Modal amplitudes radiation

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... 

Given a source of excitation, either at the waveguide endface or within the waveguide, the modal amplitudes aj Q) of radiation modes are found by analogy with the bound-mode amplitudes aj. 

If current sources with density J are present within the waveguide, the radiation field is given by the second summation in Eq. (31-32), since the amplitudes of the radiation and evanescent modes are z-dependent within the region occupied by currents. Outside of this region the modal amplitudes are constant. We deduce from Eq. (31-37) that... 

We determine the correction to the radiation from the current dipole of Section 25-12, when located on the axis of a weakly guiding, step-profile fiber. If the z-axis of Fig. 25-1 (a) coincides with the axis of the fiber, we can repeat the analysis of Section 25-12 using the weakly guiding radiation modes instead of the Tree-space modes. The on-axis fields and nd consequently the modal amplitudes of Eq. (25-30) are multiplied... 

A tubular source of radius ro is located symmetrically within the core of a weakly guiding, step-profile fiber, i.e. 0 < ro < p, where p is the core radius. To account for the fiber profile, we repeat the analysis of Section 25-13 using the weakly guiding radiation modes of Table 25-4 instead of the free-space modes of Table 25-2. The modal amplitudes of Eq. (25-34a) are replaced by... 

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