Synthesis of long-period fiber gratings with a Lagrange multiplier optimization method

Based on the Lagrange multiplier optimization (LMO) method, a new synthesis approach for designing complex long-period fiber grating (LPG) filters is developed and demonstrated. The proposed synthesis method is a simple and direct approach. It was used to efficiently search for optimal solutions and constrain various parameters of the designed LPG filters according to practical requirements. The inverse scattering algorithm is a good tool for designing FBG filters; as well as for designing transmission-type fiber grating filters like LPGs. Compared to the results of the discrete layer-peeling (DLP) inverse scattering algorithm for LPGs, the synthesized LPGs, using the LMO approach, are more flexible and workable for the constraint conditions can be easily set in the user-defined cost functional, such as the limitation on the maximum value of the refractive index modulation and the parameters of the initial guess in LMO algorithm. Linear transmission LPG filters and EDFA gain flattening filters are synthesized and analyzed systematically by using the proposed method with different parameters. Moreover, as a variation-based method, we find that the convergence and the synthesized results of the LMO method are strongly dependent on the initial guess parameters.