Maclaurin-series method for calculating dispersion in arrayed-waveguide grating multiplexers.

We present a Maclaurin-series method for calculating the dispersion from phase error and amplitude distributions in arrayed waveguide grating (AWG) multiplexers. By using this method, we can easily derive the intercept, the gradient, and the curvature of the dispersion in the center frequency region of a passband. A third-order Maclaurin series was calculated by using the measured phase error and amplitude distributions of AWGs having a channel frequency spacing of 12.5 GHz. The calculated results are in good agreement with the dispersions measured with an optical network analyzer. We also discuss the physical effect of the phase error on dispersion by assuming certain limited cases.