Electromagnetic theory of radiation

The magnitude of this pressure cannot be calculated by thermodynamical methods. From Maxwell s electromagnetic theory of radiation, however, it follows that the pressure exerted by radiation (force per unit area) is given by... 

This law was found 1879 by J. Stefan10 as a result of many experiments and was derived in 1884 by L. Boltzmann11 from the electromagnetic theory of radiation using the second law of thermodynamics. It contains an universal constant, known as the Stefan-Boltzmann constant a, which has a value of... 

In the following sections we will look at the radiation properties of real bodies, which, with respect to the directional dependence and the spectral distribution of the radiated energy, are vastly different from the properties of the black body. In order to record these deviations the emissivity of a real radiator is defined. Kirch-hoff s law links the emissivity with the absorptivity and suggests the introduction of a semi-ideal radiator, the diffuse radiating grey body, that is frequently used as an approximation in radiative transfer calculations. In the treatment of the emissivities of real radiators we will use the results from the classical electromagnetic theory of radiation. In the last section the properties of transparent bodies, (e.g. glass) will be dealt with. 

First comes the question of the crude charge distribution within the molecule, which largely determines the nature of its interaction with radiation. Then there comes the quantum theory of molecular emission and absorption, and finally the electromagnetic theory of radiation itself. 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

In addition to describing the conformation of the hydrocarbon chains for amphiphilic molecules at the A/W interface, external reflectance infrared spectroscopy is also capable of describing the orientation of the acyl chains in these monolayers as a function of the monolayer surface pressure. The analysis of the orientation distribution for an infrared dipole moment at the A/W interface proceeds based on classical electromagnetic theory of stratified layers (2). In particular, when parallel polarized radiation interacts with the A/W interface, the resultant standing electric field has contributions from both the z component of the p-polarized radiation normal to the interface, as well as the x component of the p-polarized radiation in the plane of the interface. The E field distribution for these two... 

This is reminiscent of Planck s formula for the energy of a photon. It comes as no surprise then that the quantum theory of radiation has the structure of an assembly of oscillators, with each oscillator representing a mode of electromagnetic waves of a specified frequency. 

The Rayleigh-Jeans picture of the radiation field as an ensemble of different modes of vibration confined to an enclosure was applied to the blackbody problem in Chapter 1. The quantum theory of radiation develops this correspondence more explicitly, identifying each mode of the electromagnetic field with an abstract harmonic oscillator of frequency coa- The Hamiltonian for the entire radiation field can be written... 

Some fundamental concepts pertaining to our subject were discussed in earlier chapters. The necessary concepts from electromagnetic theory and radiation-matter interaction were discussed in Chapter 3. A simple framework suitable for treating linear spectroscopy phenomena was described in Sections 9.2 and 9.3. A prototype model for many problems in optical spectroscopy involves two electronic states, ground and excited, and at least two continuous manifolds of states associated with the radiative and nonradiative environments. Such models were discussed in Sections 9.3 and 10.5.2. 

In this chapter we have reviewed some results concerning the quantum multipole radiation. Although the representation of quantum electromagnetic radiation in terms of spherical waves of photons known since the first edition in 1936 of the famous book by Heitler on quantum theory of radiation [2], where this subject is discussed in the Appendix, this representation is not a widespread one. The spherical waves of photons are considered in very few advanced monographs on quantum optics [26]. The brilliant encyclopedic monographs [14,15] just touch on the subject. 

Without going beyond thermodynamics and the electromagnetic theory of light, we can deduce two laws regarding the way in which black body radiation (or, as it is also called, cavity radiation) depends on the temperature. Stefan s law (1879) states that the total emitted radiation is proportional to the fourth power of the temperature of the radiator the hotter the body, the more it radiates. Proceeding a step further, W. Wien found the displacement law (1893) which bears his name, and which states that the spectral distribution of the energy density is given by an equation of the form... 

What are the limitations of classical theories, such as electromagnetics, optics, and thermodynamics, for thermal radiation and what fact originally prompted the modern theory of radiation State briefly the foundations of the modem theory. 

Powerful as the theory of photons has proved itself, and deeply as the statistical method permits us to penetrate into the nature of radiation, there are aspects of the subject which can only be understood in terms of the electrical theory of matter and of the electromagnetic theory of light. The introduction of the electrical theme cannot be much longer deferred. 

Einstein coefficients Coefficients used in the quantum theory of radiation, related to the probability of a transition occurring between the ground state and an excited state (or vice versa) in the processes of induced emission and spontaneous emission. For an atom exposed to electromagnetic radiation, the rate of absorption is given by... 

In the quantum theory of radiation [93], all electromagnetic radiation are considered to be beams of particles. As stated above, they are called photmis. Each photmi has an energy E that is defined by the Planck relationship,... 

T. Inoue, H. Hori, in Quantum Theory of Radiation in Optical Near Field Based on Quantization of Evanescent Electromagnetic Waves Using Detector Mode, ed. by M. Ohtsu. Progress in Nano- Electro-Optics IV (Springer, Berlin 2005), pp. 127-199... 

The Poynting vector has a dual role for it can be shown that the electromagnetic radiation fields transport momentum as well as energy, and tliat the momentum density is given by R/c. This relationship is most easily derived by making use of the idea tliat radiation consists of photons of energy hu whose momentum in vacuo is tioi/c, which follows from the quantum theory of radiation (Problem 2.7). 

In his doctoral dissertation de Broglie postulated that particles such as the electron, proton, etc. should also possess wave-like properties in exact analogy with the particle-like properties exhibited by electromagnetic waves in the quantum theory of radiation. For motion in one dimension he postulated that the momentum of the particle p and its kinetic energy E were related to the wavevector k and angular frequency w of the guiding wave, I, by the relations... 

---