## 1 Introduction
In this context, by incorporating an IRS into indoor VLC systems, significant improvements can be achieved in terms of resistance to LoS link blockages between the receiver and the transmitter, which means improvements in lighting, communication quality, location services, energy harvesting, and interference mitigation [9; 10]. IRSs make it possible to convert the physical propagation space, over which there is no control, into a fully controllable and customizable space, considering that the cost and energy consumption parameters are low [8; 11], using adjustable surfaces consisting of metasurfaces or sets of mirrors, which can induce certain phase shifts and/or amplitude modifications in electromagnetic waves. This transformation occurs by changing the properties of the incident light wave, such as its phase, amplitude, polarization, dispersion, and momentum [12]. Using these surfaces, wave propagation behavior can be altered, thus improving desired signals, and mitigating or eliminating unwanted signals, to achieve an improvement in the capacity and reliability of wireless communication [4; 13]. In IRS-aided VLC systems, the improvement also occurs in the lighting field. IRSs are generally flat surfaces composed of many passive reflective elements, each of which can independently induce a controllable phase and/or amplitude change in the incident signal [14]. Typically, these surfaces in the range of light waves can be grouped into three categories, namely metasurface, mirror array, and liquid crystal switch. The metasurface is a material made up of arrays of subwavelength dielectric or metallic structures that are used to modify the propagation of light in anomalous ways compared to classical optical devices. These surfaces are the two-dimensional equivalent of metamaterials, consisting of adjacent patches, where each patch can dynamically manipulate the incident wave in terms of amplitude, phase, dispersion, momentum, and polarization, independently from the other patches. The generalized Snell law supports reflection on these surfaces and is commonly referred to as anomalous reflection, where the angle of reflection can be adjusted and controlled and is no longer equal to the angle of incidence [15; 16]. Liquid crystal switch-based IRSs, sometimes classified as a particular case of the metasurfaces, consist of any reflector covered by a layer composed of arrays of liquid crystal molecules, which determines whether the reflected wave can spread. For this scenario, the specular Non-LoS paths can be managed electrically, and the configuration of these surfaces is simplified to a binary problem [17]. A mirror array consists of multiple adjacent small mirrors, where each small mirror can adjust its rotation to affect the propagation of the light wave. This reflection is based on the Snell law of reflection, where the angle of reflection is equal to the angle of incidence. A basic schematic of an IRS-aided VLC system based on metasurfaces is shown in Figure 1. We can see that, when the LoS component of the channel is blocked, the light wave reaches the PD through the IRS. Therefore, several otherwise Non-LoS components are mirrored in a controlled manner using the IRS, where an element called the IRS controller handles the control and programming of the tunable surfaces for phase shift and/or amplitude modification. Motivated by the potential of IRSs to enhance the performance in the aforementioned scenarios, we believe that it is necessary to further explore, investigate, and analyze indoor scenarios that combine VLC communication and IRS technology. Therefore, in this article, we present the following contributions:  
* We present an in-depth analysis of the behavior of an optical signal in a VLC system assisted by an IRS on metasurfaces. Figure 1: Basic schematic of an IRS-aided VLC System. * We obtain mathematical expressions of the LoS and Non-LoS channel components, including the effect of the reflection of the optical signal in the IRS and obstacles and obstacles that can cause shadowing.