## 3 Analysis of Measurement Data  
The spectra of TFBG gratings are measured in the transmission system because cladding modes are not visible in the reflection spectrum. The modes propagating in the cladding decay quickly due to the high value of cladding attenuation. The cladding modes are transferred from the core to the cladding due to the tilt of the changes in the refractive index in the core. For cladding modes, the propagation takes place in the cladding and at the boundary of the cladding and its surroundings in the direction opposite to the propagation of light in the fibre core. For these modes, total internal reflection occurs at the boundary of the cladding and the surroundings. The effective refractive index of individual cladding modes depends on the refractive index of the surroundings. For gratings with a medium tilt angle of the refractive index, increasing the SRI value causes the cladding modes to switch from total internal reflection to leakage. Subsequent modes at shorter wavelengths decrease in amplitude and are broadened. A mode that becomes leaky decreases in amplitude and stops shifting. Measurements were made using a grating with a tilt angle of 4 degrees. The cladding modes of such a grating are not subject to full leakage. In the range above 1520 nm, a shift of individual modes can be observed (Figure 1). Before exceeding the leakage limit, individual modes only shift towards longer wavelengths under the influence of the increased SRI value. The mode presented in Figure 2 (1520.6 nm) for the 1.3994 refractive index value decreases its intensity compared to lower SRI values. This means that it is nearing the leakage limit. This is, therefore, the wavelength range with the greatest sensitivity to mode shift as a function of SRI. The spectra of TFBGs can only be measured in transmission mode. FBGs are measured mainly in the reflection mode. If the local shifts of individual modes or groups of modes need to be analysed, it is better to transform the spectrum in such a way that it corresponds to the reflection spectrum. Such a simple transformation highlights the characteristic features of the TFBG spectrum much better. This intensity transformation can be written as follows:  
\[\text{A}(\lambda)=1-\text{T}(\lambda). \tag{21}\]In a sense, the absorption spectrum is calculated in a similar way to the analysis of spectra in spectroscopy. The A(\(\lambda\)) spectrum allows for better use of further signal transformations. It is also possible to calculate the shift of individual cladding modes using methods used in the analysis of the shift of FBG spectra. Figure 3 shows the autocorrelation function of a part of the spectrum A(\(\lambda\)) in the 1510-1524 nm range. This part of the optical spectrum has 4000 points. The spectrum can be moved relative to itself by this number of points, which creates the shape shown in Figure 3. As can be seen, the correlation has the highest value with a zero shift, and its envelope decreases with increasing shifts. The individual cladding modes create an almost periodic signal, which is reflected in the shape of the autocorrelation function. Autocorrelation has repeating lobes (peaks), which are the result of the repeatability of the shapes of cladding modes. The decrease in the amplitude of subsequent autocorrelation side lobes (peaks) results from the decrease in the common area of the product of both functions when calculating it for larger shifts \(\delta\lambda\). If instead of autocorrelation, we calculate the cross-correlation of the spectrum for SRI = 1.334, with the spectra for subsequent SRI values, we will obtain the functions shown in Figure 4. What is characteristic here is the shifting of the main and other lobes. Various methods can be used to determine the position of the main lobe of individual cross-correlation functions. The simplest method is to determine the wavelength for maximum intensity. However, this is a low-resolution method limited by the spectral resolution of the measurement.