Tapered couplers

E. Miscellaneous Tubing Connectors. The variety of tubing couplers is enormous and a comprehensive list would be out of place in this book, but several additional types will be mentioned here which are useful in the laboratory. Metal standard taper and metal ball joints are available, and these will mate with corresponding ground-glass joints to provide one means of connecting parts made of dissimilar materials.4 As with glass standard taper joints, the seal is... 

Figure 1. Tapered slab-type MNA single crystal film waveguide with grating couplers.

Einally, a direct, reactive compatibilization by addition of an active, low molecular weight coupler can be used to upgrade and compatibilize mixtures of engineering resins. The process may be expensive (the required tapered block copolymers are usually dear), thus used only in specific cases. 

Mekis A, Joannopoulos JD (2001) Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides. J Lightwave Technol 19(6) 861-865... 

M Yaegashi, Y Matsuura, M Miyagi. Hollow-tapered launching coupler for Er YAG lasers. [Review of Laser Engineering, vol.28, no.8, pp.516-19, 2000. 

Y Matsuura, H Hiraga, W You, Y Kato, M Miyagi, S Abe, S Onodera. Lensed-taper launching coupler for small-bore, infrared hollow fibers. Applied Optics, vol.36, no.30, 20 Oct. 1997, pp.7818-21. 

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. 

Example Tapered couplers 28-8 Example Identical fibers... 

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... 

Fig. 28-2 Examples of (a) a tapered coupler of core index and core radii Pi (z) and P2 (z) in a uniform cladding of index n, and (b) two identical fibers.

Derivation of the coupled equations 29-10 Solution of the coupl equations 29-11 Example Identical fibers 29-12 Example Tapered couplers... 

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. 

Consider a tapered coupler, such as the one illustrated in Fig. 19 (a), and assume that only the first fiber carries unit initial power, i.e. hi (0) = 1 and bjiO) = 0. We can simplify the solution of Eq. (29-34) by using the fact that the fibers are optically well... 

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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