Synthesis of nonuniform long-period optical gratings with a continuous refractive index profile

In this work we present a new method for such a non-trivial problem as the synthesis of optical filters based on non-uniform Long-Period Fiber Gratings (LPGs). The method is based on a real-coded genetic algorithm (GA) with a new quasi-analytical procedure for solving the Zakharov-Shabat Inverse Problem. The method possesses an improved computational stability compared to classic numerical algorithms. The main peculiarity of the non-uniform LPG transmission gratings, compared to the Bragg gratings, is that their optical fields oscillate rapidly. However, the quasi-analytical approach proposed allows one to reduce to a minimum the number of sampling points, without, at the same time, losing accuracy in the solution, i.e. the method possesses an improved efficiency. The algorithm convergence was also improved by using the relations of the law of conservation of energy between the interacting waves. It has been shown that the algorithm works adequately even for the case of strongly over-coupled co-propagating lightwave modes, as we demonstrate in several examples of the synthesis of ultra-wide pass-band optical filters (FWHM of 100-200 nm).