## 5.1 Analysis of various optical properties of FBG

In this section, we describe how we have verified our proposed ANNs. For this, the outputs of the model are 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 various sensing applications including multiplexing/ demultiplexing.

## 5.1.1 Effective refractive index (neff)

Figure 4 shows the scattered plot of the predicted \({n}_{\text{e}\text{f}\text{f}}\) values versus the exact values of the \({n}_{\text{e}\text{f}\text{f}}\). The predicted values of \({n}_{\text{e}\text{f}\text{f}}\) are obtained from our proposed ANN model while the exact values are recorded from the simulation using MATLAB. Due to the overlap of the closely spaced predicted data, a continuous plot can be observed. A linear trained nature clearly reveals the well-trained behaviour of the model.

## 5.1.2 Bragg Wavelength (λB)

The Bragg wavelength of FBG plays a vital role in sensing purposes [20–21]. Accurate measurement of this parameter is of paramount importance in different applications. We have chosen the most useful wavelength range *i.e.*, 1500 nm − 1600 nm for our investigation and using our proposed ANN model, we have predicted the wavelength of the FBG. Figure 5 depicts a linear relationship between the actual and the predicted values of Bragg wavelength. 500 epochs are considered to predict the wavelength accurately. Evidently, this signifies how well our model can accurately predict the unknown wavelength.

The demodulation technique of FBG-based sensors relies on the precise detection of the wavelength shift of the sensor peak at the Bragg wavelength. Hence, it is important to analyse this aspect of the spectral characteristics of an FBG sensor. It is reported that the grating length plays a significant role to design a high-performance FBG sensor [10]. Therefore, the two most important parameters of the spectrum *i.e.*, reflectivity and bandwidth are considered for higher order study. To procure the input data, well-known coupled-mode equations are solved by the transfer matrix method.

## 5.1.3 Reflectivity

The most important parameter to consider, while fabricating a grating for a target application with a set of given geometrical parameters, is the reflectivity of the grating. Reflectivity is quantified as the percentage of light reflected at the Bragg wavelength. It changes with increasing grating length. In this study, the change of reflectivity has been analyzed using our proposed ANN model with the elevation of the grating length. The result is compared with that simulated directly using MATLAB.

For grating lengths varying from 1 mm to 50 mm, the change in reflectivity is computed and shown in Fig. 6 (a). The figure depicts the relationship and comparison between MATLAB results using the aforesaid parameters and those of our proposed ANN model. Clearly, a very good matching of these results is observed. Reflectivity increases rapidly with the increase in the grating length. The highest reflectivity is 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 behaviour of the parameters.

Furthermore, the scatter plot between the actual and the predicted reflectivity has shown in Fig. 6 (b). A linear relationship between the two parameters ensures the well-trained behaviour of the model. Due to the coherent nature of the input data set, more data are accumulated over the range of 90 to 100% in the plot.

## 5.1.4 Bandwidth

The bandwidth, a measure of the spectral width of the reflected signal is measured at the full-width half maxima (FWHM). To investigate the dependence of grating length on the bandwidth of the FBG spectrum, the grating length is varied in range from 1 mm to 50 mm. Figure 4.1.4 shows 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. 7 (a) while an exact match in the relationship is observed while performing using the proposed ANN model. In the case of a 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 a 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. 7 (b). A linear relationship between the actual and the predicted values of bandwidth is observed. Hence the well-trained nature of the proposed model is established.

## 5.2 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 [22]. Furthermore, dynamic strain measurement with higher resolution (pico-strain) is an important area of research and development [23].

With normal FBG it 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 center of the grating. Due to the very sharp resonance peak, this type of FBG shows a higher resolution and enhance sensing capabilities [24].

Keeping all these aspects in mind, this section is devoted to describing how the proposed ANN model predicts the reflected spectrum of three different types of FBG: normal, π phase-shifted and chirped FBG using.

The reflected spectrum for three different types of FBGs is shown in Fig. 8. The spectra obtained using our proposed ANN model have been compared with those obtained using MATLAB coding of the analytical equations. A nearly exact match between these is observed. Hence it can be concluded that our proposed model can predict the output spectrum of different types of FBGs accurately within seconds, while numerical simulation methods require a few minutes to solve.

Furthermore, it should be noted that our proposed model can predict the non-linear behaviour and complexity of the spectrum entirely as expected. To avoid ambiguity in reading the graphs, it is mentioned that the wavelength values along the x-axis of Fig. 8 (a) and (b) are not in the range of \(- 0.15\) to \(0.15\). Each specified value is added by a constant number of + 1.55e3 as depicted at the rightmost end of the x-axis which signifies the wavelength range 1549.85 nm- 1550.15 nm. This is considered to be a default plotting feature in the python programming language.

Seven hidden layers with 500 nodes in each are used throughout the code, which offers rapid convergence and sufficient accuracy in predicting the output for unknown dimensions. Thus it is emphatically inferred that the proposed model will find a wide range of applications in the field of guided wave optics and photonic devices.