## 1 Introduction  
Electronic integrated circuits (EICs) have been the foundation of modern technology, enabling the development of a wide range of electronic devices and systems. These circuits manipulate electrical signals using semiconductor materials such as silicon (Si) [1, 2]. However, as demands for higher data speeds, lower energy consumption, and increased bandwidth continue to grow, EICs face limitations due to factors like resistive losses and electromagnetic interference. Photonic integrated circuits (PICs) offer a compelling alternative by leveraging light, rather than electrons, for signal transmission [3]. PICs utilize components like optical fibers, waveguides (WGs), and photonic crystals to process and transmit data, offering advantages such as higher speed, lower energy consumption, and reduced signal loss over long distances [4, 5, 6, 7]. Table 1 provides a general overview of the differences between PICs and EICs, highlighting their respective characteristics and typical applications. Integrated optics refers to the technology and study of integrating multiple optical devices and functions onto a single chip, similar to the way EICs combine multiple electronic components. The term was introduced by [PERSON] in 1969, who envisioned the integration of optical circuits to perform complex functions within a compact and efficient framework [8]. The development of integrated optics was driven by the need for miniaturization and improved performance in optical communication systems. In the realm of modern optics, the need for PICs arises from the ever-growing demand for faster, more efficient, and compact optical systems [9]. PICs offer a revolutionary approach by integrating numerous optical components onto a single chip, mimicking the functionality of traditional EICs [10]. This integration drastically reduces size, weight, and power consumption while enhancing performance and reliability. Integrated photonics traces its originsback to the late 20 th century when researchers began exploring ways to scale down and integrate optical components onto a single platform [11]. The basics of integrated photonics lie in leveraging the properties of light to process, transmit, and detect information. It implicates the integration of optical elements such as WGs, modulators, and detectors on a common substrate, typically Si, silicon nitride (Si\({}_{3}\)N\({}_{4}\)) or lithium niobate (LN) [12; 13; 14; 15; 16]. This integration enables the manipulation and control of light at the nanoscale, leading to compact and efficient photonic devices [10; 17]. Over the years, evolution in fabrication techniques, materials science, and device design has propelled integrated photonics to the forefront of innumerable technological domains, including telecommunications, computing, sensing, and quantum technologies [18; 19]. Today, integrated photonics stands as a basis of contemporary optics and continues to drive innovations that reshape the way we communicate, compute, and interact with light. PICs exhibit advanced multiplexing capabilities that significantly enhance their functionality in optical communication systems [20]. These circuits can efficiently manage multiple light signals of different wavelengths simultaneously, a technique known as wavelength division multiplexing (WDM) [21]. This allows a single optical fiber to carry multiple channels of data, greatly increasing the bandwidth and data transmission capacity without requiring additional physical infrastructure. Additionally, PICs support space division multiplexing (SDM) [22], enabling multiple spatial channels within a single fiber, and time division multiplexing (TDM), which divides signals into different time slots [23; 24]. The integration of these multiplexing techniques within a compact and scalable platform makes PICs highly advantageous for high-speed, high-capacity optical networks, driving advancements in telecommunications, data centers, and various sensing applications [25].