Empirical models to describe the effects of gold nanoparticle on etched FBG response

This work presents a numerical study on the response of etched fiber Bragg gratings (EFBGs) functionalized with gold nanoparticles (AuNPs). Based on numerical simulations, we propose models to analyze the attenuation and sensitivity of EFBGs as functions of the external refractive index and AuNP separation distance. The results reveal a decrease in electric field intensity within the fiber core and an increase around the AuNPs. The simulations indicate two distinct effects: electric field coupling between AuNPs and electric field scattering caused by the AuNPs. Building on these findings, we developed models incorporating AuNP separation distance to describe attenuation and sensitivity enhancement to external refractive index variations. These models predict a critical separation distance at which complete attenuation occurs for all external refractive indices and a maximum sensitivity enhancement at this distance. Experimental validation was performed on three EFBGs with different average AuNP separation distances: (189 ± 61) nm, (83 ± 15) nm, and (64 ± 15) nm. Despite simplifications in the simulation model, both attenuation and sensitivity enhancements observed experimentally align well with the predictions. These results confirm that the models’ free parameters allow the description of more complex conditions beyond those initially simulated. Thus, the empirical models proposed in this work provide a reliable background for describing attenuation and sensitivity as functions of AuNP separation distance and may serve as valuable tools for optimizing EFBGs functionalized with nanoparticles.