The passband frequency response of an arrayed waveguide grating (AWG) is improved for better performance in wavelength-division multiplexing applications. Using the lengths of array arms as optimization variables, an optimization method is employed to obtain an ideal flat-top transfer function. Two different definitions of the desired transfer function to achieve the ideal flat-top response are given, and their results are compared. Rigorous mathematical derivation of the transfer function and definition of suitable objective functions generate closed-form expressions for the gradient vector of the objective function with respect to the optimization variables, thus enabling the implementation of a robust quasi-Newton optimization algorithm. This, in turn, provides accurate results and fast convergence, despite a large number of optimizing variables. It is shown that the optimized nonuniform AWG will have a flat passband with a broad bandwidth that is 2.3 times larger than that of an ordinary uniform AWG.
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