Polarization of electromagnetic waves

As is known in quantum field theory, there are four polarizations of a photon [31]. These are the x, v, z, and t polarizations, where x, y, z, and t refer to the four dimensions in a 4-space. Thus—at least in theory—there must also be four polarizations of electromagnetic waves, even though not all these waves are yet experimentally known. 

This chapter deals with basic considerations about absorption and emission of electromagnetic waves interacting with matter. Especially emphasized are those aspects that are important for the spectroscopy of gaseous media. The discussion starts with thermal radiation fields and the concept of cavity modes in order to elucidate differences and connections between spontaneous and induced emission and absorption. This leads to the definition of the Einstein coefficients and their mutual relations. The next section explains some definitions used in photometry such as radiation power, intensity, spectral power density and polarization of electromagnetic waves. 

Figure 6.2 Polarization of electromagnetic wave beams (a) completely polarized beam, (b) partly polarized beam, (c) natural unpolarized beam.

Circular polarization of electromagnetic radiation is a polarization such that the tip of E, at a fixed point in space, describes a circle as time progresses. E, at one point in time, describes a helix along the direction of wave propagation k. The magnitude of the electric field vector is constant as it rotates. Circular polarization is a limiting case of elliptical polarization. The other special case is the easier-to-understand linear polarization. Circular (and elliptical) polarization is possible because the propagating E and El fields... 

Light consists of electromagnetic waves whose vibrations are transverse to the propagation direction. Such a wave package contains beams vibrating randomly in different manners. If the vibrations, however, exhibit some spatial preference then the light beam is said to be polarized. 

In view of the experimental difficulties a theory for radiation properties is desirable. The classical theory of electromagnetic waves from J.C. Maxwell (1864), links the emissivity e x with the so-called optical constants of the material, the refractive index n and the extinction coefficient k, that can be combined into a complex refractive index n = n — ik. The optical constants depend on the temperature, the wavelength and electrical properties, in particular the electrical resistivity re of the material. In addition, the theory delivers, in the form of Fresnel s equations, an explicit dependence of the emissivity on the polar angle / , whilst no dependence on the circumferential angle ip appears, as isotropy has been assumed. 

Figure 25-4 Light from a lamp or from the sun consists of electromagnetic waves that vibrate in all directions perpendicular to the direction of travel. Polarizing filters absorb all waves except those that vibrate in a single plane. The third polarizing filter, with a plane of polarization at right angles to the first, absorbs the polarized light completely.

In classical terms, radiation is represented by an electromagnetic wave. The polarization of plane-wave radiation is defined by the way the oscillating electric field evolves in space, in a plane perpendicular to the direction of propagation. The most general polarization state is called elliptical polarization [23], but for luminescence applications the subset of linear polarization states usually suffices. In these cases the electric field vector oscillates along a well defined direction in a plane perpendicular to the direction of propagation. This direction is the polarization direction, and radiation with this characteristic is said to be linearly polarized. 

Conversion of electromagnetic wave (EW) polarization provides an efficient and powerful method for diagnostics of media a nd s tructures with reduced symmetry (e.g. anysotropic crystals, media with natural and artificial gyrotropy, periodic structures, solid-state surfaces and thin films). On the other hand, such media and structures can be used as polarization converters. The conversion of the polarization in surface layers and thin films is usually small [1,2] and achromatic because in this case the region of interaction of the EW with the polarization active medium is small and the interaction itself is non-resonant. However, the effect may increase substantially (resonantly) and the polarization converted radiation becomes colored when the external EW excites eigen-oscillations on optically active surface or in an optically active film. For example, under the non-uniform cyclotron resonance excitation in two-dimensional (2D) electron system, high conversion efficiency can be reached [3]. 

From Maxwell s theory of electromagnetic waves it follows that the relative permittivity of a material is equal to the square of its refractive index measured at the same frequency. Refractive index given by Table 1.2 is measured at the frequency of the D line of sodium. Thus it gives the proportion of (electronic) polarizability still effective at very high frequencies (optical frequencies) compared with polarizability at very low frequencies given by the dielectric constant. It can be seen from Table 1.2 that the dielectric constant is equal to the square of the refractive index for apolar molecules whereas for polar molecules the difference is mainly because of the permanent dipole. In the following discussion the Clausius-Mossoti equation will be used to define supplementary terms justifying the difference between the dielectric constant and the square of the refractive index (Eq. (29) The Debye model). 

Plane-polarized light consists of electromagnetic waves with their electric and magnetic fields oscillating in the same direction. 

Let linearly polarized, plane electromagnetic wave of amplitude Eq is incident on a free electron, Fig. 5.3. The equation of oscillatory motion of the electron about the centre of coordinate is ... 

According to Frank and Tamm (1937) in this case the medium becomes polarized and the polarization ceases via the emission of electromagnetic waves. The energy loss via Cherenkov radiation is... 

Antennas create a state of electromagnetic polarization generally described as linear, circular or elliptical. Figure 13.4(a) depicts a linear polarized electric held (vertical polarization in this case). This would result from one of the dipoles shown in Fig. 13.1(c). The polarization of the wave is related to the orientation of the antenna wire. The electric held in Fig. 13.4(a) oscillates up and down at the angular frequency co. 

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