Field electromagnetic wave

Further, in 1904 Whittaker [56] (see also Section V.C.2) showed that any electromagnetic field, wave, etc. can be replaced by two scalar potential functions, thus initiating that branch of electrodynamics called superpotential theory [58]. Whittaker s two scalar potentials were then extended by electrodynamicists such as Bromwich [59], Debye [60], Nisbet [61], and McCrea [62] and shown to be part of vector superpotentials [58], and hence connected with A. 

The electromagnetic field created by the transducer propagates through the examined material as a wave with the length... 

The necessary boundary conditions required for E and //to satisfy Maxwell s equations give rise to tire well known wave equation for tire electromagnetic field ... 

Altliough a complete treatment of optical phenomena generally requires a full quantum mechanical description of tire light field, many of tire devices of interest tliroughout optoelectronics can be described using tire wave properties of tire optical field. Several excellent treatments on tire quantum mechanical tlieory of tire electromagnetic field are listed in [9]. 

For tire electromagnetic fields E and H tire fonn of tire waves of interest is... 

The last attribute of tire electromagnetic field we need to discuss is wave polarization. The nature of tire transverse field is such tliat tire oscillating field disturbance (which is perjDendicular to tire propagation direction) has a particular orientation in space. The polarization of light is detennined by tire time evolution of tire direction of tire electric field... 

As already mentioned, the results in Section HI are based on dispersions relations in the complex time domain. A complex time is not a new concept. It features in wave optics [28] for complex analytic signals (which is an electromagnetic field with only positive frequencies) and in nondemolition measurements performed on photons [41]. For transitions between adiabatic states (which is also discussed in this chapter), it was previously intioduced in several works [42-45]. 

The question of determination of the phase of a field (classical or quantal, as of a wave function) from the modulus (absolute value) of the field along a real parameter (for which alone experimental determination is possible) is known as the phase problem [28]. (True also in crystallography.) The reciprocal relations derived in Section III represent a formal scheme for the determination of phase given the modulus, and vice versa. The physical basis of these singular integral relations was described in [147] and in several companion articles in that volume a more recent account can be found in [148]. Thus, the reciprocal relations in the time domain provide, under certain conditions of analyticity, solutions to the phase problem. For electromagnetic fields, these were derived in [120,149,150] and reviewed in [28,148]. Matter or Schrodinger waves were... 

This part of our chapter has shown that the use of the two variables, moduli and phases, leads in a direct way to the derivation of the continuity and Hamilton-Jacobi equations for both scalar and spinor wave functions. For the latter case, we show that the differential equations for each spinor component are (in the nearly nomelativistic limit) approximately decoupled. Because of this decoupling (mutual independence) it appears that the reciprocal relations between phases and moduli derived in Section III hold to a good approximation for each spinor component separately, too. For velocities and electromagnetic field strengths that ate nomrally below the relativistic scale, the Berry phase obtained from the Schrddinger equation (for scalar fields) will not be altered by consideration of the Dirac equation. 

P. Lorrain and D. Corson. Electromagnetic Fields andWaves. W. H. Freeman, San Francisco, 1970, p. 518. A general and clear text on electromagnetic wave phenomena at the undergraduate level. 

Fig. 4.1. Interference of incoming and the reflected X-ray waves inthe triangular region above a flat and thick reflecting substrate. The strength ofthe electromagnetic field is represented on the gray scale by instantaneous crests (white) andtroughs (black). Inthe course of time, the pattern moves from the left to the right [4.21].

Rojansky, V. (1979). Electromagnetic Fields and Waves. Dover Publications, Inc., New York. 

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