The general aberration theory of arrayed waveguide grating (AWG) is proposed in this paper. The derived conclusions can be applied to any symmetrical AWGs. With the aberration theory, the spectral response can be optimized. Some performances of an AWG, for example, crosstalk and channel number, are expected to be improved by reducing the aberrations. A common AWG with the Rowland geometry has low aberrations for the absence of the second-order aberration. To further reduce the aberrations, nonstandard AWGs are considered. The AWG based on three stigmatic points is proved to have a perfect performance.
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