Homogeneous electromagnetic field

The electromagnetic fields (x,r) and H(x, t) associated with scattering from a microsphere satisfy Maxwell s equations. For a homogeneous, isotropic linear material the time-harmonic electrical held E and the magnetic held H satisfy vector wave equations, which in SI units are (Bohren and Huffman, 1983)... 

We showed in Chapter 3 that a physically realizable time-harmonic electromagnetic field (E, H) in a linear, isotropic, homogeneous medium must satisfy the wave equation... 

In utilizing a complex three-vector (self-dual tensor) rather than a real antisymmetric tensor to describe the electromagnetic field, Hillion and Quinnez discussed the equivalence between the 2-spinor field and the complex electromagnetic field [63]. Using a Hertz potential [64] instead of the standard 4-vector potential in this model, they derived an energy momentum tensor out of which Beltrami-type field relations emerged. This development proceeded from the Maxwell equations in free homogeneous isotropic space... 

Let us carefully note that the emergence of Beltrami field relations from the Hillion-Quinnez model, is not due to an ad hoc rendering of the EM field relations, but is a logically consistent result that follows from recognizing that any electromagnetic field in a homogeneous, isotropic medium in free space, away from charges and currents, can be expressed either in terms of the spinors fa, or in terms of the complex Hertz-vector II. 

Electromagnetic fields of a light pulse propagating along the z axis can be expanded into modal contributions that reflect the geometry of the waveguide (we consider homogeneous medium a special case of the latter). 

We employ matrix methods in order to obtain the reflection and transmission coefficient of the electromagnetic field within the device. Stratified structures with isotropic and homogeneous media and parallel-plane interfaces can be described by 2 x 2 matrices because the equations governing the propagation of the electric field are linear and the tangential component of the electric field is continuous [15,16], We consider a plane wave incident from the... 

An instrumental development of considerable importance to the p.m.r. spectroscopy of carbohydrates has been the introduction of high-resolution magnets based on superconducting solenoids.47 As already mentioned, the (homogeneous) magnetic field-intensity in conventional electromagnets is restricted by the properties of the iron core and by the fact that the addition of auxiliary coils that are... 

An NMR spectrum is obtained by placing a sample in a homogeneous magnetic field and applying electromagnetic energy at suitable frequencies to conform to Eq. 1.1. In Chapter 2 we examine in detail just how NMR spectra arise, and in Chapter 3 we delve into the procedures by which NMR is studied. Before we do so, however, it may be helpful to see by a few examples the type of information that can be obtained from an NMR spectrum. 

In free space, an electromagnetic field of frequency w is governed by the homogeneous vector Helmholtz wave equation... 

It will prove useful in the sequel to use the hertz potentials (Born and Wolf, 1980, pp. 76-84) to describe the electromagnetic field. The hertz potentials also satisfy the homogeneous vector Helmholtz equation in free space. The advantage of the hertz potentials is that they display much higher symmetry than the conventional vector and scalar potentials. Furthermore, they may be written in a form that displays the paraxial approximation of quasioptics directly. 

Meanwhile, let us consider a few simple examples, illustrating the spatial behavior of the migrated electromagnetic fields. The first example represents the results of migration of the magnetic component of the field generated by a local horizontal electric dipole, located at some depth, zq, in the homogeneous lower half-space of conductivity ab- The current in the dipole is described by the delta-pulse ... 

Direct calculations show that within any homogeneous domain the electromagnetic field described by formulae (12.80) and (12.81) satisfies the system of Maxwell s... 

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