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Soviet Physics Uspekhi

Light absorption by a dipole

Henryk Paul, R Fischer

Published Oct 31, 1983• 38 citations
Publisher

Abstract

In semiclassical radiation theory, the electric dipole moment induced on an atom by a strong incident field, absorbs much more energy, per sec, than is flowing through its geometrical cross section. This means, the atom has the capability to suck electromagnetic energy from a spatial region that is by far larger than its own volume. An intuitive understanding of this effect is provided by studying, in the framework of classical electrodynamics, the energy flow in the total field made up by superposition of the incident wave and the field that is generated by the dipole also in the absorptive case.

DOI
10.1070/pu1983v026n10abeh004523

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In semiclassical radiation theory, the electric dipole moment induced on an atom by a strong incident field, absorbs much more energy, per sec, than is flowing through its geometrical cross section. This means, the atom has the capability to suck electromagnetic energy from a spatial region that is by far larger than its own volume. An intuitive understanding of this effect is provided by studying, in the framework of classical electrodynamics, the energy flow in the total field made up by superposition of the incident wave and the field that is generated by the dipole also in the absorptive case.
Light absorption Whereas receiving radio waves is a macroscopic process and hence belongs to the area of classical electrodynamics – in a macroscopic antenna an electric voltage is induced whereby a large number of electrons follow the electric field strength of the incident wave, in a kind of collective motion – the detection of light, so far as the elementary process is concerned, takes place in microscopic type objects such as atoms and molecules. As a consequence, the response of an optical detector is determined by the microstructure of matter. In particular, it is impossible – due to the enormously high frequency of light (in the region of 10 15 Hz) – to measure the electric field strength. What is in fact detectable is the energy transfer from the radiation field to the atomic receiver, and this allows us to draw conclusions about the (instantaneous) intensity of light. We might ask what we can say about the above-mentioned absorption process from an experimentalist's point of view. Among the basic experiences that provide an insight into the structure of the micro-cosmos is the resonance character of the interaction between light and an atomic system. The atomic system, when hit by light, behaves like a resonator with certain resonance frequencies; i.e. it becomes excited (takes up energy) only when the light frequency coincides with a value that is characteristic for the particular atom. Hence, an incident light wave with an initial broadband frequency spectrum that has passed through a gas exhibits in its spectrum dark zones, the so-called absorption lines.
The classical theory of the interaction of light with the electron clouds of atoms and molecules will be discussed in this chapter. The discussion will begin with the interaction of a steady electric field with a collection of point charges, leading to the development of terms describing the electric dipole and quadrupole moments. The classical Lorentz model is then introduced to describe interaction of an oscillating electric field with the electron cloud of an atom, and the concepts of absorption and emission are introduced. The propagation of a light wave through a medium with electric dipoles is then discussed. Finally, the classical theory of radiation from an oscillating dipole is discussed.
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.
Within the framework of quantization of the macroscopic electromagnetic field, equations of motion and an effective Hamiltonian for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual- and real-photon exchange in the energy transfer between the atoms. In particular, it is shown that for weak atom-field interaction there is a time window, where the energy transfer follows a rate regime of the type obtained by ordinary second-order perturbation theory. Finally, it is shown that the resonant dipole-dipole interaction can change the singlet line of the emitted light to a doublet spectrum for weak atom-field interaction and the doublet spectrum to a triplet spectrum for strong atom-field interaction.
Abstract Optical gain can be regarded as the growth of an electromagnetic wave propagating through a dielectric as described by Maxwell’s equations, with electric polarisation due to dipoles induced by the field of the wave in classical atomic oscillators. The real and imaginary parts of the complex susceptibility give the amplitude gain and refractive index change respectively. Over time the phase relation between oscillation of individual dipoles is lost by collisions; this loss of coherence causes the optical response of the ensemble to be broadened in energy or wavelength. The response is also broadened by gradual energy loss (damping) causing a reduction in the amplitude of the oscillating field. These effects are characterised by time constants T22 and T1 respectively, which combine to produce homogeneous broadening with Lorentzian lineshape. Absorption by an atomic ensemble is expressed as an optical cross section of each atom.
We introduce quantum optical dipole radiation fields defined in terms of photon creation and annihilation operators.These fields are identified through their spatial dependence, as the components of the total fields that survive infinitely far from the dipole source.We use these radiation fields to perturbatively evaluate the electromagnetic radiated energy-flux of the excited dipole.Our results indicate that the standard interpretation of a bare atom surrounded by a localised virtual photon cloud, is difficult to sustain, because the radiated energy-flux surviving infinitely far from the source contains virtual contributions.It follows that there is a clear distinction to be made between a radiative photon defined in terms of the radiation fields and a real photon, whose identification depends on whether or not a given process conserves the free energy.This free energy is represented by the difference between the total dipole-field Hamiltonian and its interaction component.