## 4.1 Analysis of different optical properties of FBG

In this section, we have verified our proposed ANN models. For this, the outputs of the model were assessed for the unknown input parameters. Attention is paid to the effective refractive index, bandwidth, reflectivity and wavelength of the FBG that are the main parameters when used in different sensing applications including multiplexing/demultiplexing.

## 4.1.1 Effective refractive index (neff)

Figure 4.1.1 shows the scattered plot between the predicted and the actual values of the neff. The predicted values of neff were obtained from our proposed ANN model while the actual values from the simulation using MATLAB. Due to the overlapping of the predicted data, a continuous plot can be observed. A linear trained state the well-trained behavior of the model.

## 4.1.2 Bragg Wavelength (λB)

Bragg wavelength of FBG plays a vital role in sensing purposes [17–18]. Accurate measurement of this parameter is of paramount importance in different applications. We have chosen the most useful wavelength range i.e., 1500–1600 nm for this purpose.

Here we have predicted the wavelength of the FBG using our proposed ANN model. Figure 4.1.2 depicts a linear relationship between the actual and the predicted values of Bragg wavelength. This signifies that our model can predict the unknown wavelength accurately. 100 epochs were considered to predict the wavelength accurately.

The demodulation technique of FBG sensors relies upon the detection of the wavelength shift of the sensor peak at the Bragg wavelength. Hence, it is important to analyze the spectral characteristics of the FBG sensor. It was reported that the grating length plays a significant role to design a high-performance FBG based sensor [10]. Therefore, the two most important parameters of the spectrum i.e., reflectivity and bandwidth were considered for further analysis. Well-known coupled-mode equations solved by the transfer matrix method was used to collect the input data.

## 4.1.3 Reflectivity

One of the most important parameters to fabricate a grating for a particular purpose is the reflectivity of that grating. Reflectivity is the percentage of light reflected at the Bragg wavelength. Reflectivity changes with an increase in grating lengths.

In this portion, the change of the reflectivity has been analyzed using our proposed model with the elevation of the grating length. The result was compared with the simulated result using MATLAB.

The change of the reflectivity with the grating lengths ranging from 1 mm to 50 mm was analyzed as shown in Fig. 4.1.3. Figure 4.1.3 (a) depicts the relationship between the aforesaid parameters using MATLAB while Fig. 4.1.3 (b) using our proposed ANN model. A good agreement between both results was observed. Reflectivity increases rapidly with an increase in the grating length. The highest reflectivity was observed from the length of the grating of 8.5 mm onwards.

It is worthy to note that, our model can predict the non-linear behavior of the parameters.

Furthermore, the scatter plot between the actual and the predicted reflectivity has shown in Fig. 4.1.3 (c). A linear relationship between the two parameters ensures the well-trained behavior of the model. Due to the coherent nature of the input data set, more data are accumulated over the range of 95 to 100% in the plot.

## 4.1.4 Bandwidth

Bandwidth is the measure of the reflected signal spectral width. It is usually measured at the full-width half maxima (FWHM). To investigate the grating length dependence on the bandwidth of the FBG spectrum, the grating length ranging from 1 mm to 50 mm was considered. Figure 4.1.4 depicts the relationship between the aforesaid parameters. The tendency is very similar to the results of reflectivity change but in an inverse direction. Here 3-dB bandwidth change shows an exponential decrease over the elevation of the grating lengths. The simulated result is shown in Fig. 4.1.4 (a) while an exact match in the relationship is observed while performing using the proposed ANN model. In case of 1 mm FBG sensor, the bandwidth is around 1.40 nm. The bandwidth reduces as the grating length increases. The grating length reduces to around 1.03 nm at grating length of 5 mm. A constant value of the bandwidth is maintained beyond the grating length of 5 mm.

The scatter plot between the actual and predicted data for the bandwidth is shown in Fig. 4.1.4 (c). A linear relationship between the actual and the predicted values of bandwidth is observed. Hence the well-trained nature of the proposed model is proved.

## 4.2 Predicting the reflection spectrum of the different FBGs

FBGs are distributed Bragg reflectors that reflect a particular wavelength of light and transmit others. This is achieved by the periodic variation of the refractive index along with the core of the fiber. By changing the periodicity of the gratings, different types of the reflected spectrum of FBGs can be achieved. Chirped FBG is one of these types of FBG having non-uniform periodicity along the length of the fiber [19]. Furthermore, dynamic strain measurement with higher resolution (pico-strain) is an important area of research and development [20]. With normal FBG is quite impossible to breach the limit. π phase-shifted FBG, expected to be used widely in near future is a successful candidate in these aspects. π phase-shifted FBG can be fabricated on a standard FBG by introducing a phase jump at the centre of the grating. Due to the very sharp resonance peak, this type of FBG shows a higher resolution and enhance sensing capabilities [21].

Keeping all these aspects in mind, this section is devoted to predicting the reflected spectrum of three different types of FBG: normal, πphase-shifted and chirped FBG using our proposed ANN model.

The reflected spectrum for three different types of FBGs has shown in Fig. 4.2. The spectra obtained using our proposed ANN model have been compared with those using MATLAB programming. An exact match between these was observed. Hence it can be concluded that our proposed model can predict the output spectrum of different FBGs accurately within seconds, while numerical simulation methods a few minutes.

Moreover, it should be noted that our proposed model can predict the non-linear behaviour and complexity of the spectrum entirely as expected.

Seven hidden layers with 500 nodes in each were used throughout the code, which offers rapid convergence and sufficient accuracy in predicting the output for unknown dimensions. The authors believe that the proposed model may find a wide range of applications in future.