Statistical analysis of correlated phase error in transmission characteristics of arrayed-waveguide gratings

Transmission characteristics of arrayed waveguide gratings (AWGs) are significantly influenced by phase errors in a waveguide array, which are easily caused by the variation of fabrication process. In this paper, the statistical analysis of transmission characteristics is presented using correlation and spectral density of phase errors. A simple statistical approach, based on a simplified model of a waveguide array, is newly introduced to clarify statistical behavior of phase errors in AWGs. Spectral density is modeled from measured phase errors, and then average transmission characteristics are simulated for AWGs with different channel spacing. Average transmission characteristics, simulated with the spectral density model, almost describe measured results in the cases of various channel spacing. It is also indicated that an AWG may have larger adjacent-channel crosstalk with narrower channel spacing because the adjacent-channel crosstalk is affected by phase errors with a smaller spatial frequency.