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Soviet Journal of Quantum Electronics

Explosive absorption of radiation

А. Н. Ораевский, Игорь Евгеньевич Проценко

Published Nov 30, 1985• 2 citations
Publisher

Abstract

An analysis is made of the mechanism of absorption of electromagnetic radiation when the initial energy level of the absorbing transition is not the ground state. It is found that energy exchange in a system of absorbing levels results in complex absorption dynamics: the existence of a radiation intensity threshold, hysteresis effects, and pulsating conditions.

DOI
10.1070/qe1985v015n11abeh007969

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An analysis is made of the mechanism of absorption of electromagnetic radiation when the initial energy level of the absorbing transition is not the ground state. It is found that energy exchange in a system of absorbing levels results in complex absorption dynamics: the existence of a radiation intensity threshold, hysteresis effects, and pulsating conditions.
The absorbed/emitted radiation will be treated classically, as a monochromatic plane wave, whereas the atomic system that can absorb/emit such radiation will be described quantum-mechanically. However, no incident radiation beam is needed, and the atom “falls down” after a certain time interval to the ground state without any external reason. In the spontaneous emission processes the emitting atom can be thought of as a classical oscillating dipole, whose amplitude decreases due to the energy loss through the radiation. If an ensemble of identical atoms is considered and if, for simplicity, each atom emits radiation with the same spectral shape and full width at half maximum, it is impossible to ascribe a definite spectral component with intensity to a definite atom. In this case, such a broadening is identical for all atoms in the ensemble. On the microscopic scale, absorption of radiation is reduced to the transitions between pairs of energy levels of a discrete atomic spectrum.
In many practical cases a stationary system is perturbed in some way, inducing it to undergo transitions between the otherwise stationary states. Perhaps the best example concerns the radiative transitions of atomic electrons in which the disturbance of an external electromagnetic field causes the electrons to jump between energy levels, emitting or absorbing photons. Equation is a statement of the classical law of conservation of energy. The stimulated emission and absorption of radiation both have close classical analogues. If a simple harmonic oscillator is driven by a sinusoidal electromagnetic field it can gain or lose energy depending on phase angles. The existence of spontaneous emission implies that all excited states of electrical systems are unstable and will eventually decay to the ground state by photon emission. Quantum systems thus comply with the fundamental principle that physical systems tend to seek out their state of lowest energy and maximum entropy.
Introduction Until now, our discussion of the interaction between radiation and matter has concentrated only on the spectral aspects of radiation. The results could determine the wavelengths for absorption and emission or the selection rules for such transitions, but could not be used to determine the actual extent of emission or absorption. These too are important considerations which are needed to fully quantify radiative energy transfer. Unfortunately, none of the classical theories can predict the extent of emission from an excited medium, or even the extent of absorption. Although the discussion in Section 4.9 (on the propagation of electromagnetic waves through lossy media) touched briefly on the concept of attenuation by absorption, it failed to show the reasons for the spectral properties of the absorption or to accurately predict its extent. We will see later that the classical results are useful only as a benchmark against which the actual absorber is compared. The objective of this chapter is therefore to present an introduction to quantum mechanical processes that control the emission and absorption by microscopic systems consisting of atoms and molecules. The results will then be used to predict the extent of emission by media when excited by an external energy source and to evaluate the absorption of incident radiation. It is now well recognized that all emission or absorption processes are the result of transitions between quantum mechanical energy levels.
Radiative transitions When a system changes its energy as the result of the emission or the absorption of a photon, it is said to undergo radiative transition. There are three kinds of radiative transition. In the presence of an electromagnetic field the system can absorb a photon, so that its energy is raised to a higher level. If the system is initially in a state other than the ground state, it can emit a photon and so shed energy. This can happen without the presence of any external electromagnetic field, in which case a spontaneous emission is said to occur. On the other hand, if the excited system is placed in an electromagnetic field that varies in time with the appropriate frequency, the probability that it will emit a photon can be greatly enhanced. In this case the emission process is known as stimulated emission . Stimulated emission is the basis of maser and laser action, which we describe in this chapter. First, we construct a simple model that allows us to investigate how the internal structure of a quantum system changes as the result of a radiative transition. Although the model is very simple, it will allow us to understand the main features of the proper, more exact treatment. We shall deal mainly with absorption and stimulated emission, the two types of radiative transition where there is an external electromagnetic field.