Optical Filter Design and Analysis: A Signal Processing Approach

CHAPTER FIVE

Multi-Stage AR Architectures

Optical filters with feedback paths and at least one all-pole response are discussed in this chapter. Filters consisting of ring resonators, thin film dielectric stacks, and Bragg gratings are included in this category. In many cases, these filters have both AR and ARMA responses; however, the pole and zero locations of the ARMA response are coupled, which prohibits the realization of a general ARMA response. Filters capable of realizing general ARMA responses are discussed in Chapter 6. A major advantage for AR and ARMA filters is their steeper rolloff and larger stop-band rejection characteristics compared to MA filters with the same number of stages. Although a more ideal magnitude response can be achieved, one drawback is that a dispersionless AR or ARMA filter cannot be realized.

Feedback paths may be realized by looping the delay line back on itself to form a ring or by reflecting the signal between two partial reflectors as in a Fabry–Perot cavity. Filters with ring-resonator feedback paths are discussed first, including both cascade and lattice structures. Using the Z-transform description and synthesis algorithm developed for the lattice structure, design examples are presented for bandpass, gain equalization and dispersion compensating filters. The maximum FSR for ring-based filters is limited by the minimum bend radius. The use of Vernier operation to effectively extend the FSR is discussed, along with the limitations that it ...