Radiation, electromagnetic spontaneous emission

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

An important process has not been included in the analysis. It is the possibility of spontaneous emission. Were it not for such a process, in the absence of electromagnetic radiation a molecule in the excited state ro would be forced to remain there forever. Thus, in Einstein s analysis of this problem three competing processes were considered to be in equilibrium, leading to tbf expression... 

From Figure 7.10 it is seen that spontaneous emission according to the Planck theory of Black body radiation as well as Einstein s work starts to dominate above 10 Hz at 300K, this corresponds to the infrared range of the electromagnetic spectram. Note, that if the temperature increases the zero crossing point moves into the visual and UV range. 

The Bloch equations by themselves cannot describe spontaneous emission, because they contain the effect of the electromagnetic field on the molecule but not vice versa. To include the effect of the molecules on the radiation field within the semiclassical formalism that led to these equations we should supplement them by a description of the radiation field using the Maxwell equations in the presence of the molecular sources, as described in Appendix 3A (see Eq. (3.75). For our present purpose we can however make a shortcut. We know that one result of Eq. (3.75) is that an oscillating dipole emits radiation, so we can obtain the intensity of emitted radiation by calculating the expectation value P(Z) of the oscillating dipole induced in the system and evaluate the emission intensity (energy per unit time) from the classical formula... 

The subject of correlated or collective spontaneous emission by a system of a large number of atoms was first proposed by Dicke [1], who introduced the concept of superradiance that the influence on each atomic dipole of the electromagnetic field produced by the other atomic dipoles could, in certain circumstances, cause each atom to decay with an enhanced spontaneous emission rate. The shortening of the atomic lifetime resulting from the interaction between N atoms could involve an enhancement of the intensity of radiation up to N2. 

In addition to the spontaneous emission of excited molecules, fluorescence and phosphorescence (Section 2.1.1), the interaction of electromagnetic radiation with excited molecules gives rise to stimulated emission, the microscopic counterpart of (stimulated) absorption. Albert Einstein derived the existence of a close relationship between the rates of absorption and emission in 1917, before the advent of quantum mechanics (see Special Topic 2.1). 

Nuclei outside the belt of stability, as well as nuclei with more than 83 protons, tend to be unstable. The spontaneous emission by unstable nuclei of particles or electromagnetic radiation, or both, is known as radioactivity. The main types of radiation are a particles (or doubly charged helium nuclei, He " ) /3 particles (or electrons) y rays, which are very-short-wavelength (0.1 nm to 10 " nm) electromagnetic waves positron emission and electron capture. 

Inasmuch as a thoroughly satisfactory quantum-mechanical theory of systems containing radiation as well as matter has not yet been developed, we must base our discussion of the emission and absorption of radiation by atoms and molecules on an approximate method of treatment, drawing upon classical electromagnetic theory for aid. The most satisfactory treatment of this type is that of Dirac,1 which leads directly to the formulas for spontaneous emission as well as absorption and induced emission of radiation. Because of the complexity of this theory, however, we shall give a simpler one, in which only absorption and induced emission are treated, prefacing this by a general discussion of the Einstein coefficients of emission and absorption of radiation in order to show the relation that spontaneous emission bears to the other two phenomena. 

In 1900 Rayleigh introduced density of electromagnetic modes in the theory of equilibrium electromagnetic radiation [16]. In 1916 Einstein showed that the ratio of spontaneous to stimulated emission coefficients was /zta3/ji2c3. Then in 1927 Dirac [18] introduced the quantization of electromagnetic field and showed that for the Einstein relationship to be fulfilled the spontaneous emission rate should be proportional to the number of modes available for light quanta to be emitted. Later, in solid state theory concept of the density of modes was developed with respect to electrons and other elementary excitations and evolved towards a consistent density of states (DOS) inherent in every quantum particle of matter. The notion of local density of states was introduced in complex solids. 

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... 

R = Bp, where p is the density of electromagnetic radiation and Bis the Einstein B coefficient associated with absorption. The rate of induced emission is also given by Bp, with the coefficient B of induced emission being equal to the coefficient of absorption. The rate of spontaneous emission Is given by A, where A is the Einstein A coefficient of spontaneous emission. The A and B coefficients are related byA = 8nhv B/( , where h is the Planck constant, v is the frequency of electromagnetic radiation, and c is the speed of light. The coefficients were put forward by... 

The spontaneous emission of electromagnetic radiation from an excited molecule is a imimolecular process that follows first-order kinetics. Suppose a photoexcited molecule exhibits fluorescence as its only decay pathway. If there are No photoexcited molecules at time to, then at a subsequent time t the number of molecules still in the excited state (N) is given by... 

The book begins with a discussion of the fundamental definitions and concepts of classical spectroscopy, such as thermal radiation, induced and spontaneous emission, radiation power and intensity, transition probabilities, and the interaction of weak and strong electromagnetic (EM) fields with atoms. Since the coherence properties of lasers are important for several spectroscopic techniques, the basic definitions of coherent radiation fields are outlined and the description of coherently excited atomic levels is briefly discussed. 

The basic principle of semiconductor lasers [409-413] may be summarized as follows. When an electric current is sent in the forward direction through a p-n semiconductor diode, the electrons and holes can recombine within the p-n junction and may emit the recombination energy in the form of electromagnetic radiation (Fig. 5.69). The linewidth of this spontaneous emission amounts to several cm and the wavelength is determined by the energy difference between the energy levels of electrons and holes, which is essentially determined by the band gap. The spectral range of spontaneous emission can therefore be varied within wide limits (about 0.4-40 pm) by the proper selection of the semiconductor material and its composition in binary compounds (Fig. 5.70). 

When electromagnetic radiation and atomic or molecular systems interact, there are three distinct processes which are relevant to photochemistry absorption, stimulated emission and spontaneous emission. These were treated theoretically by Einstein and are shown diagramaticaUy for a system involving two states, 1 and 2, in Fig. 1.19. 

Fig. 1.19 The processes of absorption, spontaneous emission and stimulated emission observed upon interaction of electromagnetic radiation with atoms or molecules...

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