The fractional Fourier transform in the analysis and synthesis of fiber Bragg gratings

An approach based on the fractional Fourier transform is proposed for both analysis and synthesis of fiber Bragg gratings. The method is shown to be simple and accurate. A comparison is made with the results of the numerical integration of the full Riccati equation, which are valid for arbitrary reflectivities. The method being very efficient, processing times can be short enough for a real-time control of the writing process, during grating manufacturing. The effects of profile random irregularities on FBG performance are studied, and several examples, useful for design purposes, are given.