Slightly elliptical fibers

The polarization corrections, and SPy, to the scalar propagation constant P for the Xq- and yo-polarized modes on the perturbed, noncircular fiber are in general unequal, and their difference describes the anisotropic, or birefringent, nature of propagation. This is of basic interest for the two fundamental modes on single-mode fibers. The calculation of the corrections from the formula in Table 13-1, page 288, requires first-order corrections to the approximation We derive these corrections for the slightly elliptical fiber in Section 18-10. 

A step-profile, circular fiber with core and cladding indices n and is deformed into the slightly elliptical fiber of Fig. 18-2(a) in such a way that the core cross-sectional area is unchanged. If the semi-major and semi-minor axes of the elliptical fiber have lengths Px und Py, and e is the eccentricity, then... 

Example Slightly elliptical fibers 34-9 Example Far-field corrections... 

For the fundamental modes on a circular fiber, is independent of 0. Consequently —tiy and p = p in Eq. (18-21). In other words, the propagation constants for the circular and elliptical fibers are identical for slight eccentricity, provided the core areas are equal [6]. The latter condition is equivalent to requiring equal profile volumes, as is clear from Eq. (17-13). Hence the present result is consistent with the more general result of Section 17-3, which showed that, within the Gaussian approximation, P = on an arbitrary, elliptical-profile fiber of slight eccentricity, provided the profile volumes are equal. 

The physical stmcture of wool is complex. The cross-section of wool is circular, or slightly elliptical in shape. The diameter of wool fibers is in the range of 20-40 //m. Figure 5.14 shows a schematic of the cross-section of a wool fiber, which consists of three major components, cuticle, cortex, and medulla. 

When the asymmetry is slight, it is sometimes possible to simplify the above analysis by treating the noncircular fiber as a small perturbation of a circular fiber. Thus, for example, the ray invariant I of the circular fiber can be replaced by an approximate invariant l(z) which varies very slowly along the noncircular fiber. The spatial transient on the elliptical, clad parabolic-profile fiber can be determined within this approximation. Details are given elsewhere [13]. 

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