Transverse electromagnetism standing waves

XVIII. Beltrami Vector Potential Associated with TEM (Transverse Electromagnetic) Standing Waves with E//B... 

XVIII. BELTRAMI VECTOR POTENTIAL ASSOCIATED WITH TEM (TRANSVERSE ELECTROMAGNETIC) STANDING WAVES WITH E//B... 

From the definition of the Hermitian polynomials [5.31], one can see that the indices m and n give the number of nodes for the amplitude A(x, y) in the X- (or the y-) direction. Figures 5.9,5.10 illustrate some of these transverse electromagnetic standing waves, which are called TEM, modes. The diffraction effects do not essentially influence the transverse character of the waves. While Fig. 5.9a shows the one-dimensional amplitude distribution A(x) for some modes. Fig. 5.9b depicts the two-dimensional field amplitude A(x, y) in Cartesian coordinates and A(r, d) in polar coordinates. Modes with m = n = 0 are called fundamental modes or axial modes (often zero-order transverse modes as well), while configurations with m > 0 or n > 0 are transverse modes of higher order. The intensity distribution of the fundamental mode /qq oc Aqo qo derived from (5.30). With... 

Whittaker s early work [27,28] is the precursor [4] to twistor theory and is well developed. Whittaker showed that a scalar potential satisfying the Laplace and d Alembert equations is structured in the vacuum, and can be expanded in terms of plane waves. This means that in the vacuum, there are both propagating and standing waves, and electromagnetic waves are not necessarily transverse. In this section, a straightforward application of Whittaker s work is reviewed, leading to the feasibility of interferometry between scalar potentials in the vacuum, and to a trouble-free method of canonical quantization. 

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