Pole-Zero Diagram Approach to the Design of Ring Resonator-Based Filters for Photonic Applications

Abstract

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.

Efficient Design of Coupled Microcavities at Optical Frequencies

“…This representation can be further utilized to simplify both the analysis and synthesis of the cascaded system [24]. Similar to the procedure of discrete digital filters design, we utilize Z domain representation of the optical filter response [24]. This is accomplished by utilizing z…”

“…It is also based on add drop filters, where the output is only at the drop port of the coupled structure. Other approaches are developed for the optimal placement of zeros and poles of the filter transfer function [23] and [24]. These approaches are intended for the design of parallel and series coupled ring resonators [24].…”

“…Other approaches are developed for the optimal placement of zeros and poles of the filter transfer function [23] and [24]. These approaches are intended for the design of parallel and series coupled ring resonators [24]. They utilize resonators of equal coupling parameters to overcome the complexity of the design.…”

“…They utilize resonators of equal coupling parameters to overcome the complexity of the design. Using these approaches, tapering of the coupling parameters is done intuitively [24]. This intuitive tuning is successful for a small set of cascaded series or parallel ring resonators.…”

Ring-Resonator-Based Wavelength Filters

“…Examples are considering the cascade as a generalized DFB grating [63,66], describing the filter in terms of a prototype filter as known in the microwave domain [61] or using the scattering matrix description [64,65]. Recently, the z-transform description of these filters has also been applied [67].…”