Fundamental modes single polarization fibers

A waveguide is said to be multimoded or overmoded if V> when many bound modes can propagate. At the opposite extreme, when V is sufficiently small so that only the two polarization states of the fundamental mode can propagate, the waveguide is said to be single-moded. For example, the step-profile, circular fiber is single-moded when V < 2.405, as we show in Section 12-9. 

We showed in the discussion of structural anisotropy above, that the core index must greatly exceed the cladding index for the propagation characteristics of the two fundamental modes to differ significantly. Here we show that a relatively small amount of material anisotropy can dramatically influence propagation by removing one of the two possible polarization states of the fundamental mode. This results in a fiber that is truly single moded. 

If V is below the cutoff value 2.405 of the second mode in iFig. 14-4, the fiber is single moded and only the even and odd fundamental modes can propagate. Both modes have the same propagation constant j8. Consequently the group velocity and the transit time of Eq. (11-36) are independent of polarization. In the weak-guidance approximation, the expression for in Table 14—3 follows from Eq. (13-17), and is plotted against V in Fig. 14—3(d) as the dimensionless quantity (n — c)/cA. 

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. 

Consider a single-mode, elliptical fiber whose refractive-index profile rotates along its length, as shown in Fig. 19-2. We recall from Section 13-5 that in the weak-guidance approximation one fundamental mode of the cylindrically symmetric, elliptical fiber is plane polarized with its transverse electric field parallel to the x-axis in Fig. 19-2(a) and has propagation constant The other fundamental mode s field is parallel to the y-axis... 

Radiation from the sinusoidally perturbed interface of a weakly guiding, step-profile fiber was discussed in Section 22-5 in terms of the induced current of Eq. (22-15). When the fiber is single moded, power is scattered into both forward- and backward-propagating x-polarized fundamental modes from the incident mode. Following the discussion of Section 22-5, we set... 

We are primarily interested in radiation from the fundamental modes of bent, single-mode fibers. Within the weak-guidance approximation, the power radiated is insensitive to polarization, since p. Thus we can conveniently assume that the transverse electric field is parallel to the Z-axis in Fig. 23-2(a), i.e. orthogonal to the plane of the bend. Close to and within the core, the magnitude of the electric field on the bend is given by aj Fo (R) exp (ifiz), using the local-mode approxinution, where is the modal amplitude, Fq (R) is the... 

The two fibers in Fig. 29-1 have core refractive-index profiles (x, y) and 2 (x, y), referred to a common set of axes, and a uniform cladding of index n i. For convenience we assume both fibers are single moded in isolation of each other, and, within the weak-guidance approximation, we work with the x-polarized fundamental modes. Hence if iVj and N2 are the normalizations of Table 13-2, page 292, we set... 

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