Circular wave guide

In this even simpler cell shown in Figure 3b, the volume beyond the end of the coaxial line center conductor (supported by a disk with dimensions to match the coaxial line admittance) is filled with dielectric. The sample is thus in the fringing field at the end of the line, or more generally can be regarded as filling a section of circular wave guide used at frequencies below cutoff for wave propagation. 

The efficiency with which beams excite the fundamental modes of circular fibers, with the fields of Eq. (13-9), is of particular interest when the fiber is single moded. In order to account for weakly guiding fibers of otherwise arbitrary profile, when analytical solutions of the scalar wave equation for Fo (r) are not available, we use the Gaussian approximation of Chapter 15. The radial dependence of the fundamental-mode transverse fields is approximated in Eq. (15-2) by setting... 

The combination of solutions of the scalar wave equation for the transverse fields of weakly guiding fibers of circular cross-section are given in Table 13-1, page 288. As we showed in the previous section, these combinations can be derived using perturbation theory. In this section we show how the combinations can be deduced using only symmetry arguments [2]. We start with the four vector solutions constructed from the solutions of the scalar wave equation with the common propagation constant P, and denote them by... 

Our discussions of weakly guiding circular fibers both in this chapter, and in Chapters 13 and 14, have tacitly assumed that the combinations in Table 13-1, page 288, form the most basic set of modes for describing approximate solutions of the vector wave equation. For example, we might have considered the set of four right- and left-handed, circularly polarized fields which have the complex forms... 

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