**5. Conclusions**

In Summary, the CO2 laser irradiation technique is a highly efficient, low cost and versatile technique to write high-quality LPFGs in different types of optical fibers, such as conventional single mode fibers, polarization-maintaining fibers, and photonic crystal fibers. This technique offers a number of advantages over other fabrication techniques. It eliminates the need of using a mask as well as the need for pre-hydrogenation of the fiber and consequent post-thermal annealing to stabilize the gratings. The LPFGs induced by CO2 laser exhibits unique grating properties, such as high thermal stability.

Although simplifications can lead to analytical equations, FEM modelling allows more realistic simulations of the physical processes involved in the writing of LPFGs using MIR radiation. The 3D model presented simulates the writing of one period and allows the analysis of both thermal and stress data. All the main practical parameters are considered as inputs and thermal dependence of the material's data is included.

The model performance was evaluated by considering a practical example of writing LPFGs on a Ge-doped fiber. Different analysis were presented and it was demonstrated that refractive index changes predicted by the FEM model led to transmission spectra with resonance peaks similar to those obtained experimentally. So, although additional work should be performed to further validate the analysis done (mainly regarding the characterization of stresses acting in the optical fiber and experimentally measuring refractive index changes), the FEM results are in accordance with literature and experimental data.
