Optimization based synthesis methods to design multi-channel sampled fiber Bragg gratings with phase-shift

In this paper, two synthesis methods are proposed for designing multi-channel sampled gratings with phase-shifts. The first synthesis method uses non-equally separated π-phase shifts and the second uses variable but equally separated phase shifts in sampling period of fiber grating. In both methods, the Fourier transform derived from the phase shifts is related with the reflection spectrum of the fiber Bragg grating. It is demonstrated that a reflection spectrum with desired number of channels can be easily synthesised using a general optimization method. Besides, a comparison is given between these two methods according to the target reflection spectrum.