Local modes composite waveguides

The local-mode concept also applies to slowly varying composite waveguides, such as the two identical fibers in Fig. 19-3(a) and the pairs of nonidentical fibers in Fig. 19-4, and is therefore a powerful method for studying the properties of nonuniform couplers. 

One immediate consequence of using local modes for pairs of identical, slowly varying fibers is a simple description of power transfer due to cross-talk between fibers. If fiber 1 in Fig. 19-3(a) is initially illuminated with unit power and fiber 2 with zero power, the distribution of power along the composite waveguide is given by a simple modification to the corresponding problem for cylindrically symmetric fibers in Section 18-13. We... 

The coupling of local modes on composite waveguides, such as two parallel, slowly varying fibers, is described by the results of this chapter, provided we... 

Propagation along slowly varying, tapered couplers of the type illustrated in Fig. 28-2 (a) can be described by the local modes of the composite waveguide, as discussed in... 

The analysis of the previous section also applies to the special case qf identical fibers, such as those illustrated in Fig. 28-2(b). At each position along the composite waveguide Pi = P2 and = /32, whence Eq. (28-32) and (28-37) show that x = Hz) = 0. In other words there is no coupling to the E mode within the accuracy of the analysis. This is also obvious from symmetry arguments. Consequently coupling only occurs with higher-order local or radiation modes with the symmetry properties of 4 +. 

To complement the analysis of cross-talk between cylindrically symmetric fibers, we now consider pairs of fibers which vary slowly along their length, such as the identical fibers of Fig. 19-3(a) and the tapered coupler of Fig. 19-4(a). Propagation along these systems was described in Chapter 19 using the local modes of the composite waveguide. Our purpose here is to describe cross-talk in terms of the coupUng of the local modes of each fiber in isolation of the other. 

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