# Comparative Analysis of the Methods for Fiber Bragg Structures Spectrum Modeling
## 4 Conclusions  
The results of the FBG modeling using both the Layer Sweep (LS) and Transfer Matrix (TM) methods are generally close to the ones obtained using the specialized software. However, in order to mitigate the deviation of the LS method spectrum from the reference one, it is necessary to decrease the partition interval of the refractive index profile.  
It was also established that at certain values of the partition interval of the LS method, the deviations of the modeled phase-shifted FBG spectrum significantly increase due to its asymmetrical distortion. Based on the analysis of the refractive index profile of the grating model, it was concluded that the asymmetry of the refractive index profile partition near the phase shift relative to its center causes the asymmetry of the spectral response of the simulated grating.  
A solution to eliminate the discussed negative effect in phase-shifted FBG simulation was proposed, which presupposes an additional condition to the choice of the partition interval, according to which each FBG period must contain only integer (odd) number of partition points.  
It must be noted that the Layer Sweep method offers more flexibility in terms of the modeled fiber optic structure configuration, since it can simulate any refractive index profile of the fiber medium, such as two or more FBGs recorded one over the other (also known as the moire recording) [4], which is not possible to model using the transfer matrix (TM) approach, while the latter offers benefits in terms of computational performance, especially when small partition interval is required to provide the desired accuracy of the LS method implementation.  
Further research will be dedicated to the modeling of other types of fiber-optic structures, including the combined structures incorporating FBGs and Fabry-Perot interferometers, moire-recorded FBGs, etc., as well as to the enhancement of the LS method computational performance. The latter can be achieved, for instance, by applying the variable partition interval.  
**Author Contributions:** Conceptualization, A.S. and V.A.; methodology, A.S. and T.A.; software, A.S. and B.V.; validation, T.A., B.V., A.S., A.N. and Y.G.; formal analysis, V.A.; investigation, T.A. and B.V.; resources, O.M.; data curation, A.S.; writing--original draft preparation, T.A.; writing--review and editing, A.S., V.A., T.A. and A.N.; visualization, A.S., T.A. and Y.G.; supervision, O.M.; project administration, O.M. and A.S.; funding acquisition, O.M. All authors have read and agreed to the published version of the manuscript.  
Figure 12: Values of the root-mean-square deviation (RMSD) of the phase-shifted FBG spectrum modeled using the LS method with odd number of partition points in the FBG period (blue dots) depending on the partition interval \(\Delta\)z, and their approximation (blue solid line).  
**Funding:** This work was financially supported by the Ministry of Science and Higher Education as part of the \"Priority 2030\" program.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.