this paper, a reconfigurable patch array organized in high order is proposed to realize tunable wide beam steering, focusing and generation of OAM vortex beams. The patch array is composed of \(7\times 7\) elements and phase shifters, which can be controlled by diode switches. This proposed patch array resonates at 300 GHz so that it can be used in THz communication and other THz applications. By using this structure, a patch array with phase gradient of the 3 rd order is numerically designed and simulation results show that the beam scanning angle could be actively tuned from \(-55^{\circ}\) to \(55^{\circ}\). In addition, this patch array is used to achieve tunable beam focusing, in which the focus is controlled at three positions with a distance of five times of the wavelength away from the patch array. In addition, vortex beams carrying topological charges of \(l=1,2,3\) can be reconfigurable and generated by exciting array elements with the above phase gradient. The results verify that the proposed patch array has multiple functions of beam steering, beam focusing and generation of multi-mode OAM vortex beams.