## 1 Introduction
The synergy of Si\({}_{3}\)N\({}_{4}\) with standard semiconductor fabrication processes positions it as a compelling choice for integrated photonic circuits, driving advancements in communication, sensing, and quantum information processing [24]. The versatility and exceptional performance of Si\({}_{3}\)N\({}_{4}\) in the realm of photonic devices underscore its pivotal role in the continuous evolution of integrated optics [16]. The RR structure holds immense significance in the realm of sensing technologies, offering a novel and highly sensitive approach to detecting various physical and chemical parameters [4]. Utilizing the principles of light confinement within a circular waveguide, these RRs enable the precise interrogation of changes in their immediate environment [25]. This technology has been proven instrumental in applications such as biosensing, environmental monitoring, and telecommunications. Its high sensitivity allows for the detection of minute changes in the refractive index, making it particularly valuable in medical diagnostics and the study of biological interactions at the molecular level [26]. Moreover, the compact nature of photonic RRs enhances their integration into micro- and nanoscale devices, paving the way for advancements in miniaturized sensing platforms [27]. As researchers continue to explore and refine this technology, the RR sensor stands as a beacon of innovation, promising breakthroughs in fields where precision and sensitivity are paramount [28]. Refractive index sensing assumes a crucial role in advancing label-free biosensing methodologies, offering a direct and highly sensitive approach to detecting molecular interactions. In the context of label-free biosensing, alterations in the refractive index become a key parameter for monitoring changes in the optical characteristics of a sensing surface resulting from biomolecular binding events [29]. As biomolecules bind to the sensor surface, they induce variations in the local refractive index, leading to observable shifts in the resonance angle or interference patterns [30]. These shifts exhibit high sensitivity and are proportionate to the mass and concentration of the bound molecules. The real-time measurement of these changes allows us to gather valuable insights into the kinetics, affinity, and concentration of biomolecular interactions without the need for labeling agents. Consequently, refractive index sensing emerges as a potent tool in the realm of label-free biosensing, facilitating a more profound understanding of biological processes and finding applications in diverse fields, including medical diagnostics, pharmaceutical development, and environmental monitoring [4; 31]. In this study, we have showcased a comprehensive investigation into a Si\({}_{3}\)N\({}_{4}\) platform-based RR device designed to detect refractive index variations in the ambient medium. Our approach integrates both numerical simulations and experimental validations to thoroughly assess the device's sensing capabilities. Numerical analysis is carried out using the two-dimensional finite element method (2D-FEM) via COMOL Multiphysics software 6.1, offering a reliable approximation of the device's sensing performance. The significance of this work lies in the remarkable accuracy of the 2D-FEM simulations, which can significantly reduce the computational time. These simulations are so precise that they effectively confirm the experimental validation of the RR structure. This achievement underscores the potential of 2D-FEM simulations in advancing the design and analysis of complex structures, facilitating faster and more cost-effective research and development processes. The fabrication of the photonic sensor involves sophisticated techniques such as electron beam lithography (EBL) and reactive ion etching (RIE) processes. By employing these cutting-edge manufacturing methods, we ensure the precision and reliability of the RR device. Our experimental results align closely with the numerical findings, validating the efficacy of our approach.