## 1 Introduction  
Fiber-optic technology has become an integral part of modern life, revolutionizing how we communicate, access information, and entertain ourselves. The ability of the fiber to transmit data as light pulses through strands of glass or plastic enables high-speed and high-capacity communication over long distances with minimal signal loss. In telecommunications, fiber optics serve as the backbone of global networks, facilitating rapid internet connections, clear voice calls, and high-definition video streaming. The superior bandwidth and reliability of fiber optics have been important in meeting the rapid and high demand for data transmission in our increasingly digital world [1]. Beyond telecommunications, fiber optics have applications in various fields. In medicine, they are used in imaging tools and minimally invasive surgical procedures. In the defense sector, fiber optics are employed for secure communication and sensing applications. Industries utilize fiber optics for precise measurements and data transmission in harsh environments [2]. The scalability and durability of fiber optic infrastructure further underscore its importance. With the capacity to support future technological advancements, fiber optics are considered a future-proof solution, capable of accommodating the growing data needs of society. Bending loss, also known as macro-bending loss, occurs when an optical fiber is subjected to a curvature or bend that exceeds a critical radius, causing a portion of the guided light to escape from the fiber core. This phenomenon leads to the attenuation or loss of optical signal power, which can degrade the performance of fiber optic systems. This bending may occur for many reasons, such as tight bends when the fiber is bent at a radius smaller than its critical bending radius. The light rays in the core may no longer satisfy the total internal reflection condition, and escape into the cladding. Also, mechanical stress due to tight installations or environmental factors can lead to bending losses. Moreover, poor cable management or excessive twisting during installation can cause unwanted bends [3]. As everyone is aware, there is a massive scale of fiber cable usage in many places around the world, and the large size of the signals within fiber cables are well known. Since there is loss and leakage of signal energy within fiber cables, it is essential to seriously consider collecting this lost energy and utilize it for various purposes. Many researchers have investigated fiber loss in their work. In [4], the authors found that it is challenging to calculate the macro-bending loss of an optical fiber when the bending radius is small, based on [PERSON]'s theory and its derivative theories. The authors in [3] presented an enhanced model to accurately predict macro-bending losses and power fluctuations in single-mode optical fibers. By refining the existing theoretical frameworks, the authors offer a more precise tool for designing and optimizing fiber optic systems, particularly in scenarios involving tight bends. This advancement holds significant implications for improving the reliability and performance of fiber-based communication networks. A method for calculating transfer and loss coefficients in bent slab single-mode waveguides and micro-rings, incorporating bending and coupling losses is given in [5]. The analysis considers the effects of curvature-induced loss and coupling efficiency between waveguides. Authors in [6] investigated the impact of bending on power transmission losses in G652 and G657 optical fibers. They highlighted that G657 fibers exhibit lower bending losses due to their bend-insensitive design, making them more suitable for tight installations. The study provides insights into optimizing fiber selection for various applications to minimize signal degradation. In [7], the authors utilize a modified five-layer model.