 single- pole filter is given by [78] (4.94) where WO is the resonant angular frequency Q0 is the circular cavity quality factor and Q2 are the quality factors of the coupling between the input and the output guides, respectively, and are given by Quate (4.95) where P is the ring radius Ne is the effective mode index C is the light speed in vacuum K is the coupling coefficient Telecommunication Networks Stage thru FIGURE 4.47 Scheme of a three-pole multiring filter. Theory Experiment FIGURE 4.48 Notch and passband filtering characteristic of a two poles multiring filter: theoretical (dotted line) and measured (continuous line) characteristics. (After Romagnoli, M. et al., Proc. SPIE, 6996, 699611, 2008.) As shown in Figure 4.47, microrings can be coupled together to build a complex filter with sharp transfer functions. In Figure 4.48 [79], the transfer function measured for a two- stage microring filter is compared with its theoretical estimation. The weakness of this technique, which has as many advantages in terms of power con- sumption, dimension, and functionality, is the loss that today are still too high for the use in the signal line. However, microrings are more and more diffused in the field in which losses are less critical. 4.4.3 WDM Multiplexers and Demultiplexers In principle, several types of optical filters are suitable to form arrays working as multi- plexers and demultiplexers. For example, several CWDM multiplexers are realized as shown in Figure 4.49 with an array of thin-film filters. The way in which the filters are arranged implies that the different channels undergo different loss. This problem is generally overcome by arranging the filters in the demulti- plexer in the inverse order with respect to the multiplexer arrangement. Thus, the channel undergoing the greater loss at the demultiplexer experiment the smaller at the multiplexer and SO on. Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices 11+12+13+14 filter 11 Signal 12 Signal 13 Signal 14 Signal FIGUR