## 1 Introduction
Regarding the manipulation of the radiation patterns, recent research based on magnetic meta-atoms has realized the nonreciprocal unidirectional scattering [22] and the nonreciprocal Kerker effect [23]. When applied to antennas, metasurfaces can enhance performance, for instance, by providing dynamic control over the radiation patterns, allowing for precise beam-steering. However, conventional approaches often require redesigning individual radiating elements within the antenna array, which can limit their flexibility and adaptability. To address these limitations, reconfigurable intelligent metasurfaces are employed, offering a solution that allows for dynamic beam manipulation without the need for extensive modifications to existing antenna structures [24]. This beam-steering approach offers a more pragmatic and cost-effective solution than conventional antennas. Indeed, antennas enhanced by metasurfaces feature simple design elements, and passive beam scanning capabilities eliminate the need for power-hungry and complex active RF components [25; 26]. As a result, research on these antenna systems is advancing rapidly to meet the growing mass-market demand for low-cost, low-profile beam-steering front-end devices. While this approach has demonstrated its effectiveness, current studies have yet to fully explore the wide range of degrees of freedom offered by metasurfaces. So far, most studies have focused on controlling only a few radiation pattern characteristics, such as the main beam direction [27; 28; 29]. Indeed, in our previous works, we demonstrated that metasurface coatings on linear dipole antennas can shape the antenna's radiation pattern by controlling the position of the main lobes [30]. More recently, we have shown that metasurface synthesis could be efficiently performed by leveraging a circular array model [25]. However, a key aspect that remains underexplored in these early works involving metasurfaces is their ability to enable effective sidelobe control and suppression of unwanted signals. While null-steering has been extensively studied in traditional antenna arrays, our work aims to address this gap by harnessing the potential of metasurfaces to optimize both the main beam and null positioning in the radiation pattern, employing an evolutionary algorithm as a novel approach for these configurations. Building on these advancements, this paper introduces a novel design of a cylindrical Huygens metasurface (HMS) surrounding a dipole antenna optimized through a Genetic Algorithm (GA) to improve the metasurface parameters for beamforming and null-steering applications. The GA-driven optimization is a key innovation that allows for the precise tuning of metasurface parameters. Unlike prior works, which primarily focus on beam direction, our approach introduces the control to place nulls in the radiation pattern at exact and predefined positions. This unprecedented level of precision marks a significant advancement in this field. The adaptation of methods traditionally used for rectangular antenna arrays to cylindrical geometries requires significant modifications due to the inherent differences in boundary conditions and geometry. In this work, we have extended the concept of array synthesis by carefully modifying the analysis to account for the geometry of cylindrical arrays. This study of cylindrical antenna arrays is well-established, as seen in numerous publications that have analyzed their radiation characteristics and synthesis techniques [31, 32]. For example, some studies have explored the opportunities associated with cylindrical geometry, such as its impact on mutual coupling and array factor computations [33]. However, this work aims to integrate cylindrical metasurfaces with optimization algorithms to enable precise control of beamforming and null-steering. By leveraging metasurface technologies, which are less explored in the context of cylindrical geometries, this work contributes to bridging the gap between conventional array analysis and modern metasurface-based antenna designs.