Transverse electromagnetic waves, vacuum

Here, c = l/(eo/ o) is the velocity of electromagnetic radiation in vacuum. The dependence of energy-momentum relation) for an electromagnetic wave propagating through a crystal is called the dispersion law. Hence, Eq. (1.7) represents the dispersion law of a transverse electromagnetic wave in an infinite crystal [17]. 

In the classical electromagnetic theory of light, light in vacuum consists of transverse electromagnetic waves that obey Maxwell s equations [1,2]... 

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. 

In this final section, it is shown that the three magnetic field components of electromagnetic radiation in 0(3) electrodynamics are Beltrami vector fields, illustrating the fact that conventional Maxwell-Heaviside electrodynamics are incomplete. Therefore Beltrami electrodynamics can be regarded as foundational, structuring the vacuum fields of nature, and extending the point of view of Heaviside, who reduced the original Maxwell equations to their presently accepted textbook form. In this section, transverse plane waves are shown to be solenoidal, complex lamellar, and Beltrami, and to obey the Beltrami equation, of which B is an identically nonzero solution. In the Beltrami electrodynamics, therefore, the existence of the transverse 1 = implies that of , as in 0(3) electrodynamics. 

PROBLEM 2.7.5. Show that, both in a dielectric insulator and in a vacuum, a plane-wave electromagnetic field solution propagating along x, whose amplitude depends only on the coordinate x and on the time f, can have no component along x, that is, show that it must be a transverse electric wave [13]. 

Electromagnetic waves are transverse waves that oscillate perpendicular to the direction of propagation. They spread out in a straight line and in a vacuum at the velocity of light c0 = 299 792 458 m/s. Their velocity c in a medium is lower than c0, whilst their frequency v remains unchanged the ratio n = c0/c > 1 is the refractive index of the medium. The wavelength A is linked to the frequency v by... 

In this section, we are concerned with the canonical equations of the radiation field. We consider the fact that the electromagnetic wave is a transverse wave, and convert it into the form of Hamilton kinetic equations which are independent of the transformation parameter. In this process we will reach the conclusion that the radiation field is an ensemble of harmonic oscillators. During this process we will stress the concepts of vector potential and scalar potential. The equations of an electromagnetic wave in the vacuum are summarized as follows ... 

---