## 1 Introduction  
Integrated photonic sensors hold significant importance in various fields due to their ability to accurately and efficiently detect and measure physical, chemical, and biological parameters [1; 2]. These sensors utilize light to sense changes in their surroundings, offering advantages such as high sensitivity, fast response times, and miniaturization [3]. Their integration into compact and scalable platforms enables the development of portable, low-cost, and highly sensitive sensing devices for applications ranging from environmental monitoring and healthcare diagnostics to telecommunications and industrial process control [4; 5; 6]. By leveraging the unique properties of light, integrated photonic sensors contribute to advancements in fields such as biomedical research, environmental sustainability, and the optimization of industrial processes, ultimately fostering innovation and improving quality of life [7; 8; 9].  
The Mach-Zehnder interferometer (MZI) structure holds immense significance in sensing applications due to its ability to efficiently manipulate and detect light signals [10; 11]. This structure utilizes the principle of interference to measure changes in optical properties, making it highly sensitive to external stimuli such as temperature, pressure, and refractive index variations [12; 13; 14; 15]. Its compact size, low power consumption, and high sensitivity make it ideal for a wide range of sensing applications, including environmental monitoring, biomedical diagnostics, and industrial process control [16; 17; 18]. Additionally, its versatility allows for integration with various materials and technologies, paving the way for innovative sensing solutions with improved performance and reliability.  
The Sagnac loop serves multiple purposes in optical systems. In the context of MZI, like the loop-terminated Mach-Zehnder interferometer (LT-MZI), the Sagnac loop acts as a crucial component to enhance performance and functionality. One of the key functionsof the Sagnac loop in an LT-MZI is to reduce the length of the interferometer by a factor of two. This reduction in length is advantageous for compactness and integration into miniaturized optical devices, allowing for space-efficient designs without compromising performance. Moreover, the Sagnac loop enhances the interferometer's phase sensitivity. By circulating light through the loop, it increases the effective path length travelled by the light, thereby amplifying the interference effects [19]. In interferometric sensors, including those used for refractive index sensing, common mode rejection is crucial for eliminating unwanted noise and environmental perturbations. The Sagnac loop configuration inherently provides excellent common mode rejection, as any disturbance affecting both arms of the interferometer equally will not affect the interference pattern [20].  
Carbon dioxide (CO\({}_{2}\)) monitoring is of paramount importance due to its significant implications for both environmental and human health. As a major greenhouse gas, CO\({}_{2}\) plays a crucial role in regulating the Earth's climate, influencing temperature patterns, weather phenomena, and ultimately the balance of ecosystems [21]. Moreover, in indoor environments, monitoring CO\({}_{2}\) is essential for ensuring air quality and occupant comfort. Elevated CO\({}_{2}\) levels can indicate poor ventilation, which can lead to a buildup of other pollutants and potential health risks, including headaches, fatigue, and respiratory problems [22; 23]. By monitoring CO\({}_{2}\) concentrations, it is possible to maintain optimal indoor air quality, promote productivity, and safeguard the well-being of occupants in various settings, including homes, schools, offices, and healthcare facilities. In this work, a novel design of a CO\({}_{2}\) gas sensor is proposed which is based on an LT-MZI embedded with polyhexamethylene biguanide (PHMB) functional polymer in the sensing arm to determine the minute change in the gas concentration.