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Fig. 8. Minimum relative birefringence 6,,/A for a 10-dB/km loss of the y-polarized mode of Fig. 3(b). We assume that A, = A, = A, = Aso that V, ~ V, ~ V, ~ Vin Table 2. The various curves in- vestigate the effect of the value of n, on the fiber loss. Oj. ~ 1 - (n;/n,) fori = x,y. The profiles are shown in Fig. 9. — Figure 8 Minimum relative birefringence 6,,/A for a 10-dB/km loss of the y-polarized mode of Fig. 3(b). We assume that A, = A, = A, = Aso that V, ~ V, ~ V, ~ Vin Table 2. The various curves in- vestigate the effect of the value of n, on the fiber loss. Oj. ~ 1 - (n;/n,) fori = x,y. The profiles are shown in Fig. 9.

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Fig. 1. Birefringent fiber with geometrical axes x, y, and z aligned with the principal axes of the refractive index.’

Table 2. Physical Parameters of the Anisotropic Fiber? 4k = 2n/d; p is the core radius or a suitable scaling parameter.

Fig. 2. Example of a profile of an anisotropic fiber. Vertical dis- tances are exaggerated for clarity. Because of weak guidance, n¢o* = na* and Neo” = ngy. Because of weak anisotropy, nz ~ ny ~ n. All symbols are defined in Table 2.

Fig. 4. Two examples of anisotropic profiles exhibiting the role of the relative birefringence parameter 6,,/A: (a) 100% relative bire- fringence, (b) 50% relative birefringence. We assume, for conve- nience, that A, = A, = A, All parameters are defined in Fig. 2 and Table 2.

Fig. 5. Relative birefringence 4,,/A versus leakage loss of the fun- damental y-polarized mode of Fig. 3(b). The refractive index n, for z-polarized light equals that, n,, for x-polarized light. We assume that A, = Ay = Aso that V, ~ Vy ~ V. These results are calculated from Eq. (9a), which approximates the exact result given by Eq. (25) for the range shown. B. Leaky Mode Design of Single-Mode, Single- Polarization Fiber

Fig. 6. Minimum relative birefringence 6,,/A for a given decibel- per-kilometer loss of the y-polarized mode for the fiber of Fig. 3(b) under the same conditions as those for Fig. 5: (a), (b) a1% and 0.5% difference, respectively, in the core and the cladding refractive indices. The curve labeled 0 dB/km is the minimum relative birefringence necessary for leakage and is given by Eq. (8).

Fig. 7. Normalized loss versus relative birefringence 5,,/A for the y-polarized mode of Fig. 3(b). We assume that A, = Ay = Aso that V, = Vy ~ Vin Table 2. (a), (b) Forn, =n, and n, = Ny, Tespec- tively. The loss in decibels per kilometer is y = 8.686 X 10° B! for p in micrometers. where C = [J22(U,)/Jo2(Q,)]|p2|2.. The term Jo2(Q,.) can be identified as that which is due to free-space radiation modes [U, = Q, in Eq. (A7)]. The ratio of J’s in the C term corrects for refraction across the core—cladding interface. The ps term takes account of the fiber structure, which greatly affects axially directed (Q, ~ 0) radiation.

We now derive the difference in propagation constants be- tween the x-polarized and y-polarized modes. Since @, ~ By, we have 8,2 — B,? ~ 26,(8, — By). Together with Eq. (A2) and the definitions of V,, A,, and 6,, in Table 2, this leads to