Electromagnetic theory, plane waves

The oscillating dipole is a source of electromagnetic radiation of the same frequency, polarized in the direction of the oscillations. At large distances, the wave is spherical. According to the electromagnetic theory, the resulting electric vector at a point in the equatorial plane of the dipole is a>2/ r c2 times the moment of the dipole at time t — r /c. The amplitude of the spherically scattered wave at unit distance in the equatorial plane is therefore... 

Figure 2. The three fundamental wave types of an extended electromagnetic theory with nonzero electric field divergence in the vacuum, as demonstrated by the simple case of plane waves.

Furthermore, the only electromagnetic vector present in free space in the Maxwell-Heaviside theory is the plane wave [11-20] ... 

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 order to develop a Riemannian theory of classical electromagnetism, it is necessary [109] to consider a curve corresponding to a plane wave ... 

In Maxwell s theory, this dispersion of energy is considered to be negligible, and no damping occurs during the propagation of an electromagnetic wave. Let us consider the plane waves propagating in the z direction ... 

It is instructive to pursue the interpretation of the calcite rhomb experiment beyond the simple Huyghenian construction to learn something about the polarization of the transmitted light. The electromagnetic theory of light requires that the electric vector shall be contained in the plane of the wave front. The ordinary disturbances vibrate perpendicular to a principal section. Also the extraordinary disturbance must vibrate in the principal section plane. 

In the macroscopic theory of electromagnetic waves [3], the evanescent wave (EW) arises from the requirement that the boundary conditions be satisfied at all points on the flat (ideal) interface between two materials of different optical properties that are uniform throughout the materials. The spatial functions in the exponents describing propagation of plane waves in each material are set equal... 

Having obtained expressions for the dielectric susceptibility and the dielectric response functions in terms of microscopic variables, we may proceed to express other observables in microscopic terms. Consider an electromagnetic mode whose electric component is described by a plane wave propagating in the x direction in an isotropic medium, and assume that the field is weak enough to make linear response theory valid. The field is given by... 

The intensity of a scattered wave at a distance r from its source is proportional to the square of the polarisability of the particle and inversely proportional to r1. According to electromagnetic theory, the ratio of the scattered intensity (I) to the incident intensity (/0) in the plane normal to the direction of polarisation... 

In electromagnetic theory the Faraday effect can be explained as follows. When the medium magnetization has non-zero projection on the wave vector ko of the incident radiation, two independent fundamental Maxwell equations solutions are circular polarized waves with different refractive indexes n+M n, respectively. At the output of the magnetic medium these waves gain phase shift and when added give Unearly polarized wave with rotated polarization plane. That is why Faraday effect is also called magnetic circular birefringence [26, 27]. 

The theory of reflection and transmission of an electromagnetic wave by a plane boundary was first derived by Fresnel. The geometry of specular reflection and transmission is depicted in Figure 1. The incident (i) plane wave consists of the parallel ( ) and perpendicular polarized ( ) electric field components E, and E j., respectively. The corresponding components of the reflected (r) and refracted (transmitted t) field components are denoted by Ej. E j, E, and Fresnel s equations relate the reflected and transmitted components to the corresponding incident components. 

L.W. Davis, Theory of electromagnetic beams, Phys. Rev. 19, 1177 (1979) A.J. Devaney, Quasi-plane waves and their use in radiation and scattering problems, Opt. Commun. 35, 1 (1980)... 

---