Electromagnetic wave description

We may subsume all of the complexity of the full electromagnetic wave description of the Gaussian beam and its coupling to various elements of the resonator into two phenomenological constants the mutual inductances M, and M2 of Fig. 6. This procedure is equivalent to that used to model variable iris coupling into a waveguide cavity, for example. 

This model was later expanded upon by Lifshitz [33], who cast the problem of dispersive forces in terms of the generation of an electromagnetic wave by an instantaneous dipole in one material being absorbed by a neighboring material. In effect, Lifshitz gave the theory of van der Waals interactions an atomic basis. A detailed description of the Lifshitz model is given by Krupp [34]. 

James Clerk Maxwell predicted the existence of electromagnetic waves in 1864 and developed the classical sine (or cosine) wave description of the perpendicular electric and magnetic components of these waves. The existence of these waves was demonstrated by Heinrich Hertz 3 years later. 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

The relations derived up to this point are not sufficient to solve the problem of the dispersion of the optical branch for small k values. The retardation effect must also be taken into account. Because of the finite velocity of electromagnetic waves, the forces at a certain point of time and space in a crystal are determined by the states of the whole crystal at earlier times. A precise description of the dispersion effect therefore requires the introduction of Maxwell s equations. With a harmonic ansatz for P and P which is analogous to Eq. (II.15) they lead to the relation... 

The general description of electromagnetic waves is based on Maxwell s equations. For applications in optics, as that is important here, they reduce to the special case of charge- and current-free media. A subset of the solutions of the Maxwell equations can be assumed to be a harmonic wave of the form ... 

Equation (1.5) establishes a bridge between a description of fight as an (electromagnetic) wave of frequency v and as a beam of -q energy particles. If phenomena related to time averages, such as diffraction and interference, can be easily interpreted in terms of waves, other phenomena, involving a one-to-one relation such as the photoelectric and the Compton effects, require a description based on corpuscular attributes. This wave-particle duality reflects the use of one or the other description depending on the experiment performed, while no experiment exists which exhibits both aspects of the duality simultaneously. 

All the considerations that follow are only valid for radiation that is stimulated thermally. Radiation is released from all bodies and is dependent on their material properties and temperature. This is known as heat or thermal radiation. Two theories are available for the description of the emission, transfer and absorption of radiative energy the classical theory of electromagnetic waves and the quantum theory of photons. These theories are not exclusive of each other but instead supplement each other by the fact that each describes individual aspects of thermal radiation very well. 

The fractional derivative technique is used for the description of diverse physical phenomena (e.g., Refs. 208-215). Apparently, Blumen et al. [189] were the first to use fractal concepts in the analysis of anomalous relaxation. The same problem was treated in Refs. 190,194,200-203, again using the fractional derivative approach. An excellent review of the use of fractional derivative operators for the analysis of various physical phenomena can be found in Ref. 208. Yet, however, there seems to be little understanding of the relationship between the fractional derivative operator and/or differential equations derived therefrom (which are used for the description of various transport phenomena, such as transport of a quantum particle through a potential barrier in fractal structures, or transmission of electromagnetic waves through a medium with a fractal-like profile of dielectric permittivity, etc.), and the fractal dimension of a medium. 

Molecular nonlinear optics is the description of the change of the molecular optical properties by the presence of an intense light field. Since light either can be considered a classical electromagnetic wave or as a stream of photons, we may describe the interaction between light and matter in two apparently different ways, and we will start by considering how linear and nonlinear optical phenomena can be described in these two frameworks. 

It is well known that the polarization measurements play an important role in optics and spectroscopy [87]. The description usually given of the polarization is a classical one, defining the polarization as a measure of transversal anisotrophy of the plane electromagnetic waves [57]. It is based on the fact that the field strengths (11) have only two symmetric spatial components. At the same time, these complex components may have different magnitudes and phases. The quantitative description of polarization is provided by the so-called polarization matrix with the elements [14,57]... 

The next field of applications of elementary catastrophe theory are optical and quantum diffraction phenomena. In the description of short wave phenomena, such as propagation of electromagnetic waves, water waves, collisions of atoms and molecules or molecular photodissociation, a number of physical quantities occurring in a theoretical formulation of the phenomenon may be represented, using the principle of superposition, by the integral... 

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