Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications

The pole-zero diagram is a tool that has been widely employed in digital and electronic filter design. It greatly facilitates filter design by producing a simple and direct visualization of parametrical behaviors and general spectral characteristics. In this paper, we propose new methods of applying pole-zero diagrams to photonic filter design, aimed at tailoring spectral characteristics. In particular, we demonstrate the effectiveness of this method in designing ring resonator-based filters for application to optical wavelength interleavers and deinterleavers. We show that there exist close relations between the pole-zero diagram of an optical filter and its wavelength response, and derive pole-zero diagrams for filters with various ring resonator configurations. Further, we propose a novel graphical technique using pole-zero diagrams for optimizing filter performance. As a practical example to demonstrate the effectiveness of the pole-zero approach, we present a new wavelength interleaver design with low crosstalk. This design was realized by superimposing the pole-zero diagrams of parallel and series-coupled ring resonator arrays.