Numerical optimization of the fiber Bragg gratings with fabrication constraints

We propose the iterative layer-peeling algorithm (LPA) and the genetic algorithm (GA) to numerically optimize the fiber Bragg grating (FBG) design. Fabrication constraints are introduced in the design, such that the designed FBGs satisfy the spectral specifications and are easy to fabricate. The powerful numerical optimization permits removing the phase shifts in the FBGs, so that the gratings can be fabricated with conventional high quality holographic phase masks, without need for custom made phase masks. We introduce the inverse LPA, which is faster than the conventional transfer matrix method by two orders of magnitude for analysis of the FBGs. The synthesis of the FBG using the LPA and the analysis of the FBG using the inverse LPA can be iterated in a loop, which allows applying the constraints in both grating and spectrum spaces. The impact of the applied constraints and the convergence are analyzed. The GA is powerful for achieving the global optimum with a higher probability than that of the iterative algorithm and simulated annealing. Our GA is enhanced by a new Fourier series-based real-valued encoding to provide high degrees of freedom, and a rank-based fitness function. The new GA enables us to remove phase shifts in the gratings. All the designed WDM band-pass gratings with minimum dispersion are fabricated using the holographic phase mask without phase shifts. The experimental gratings with dispersion of ± 33 ps/nm in the 0.33 nm flat-top passband will be shown.