Comprehensive and general method for the analysis and synthesis of fiber Bragg gratings

In this paper, a comprehensive, general and unified method for the complete analysis and synthesis of fiber Bragg gratings is proposed. The formalism is based on the well-known multilayer thin-film filters and transfer-matrix theories, considering the Bragg grating structure as a linear and time-invariant system. The developed analysis and synthesis algorithms have been significantly improved to be used on any kind of complex perturbation profiles, allowing the characterization and ‘ad hoc’ designs in both time and frequency domains.