Optimum design of arrayed waveguide grating based on a novel Newton recursive algorithm

A novel Newton recursive algorithm is proposed for an optimum design of arrayed waveguide gratings, which is different from the traditional complicated power-series expansion of the light-path function. The structure of an arrayed waveguide grating is represented by three constraint equations which may be chosen to meet some specific design demands. The new algorithm combines Newton algorithm with structure nonlinear constraint functions, which makes it more general and flexible for the optimum design of the device. From the initial value given, the arrayed-waveguide positions and matched waveguide lengths are determined from the numerical solutions for the roots of three constraint equations through a Newton recursive procedure in sequence. Anastigmatic mounts of arrayed waveguide gratings based on this algorithm are processed, and a three stigmatic-points one is designed. Further applications of this algorithm are also discussed, including the one that can not be designed with the theory of the power-series expansion of light-path function.