TEM wave

Besides its appearance in the FFMF equation in plasma physics, as well as associated with time-harmonic fields in chiral media, the chiral Beltrami vector field reveals itself in theoretical models for classical transverse electromagnetic (TEM) waves. Specifically, the existence of a general class of TEM waves has been advanced in which the electric and magnetic field vectors are parallel [59]. Interestingly, it was found that for one representation of this wave type, the magnetic vector potential (A) satisfies a Beltrami equation ... 

These waves were initially called "Hertzian waves",—for example, by Marconi77, the inventor of the radio. The solutions to these wave equations can be shown to be transverse electromagnetic (TEM) waves (Problem 2.7.5, Fig. 2.9). 

The same plate structure also serves as a 34 transmission line for the radio-frequency field, transporting it as a 170 MHz TEM wave traveling parallel or antiparallel to the beam direction. This is described more fully in Ref. [51]. As a bunch of molecules travels along the interaction region, a hyperfine transition can be induced at any desired position by pulsing the rf field on for a short time. This repopulates the f = 1 state and therefore produces an increase in the fluorescence signal at the detector, as shown by the rf scans in Figure 15.7. 

Being a TEM wave, the rf magnetic field between the plates is accurately perpendicular to the static electric field and we choose to define its direction as the jc-axis. This field therefore drives the transition (0) — (c) discussed in the last section. 

It should be noted that all of the theories and formulas in this chapter are based on transverse electromagnetic (TEM) wave propagation. 

The penetration depth is physically defined as the depth for an electromagnetic wave penetrating into a conductor when the wave hits the conductor surface. The physical concept of the penetration depth is very useful to explain the behavior of a current and a voltage on a conductor and also to derive impedance and admittance formulas of various conductor shapes and geometrical configuration. However, it should be reminded that the concept is based on TEM wave propagation and thus is not applicable to non-TEM propagation. Also, remind that it is just an approximation. 

However, depending on the earth resistivity and the conductor height, the admittance for the imperfectly conducting earth should be considered especially in a high-frequency region, say, above some MHz. When a transient involves a transition between TEM wave and TM/TE waves, Wise s admittance should be considered. Then, the attenuation constant differs significantly from that calculated by Equation 1.24. 

The fundamental modes of all waveguides considered in this text are cut off when F = 0. At cutoff the phase velocity of the mode is equal to that of a z-directed plane wave in an unbounded medium of refractive index n, but the modal fields are not TEM waves except in special cases. In general, a significant fraction of a mode s power can propagate within the core at cutoff, i.e. r]j of Eq. (11-24) is nonzero, and the group velocity differs from the phase velocity. Below cutoff, these modes propagate with loss and are the leaky modes of Chapter 24. 

Suppose the waveguide is composed of an unbounded uniform medium of refractive index i.e. effectively free space . The modal fields are then found from Maxwell s equations to be the fields of transverse electromagnetic, or TEM, waves propagating in the z-direction parallel to the waveguide axis. Thus, the propagation constant )S = n k, the longitudinal components satisfy e = h = 0, and the transverse electric and magnetic fields are related by... 

We next consider a waveguide with a nonuniform refractive-index profile n = n(x, y). The propagation constant now depends on the orientation of the electric field, and the modes are no longer TEM waves. In general the modal fields are not solutions of the scalar wave equation but obey the vector wave... 

The modes must therefore be nearly TEM waves with S 0, = 0, and... 

We showed above that the modes of weakly guiding waveguides are approximately TEM waves, with fields e = e, h S h, and h, related to e, by Eq. (13-1). In an exact analysis, the spatial dependence of e,(x,y) requires solution of Maxwell s equations, or, equivalently, the vector wave equation, Eq. (1 l-40a). However, when A 1, polarization effects due to the waveguide structure are small, and the cartesian components of e, are approximated by solutions of the scalar wave equation. The justification in Section 13-1 is based on the fact that the waveguide is virtually homogeneous as far as polarization effects are concerned when A 1. As we showed in Section 11-16, these effects... 

We have shown that the modes of weakly guiding waveguides are approximately TEM waves, with transverse field components e, and h,. However, the exact modal fields have longitudinal components. For the weakly guiding waveguide these components are very small, and are expressible approximately in terms of e, and h,. From Eq. (32-18) we have... 

We begin with a brief review of the weak-guidance approximation for fundamental modes on circular fibers. In Sections 13-2 and 13-4, we showed that the two fundamental modes are virtually TEM waves, with transverse fields that are polarized parallel to one of a pair of orthogonal directions. The transverse field components for the x- and y-polarized HEj j modes are given by Eq. (13-9) relative to the axes of Fig. 14-1. The spatial variation Fq (r) is the fundamental-mode solution (/ = 0) of the scalar wave equation in Table 13-1, page 288. Hence... 

In Chapter 13 we showed how the bound-mode fields of weakly guiding waveguides can be constructed from solutions of the scalar wave equation. With slight modification, the same procedure applies to the radiation-mode fields as well [4]. However, while the bound modes are approximately TEM waves because j8 = = kn, the radiation modes are not close to being... 

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