## 2 Principles of RISs  
RISs are artificial surfaces that can be electronically controlled to manipulate and control electromagnetic waves. These surfaces consist of an array of sub-wavelength elements that can be controlled individually, so as to change the wavefront of the incident electromagnetic waves. The sub-wavelength elements can be realized by various means, such as patch antennas, metallic patterns, and metamaterials [25]. The structure of an RIS typically consists of a substrate, a ground plane, and an array of sub-wavelength elements. The substrate can be made of different materials, such as glass, silicon, or plastic, providing mechanical support to the RIS [26]. The ground plane is typically a conductive material such as copper or aluminum, providing a reference point for electromagnetic waves. The sub-wavelength elements are placed on top of the substrate and the ground plane, forming an array. The size and spacing of the sub-wavelength elements determine the frequency range of the electromagnetic waves that the RIS can manipulate. The distance between the sub-wavelength elements should be smaller than the wavelength of the incident electromagnetic waves, in order to enable sub-wavelength phase control. The elements are connected to electronic circuits that can adjust the phase shift of each element, enabling the RIS to control the direction, amplitude, and phase of the incident electromagnetic waves [11]. The structure of the RIS can be flexible or rigid, depending on the application. Flexible RIS structures can be used for conformal and wearable applications, while rigid RIS structures can be used for indoor and outdoor applications [27]. The operation of the RIS is based on the principle of wave interference, which is a fundamental phenomenon in electromagnetics. When two or more electromagnetic waves interact, they can either reinforce or cancel each other out, depending on their relative phase and amplitude [28]. In the case of RISs, the electromagnetic waves are incident on an array of sub-wavelength elements, each of which can be electronically controlled to adjust its phase shift. By adjusting the phase shift of each element, the RIS can control the wavefront of the incident electromagnetic waves and create a specific interference pattern. The interference pattern can be designed to either reinforce or cancel out specific frequencies or directions of the incident waves [11]. The RIS operates based on the principle of constructive and destructive interference. When the phase shift of each element is adjusted to reinforce the incident waves, the waves constructively interfere with each other, leading to a stronger and more focused signal. When the phase shift of each element is adjusted to cancel out specific frequencies or directions of the incident waves, the waves destructively interfere with each other, leading to reduced interference and improved signal quality [29]. The physics behind RIS operation is further supported by [PERSON]'s law, which states that the angle of incidence and the angle of reflection of an electromagnetic wave are related to the refractive index of the material it passes through. By adjusting the phase shift of each element, the RIS can control the refractive index of the material it passes through, effectively manipulating the angle of incidence and the reflection of the incident waves [30]. Designing an RIS requires careful consideration of various factors, including the type of application, the frequency range of operation, the required signal quality, the number of elements in the array, and the power consumption. Next, we discuss some of the key design considerations for RIS. The frequency range of operation is a critical design consideration for RIS. The size and geometry of the RIS elements should be optimized for the frequency range of interest, so as to achieve the desired phase shift range and response time [30]. The spacing between the RIS's elements is another vital consideration.