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A comparison on design of multi-channel sampled fiber Bragg gratings with phase-shifts

Multi-channel sampled fiber Bragg gratings with purely phase shifts can be designed in three different ways using an appropriate phase shift pattern. In this paper, three syntheses methods, two of them associated with Fourier transform of phase shift pattern and one associated with Fourier transform of index variable of grating are proposed. The first synthesis method uses non-equally separated π-phase shifts, the second and the third syntheses use equally separated but variable phase shifts in the sampling period of fiber grating. In all methods, the phase shift patterns are optimized to match their Fourier transforms to a target reflection spectrum. It is demonstrated that a reflection spectrum with desired number of channels can be easily synthesised using a general multi-variable optimization method. Finally, the reflection spectra of the designed multi-channel sampled fiber Bragg gratings are analyzed and the comparisons between these three methods are given.



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