Digital design of broadband long-period fibre gratings by an inverse scattering algorithm with flip-flop optimization

A discrete inverse scattering method, known as layer-peeling, is used to synthesise a LPFG (long-period fibre grating) from a desired complex spectrum by a direct solution of the coupled-mode equations, while simultaneously determining the physical properties of the layered structure. The physical properties of the grating structure are determined in a recursive layer-by-layer manner by using causality arguments to design LPFGs exhibiting a flat-top spectral profile. The results obtained from the layer-peeling method are optimised using the flip-flop method to ease the fabrication process. We found that the layer-peeling method has the highest performance and executes in the least amount of time. A discussion of possible applications where optimised broadband LPFGs could be utilised in the field of telecommunications and sensing demonstrates the importance of the results.