All-pass filters (APF's) are devices that allow phase correction or equalization without introducing any amplitude distortion. An optical implementation of such devices is very attractive since they can be used for dispersion compensation. In contrast to other dispersion control devices, optical APF's can correct any order of dispersion. This can be achieved by careful design of multistage APF's to approximate a target phase profile. However, large dispersion is usually narrow band or requires many filter stages. These performance tradeoffs and the general phase properties of optical APF's are reviewed and clarified in the first part of this paper. In the second part, a general design methodology of optical APF's is introduced. We show that any all-pass structure may be constructed from simple N-port devices (such as directional couplers or Mach-Zehnder interferometers) with N-1 outputs fed back to any of the N-1 inputs. The feedback paths may contain delays or further APF's (recursive design). This set of design rules allows for constructing complex all-pass filters of any number of stages starting with very simple elements. We use this technique to demonstrate a number of optical all-pass structures that may be implemented in planar waveguide or using thin-film filter technology.
G. Lenz and C. K. Madsen, "General Optical All-Pass Filter Structures for Dispersion Control in WDM Systems," J. Lightwave Technol. 17, 1248- (1999)