Numerically extrapolated discrete layer-peeling algorithm for synthesis of nonuniform fiber Bragg gratings

The discrete layer-peeling algorithm (DLPA) requires to discretize the continuous medium into discrete reflectors to synthesize nonuniform fiber Bragg gratings (FBG), and the discretization step of this discrete model should be sufficiently small for synthesis with high accuracy. However, the discretization step cannot be made arbitrarily small to decrease the discretization error, because the number of multiplications needed with the DLPA is proportional to the inverse square of the layer thickness. We propose a numerically extrapolated time domain DLPA (ETDLPA) to resolve this tradeoff between the numerical accuracy and the computational complexity. The accuracy of the proposed ETDLPA is higher than the conventional time domain DLPA (TDLPA) by an order of magnitude or more, with little computational overhead. To be specific, the computational efficiency of the ETDLPA is achieved through numerical extrapolation, and each addition of the extrapolation depth improves the order of accuracy by one. Therefore, the ETDLPA provides us with computationally more efficient and accurate methodology for the nonuniform FBG synthesis than the TDLPA.