# Polarization Influence on Algorithms of TFBG Sensors Data Analysis for Bending Application
## 1 Introduction  
Fiber optic sensors are very popular due to their characteristic properties, which include small size and resistance to various factors, including electromagnetic radiation. One of the main groups of fiber optic sensors are those based on periodic structures. These include Bragg gratings. Introducing the particular tilt angle of the periodic structure during the inscription process results in the so-called tilted fiber Bragg gratings (TFBGs). Such structures have many sensing applications. The most popular application is in measuring the refractive index (RI) of the medium surrounding the optical fiber. High repeatability and the complex nature of spectral changes have resulted in the development of both the sensors themselves and the algorithms for demodulating their spectra [1, 2]. The most important advantage of periodic fiber optic structures is high sensitivity. However, the method used to create such sensors is of great importance, as it must not cause physical weakening of the optical fiber. The structure recording process does not require physical distortion of the optical fiber. The fiber is distorted only for optical radiation, which merely leads to a change in the optical properties of the fiber core, giving it new properties. Additionally, structures of this type can be used to measure at least two physical quantities simultaneously, such as temperature and stress [3] and the twist and bending radius [4]. Periodic structures produced in modified fibers can also lead to a sensor capable of measuring two quantities simultaneously [5]. Curvature or the bending radius is an important parameter that is measured for various important applications. It is used particularly often in structural health monitoring [6], shape measurements and reconstruction [7], or angular movement of manipulators [8]. The literature refers to several types of bending sensors using fiber optic technology. Most often, they exploit interferometric systems with classical Bragg gratings (FBG) [9; 10], Mach-Zehnder [11; 12; 13; 14], or Fabry-Perot [15; 16] interferometers. The use of FBGs to obtain bending sensitivity requires the creation of a grating zone away from the central axis of the optical fiber. This necessitates the use of multi-core fiber (MCF), which increases the cost of producing the sensor element [17]. The use of a hybrid structure containing sections of various special light guides for curvature measurements has also been proposed [18]; however, the production of the structure discussed requires a complicated process. Emerging spatial asymmetry within the recorded structure causes high sensitivity to radiation polarization. There are two specific orientations of the polarization plane of the introduced light, the P-type (parallel) and S-type (perpendicular), the latter marked with an S from the German equivalent term of Senkrecht. Typically, with TFBGs, changing the angle of the polarization plane from the P state to the S state causes the most significant changes in spectral parameters [19]. Maintaining the polarization state right in front of the sensor is difficult. It requires the use of special optical fibers or additional optical elements, which increase the complexity and costs of the system. It is important to survey the influence of input light polarization on the accuracy of measurement of other physical quantities. The development of methods which will provide results with reduced cross-sensitivity to input polarization could lead to the obtainment of simpler measurement setups and more reliable results. It could also be useful in cases where changing the sensing grating is necessary. Bending the fiber at the location of the written TFBG significantly affects lower-order modes with effective refractive indices close to the fundamental mode, propagating at the smallest distance from the fiber core [20]. Both the central wavelengths of individual resonances and their amplitude changes. The complex nature of these changes makes it necessary to use an appropriate method to demodulate the spectra.