Local modes radiation

The thermal stability of the centers responsible for the local modes of vibration has been investigated. In GaP, Sobotta etal. (1981) observed that annealing of the implanted samples at 240°C for one hour leads to a narrowing of the 2204 cm 1 absorption line. This is due to the annealing of the radiation damage. Annealing at 400°C for one hour decreases drasti-... 

Excitation of the local radiation modes, described in Chapter 28, is expressible by Eq. (22-35) provided we replace the jth local mode by the jth local radiation mode throughout the above analysis. 

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 ratio P /P(0) is the fraction of power radiated from the entire loop in Fig. 23-2(a), and ignores attenuation of local-mode power along the antenna. 

In addition to the radiation loss associated with bending of a fiber, there is a transition loss due to abrupt changes in curvature, as occur at the cross-sectional plane AA of the fibers in Fig. 23-4. As we show below, there is a mismatch between the fields on AA, and, consequently, the incident field on one side excites both the local modes and the radiation field on the other side. The power in the radiation field accounts for the transition loss [4-6]. 

The exact fields of an arbitrarily perturbed waveguide are expressible as a superposition of local-mode fields and the radiation field, and, provided the... 

In Section 27-1 we showed that in applying the coupled mode equations there is an intrinsic restriction to weakly guiding waveguides. This restriction does not occur in the application of the coupled local-mode equations. A general solution of the coupled local-mode equations is derived for weak power transfer in the following section, and the radiation modes are discussed later in the chapter. 

When this condition is satisfied, we can neglect coupling between the local modes and the radiation field, and the coupled local-mode equations of Eq. (28-2a) reduce to [S]... 

The coupled local-mode equations discussed in Section 28-1 implicitly include coupling to the radiation field. In keeping with the concept of local modes. 

The inclusion of the local radiation modes in Eq. (28-1) follows by analogy with the coupled mode equations derived in Section 31-11. For example, the amplitude and phase dependence bj (z, Q) of the j th forward-propagating local radiation mode satisfies the coupled local-mode equation... 

Consider the step-profile tapers of Fig. 28-1, whose ends have fixed core radii Po and p but otherwise are of arbitrary, slowly decreasing radius. We are primarily interested in radiation loss when a local mode approximates the fundamental mode on the taper, but the analysis is easily modified to describe losses from higher-order local modes. This also provides criteria for the accuracy of the local-mode description. 

The analysis of the previous section also applies to the special case qf identical fibers, such as those illustrated in Fig. 28-2(b). At each position along the composite waveguide Pi = P2 and = /32, whence Eq. (28-32) and (28-37) show that x = Hz) = 0. In other words there is no coupling to the E mode within the accuracy of the analysis. This is also obvious from symmetry arguments. Consequently coupling only occurs with higher-order local or radiation modes with the symmetry properties of 4 +. 

For convenience we only include bound modes in our derivation radiation modes are readily incorporated by analogy with the coupled mode equations of Section 31-11. We express the total transverse field of the perturbed waveguide as an expansion over the complete set of forward- and backward-propagating local modes... 

In Fig. 9, the mode field distributions of the fundamental quasi-TMoo modes of ring and disk microresonators are mutually compared. Note that the radiation is directed mainly into the substrate, and it is stronger from the ring since the field in the disk is localized closer to the center. 

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