Chapter 7. Multi-Stage ARMA Filters

Summary

This chapter covers general ARMA optical filter architectures that allow the pole and zero locations to be specified independently, in contrast to the ARMA responses. The poles and zeros can be realized as separate sections by cascading multi-stage AR and MA filters; however, such a cascade arrangement may introduce undesirable excess loss. To minimize passband loss, an ARMA lattice architecture is advantageous. A single-stage lattice ARMA filter is described to provide physical insight into the filtering action of a ring within an MZI. Then, we discuss a general multi-stage ARMA lattice architecture. A special type of ARMA filter is an all-pass filter, which ideally has a constant magnitude response. All-pass filters are well-known in analog and digital filter theory and practice. Optical all-pass filters are explained and applications for dispersion compensation are presented. All-pass filters can also be used in an interferometer to efficiently realize Butterworth, Chebyshev, elliptic and other optimal bandpass filters. The design of bandpass responses using all-pass filters is detailed. General multi-stage ARMA optical filters are very new; so, we rely mainly on theoretical descriptions and simulations in contrast to the numerous fabrication results presented for MA and AR optical filters.