An analytic approach to random phase error and its impact on the performance and design of arrayed-waveguide gratings

Random phase error due to fabrication process causes the filter, response of arrayed-waveguide grating (AWG) to degrade, especially in terms of crosstalk. In the side-lobe region, which is critical to the channel crosstalk performance, each instantiation of the random phase error can yield a significantly different filter transmission than that of the average for that level of phase error. In this report, the statistical behavior of the AWG filter transmission in the side-lobe region is studied analytically. Both the distribution of random side-lobe level at a given wavelength and an upper bound of the outage probability for side-lobe maxima are given in a simple closed form. Accordingly, a crosstalk margin needs to be allocated to ensure a given fabrication yield and this is shown to depend on the fractional bandwidth of the AWG filter. For filter shapes that are close to Gaussian, this crosstalk margin can be 8 dB or more above the average crosstalk level, for small fractional bandwidth of about 1% and fabrication yields of 80% or higher. These relations should be useful to AWG designers particularly when the underlying fabrication process is susceptible to nonnegligible random phase errors.