Design of Ultra-compact On-chip Discrete Phase Filters for Broadband Dispersion Management

This paper provides an in-depth theoretical and numerical analysis of a group-velocity dispersion (GVD) management scheme for broadband waveforms using ultra-compact on-chip discrete spectral phase filters based upon waveguide Bragg gratings (WBGs) in a silicon-on-insulator (SOI) platform. Through this technique, mm-long discrete phase filters can be designed to impart a target arbitrary GVD profile on a high-rate (typically, $\geq\!10$ GHz) periodic pulsed waveform, including fully customized and extremely large second and higher-order dispersion terms (e.g., equivalent to 10,000 km of a standard single-mode fiber), over a broad frequency bandwidth (up to $\sim\!3$ THz, demonstrated here). The capabilities and limitations of this technique to impart a target GVD profile over an arbitrary (generally, non-periodic) broadband signal are also studied. We show that customized GVD lines can be efficiently implemented offering a net group-delay excursion in the hundreds-of-ps range using mm-long integrated discrete phase filters. Additionally, we suggest and numerically demonstrate a simple and practical strategy to improve significantly the performance of the discrete phase filtering approach for application on non-periodic waveforms, by combining the discrete phase filter with a suitable periodic resonance (frequency-comb) amplitude filter. An extensive tolerance analysis is conducted, and we conclude that the proposed SOI design framework is well within practical fabrication requirements as well as robust to the expected variability in the main WBG device design parameters.