Optical Filter Design and Analysis: A Signal Processing Approach

CHAPTER FOUR

Multi-Stage MA Architectures

This chapter focuses on multi-stage optical MA (all-zero) filters. Before plunging into multi-stage architectures, it is instructive to begin with an in depth look at a single-stage MZI. Several practical issues are addressed including the impact of loss, refractive index variations, coupling ratio variations and wavelength dependence on the filter response. The discussion of multi-stage architectures begins with two structures that closely resemble their digital filter counterparts, optical cascade and transversal architectures. Then, multi-port architectures, which are advantageous for multiplexing and demultiplexing numerous channels simultaneously, are introduced. Two examples are the diffraction grating and waveguide grating router (WGR). Their principles of operation are very similar and are discussed in Section 4.4. Both of these filters break the wavefront into discrete sections that are then delayed and recombined to obtain very narrowband filters. Finally, optical MA lattice filters are developed. These 2 × 2 filters (2 inputs and 2 outputs) have power complementary outputs and can approximate any desired function. Examples are given for dispersion compensation and gain equalization applications. As the delay is made smaller and the number of stages larger for a lattice filter, we obtain filters whose frequency response is efficiently described by coupled-mode theory. Two examples of forward-propagating coupled-mode devices are ...