Local modes tapered couplers

Fig. 19-4 (a) Two tapered fibers with equal core radii p at z = z, while at zi and Z2 the core radii are reversed, (b) Qualitative behavior of the local-mode propagation constants along fibers 1 and 2 of (a) in isolation, (c) Coupler consisting of bent fibers of constant core radius, (d) Schematic representation of an arbitrary tapered coupler consisting of fibers 1 and 2 of increasing and decreasing core radii, respectively. 

The simplicity of the local-mode description of propagation on couplers is evident in the analysis of cross-talk between the constituent fibers. If only fiber 1 is illuminated at z —/in Fig. 19-4(d), it is clear from the previous section that the P+ modeofEq. (19-11) is excited and no power enters the P. mode. Consequently propagation is described entirely by the characteristics of the 4 + mode, and thus all of its power is carried by fiber 2 for z /. In other words, there is essentially a 100% transfer of power from one fiber to the other on a tapered coupler, provided only that the slowness criterion below is satisfied. 

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... 

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. 

In the central region of the coupler where the fibers are virtually identical, it follows that F = a+ =1, and each fiber carries half the total power. At the end of the taper, z = L, the dissimilarity between vhe fibers is the reverse of that at z = 0, and thus 2 la this case f = 0 and a+ p 1, so that Eq. (29-37) reduces to Pj (L) = 0, PiiL) = 1. In other words, all of the power initially in the first fiber has tran erred to the second fiber, which is the conclusion reached in Section 19-7 using the composite local modes of the coupler. 

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