Fast design method for arbitrary fiber Bragg gratings

A method for designing fiber Bragg gratings (FBGs) with arbitrary spectra is proposed according to the Fourier mode coupling theory. The index perturbation in a FBG is derived from the inverse Fourier transform of the amplitude and phase spectra, where the phase spectrum is set as odd symmetry, and the amplitude spectrum results from the square-root and inverse hyperbolic tangent of its arbitrarily desired reflectivity. In order to verify the design method, some FBGs with arbitrary triangular-, double-triangular-, Gaussian- and comb-like-reflectivities were designed and calculated on a general computer, which has the complexity of O(Nlog(2)N) where N is the number of calculation points. The reflectivities of the designed FBGs were analyzed by using the transfer matrix method or the direct Fourier transform (FT) method, agreeing with the desired reflectivities. The proposed design method was confirmed to be highly fast and sufficiently accurate for designing arbitrary FBGs.