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Uspekhi Fizicheskih Nauk

Induced radiative processes in quantum and classical theories

Igor Viktorovich Tyutin, Igor I Sobel'man

Published Jan 1, 1963• 8 citations
Publisher
DOI
10.3367/ufnr.0079.196304b.0595

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INDUCED RADIATIVE PROCESSES IN QUANTUM AND CLASSICAL THEORIES

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It is pointed out that induced radiation effects cannot be purely quantum in nature and that they must be present in the classical theory of radiation processes. The classical theory is usually built on the example of the harmonic oscillator. Several effects arising from the interaction of the oscillators with the field disappear when harmonic oscillators are considered. This is particularly true when one is concerned with radiation processes induced by the field. In addition, the interaction between the field and the radiation of nonlinear oscillators (their frequencies depend on the energy) was not previously considered from the standpoint of the classical theory. Because of these reasons and because of the interest in the problem of quantum generators the question of the role of induced radiation in classicai theory was examined. The theory is described, and some specific properties of the classical system are contrasted with those of the quantum system. The description includes a discussion of spontaneous radiation processes and both harmonic and anharmonic oscillators are considered. The limiting transition from quantum to classical theory is discussed, and a detailed comparison of the two more » theories is made. An ensemble of oscillators distributed in energy is discussed in the classical theory. It is shown, for certaln determined conditions, that classical systems do not absorb but rather enhance incident radiation. (TTT) « less

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Introduction

Guang S. He

This chapter describes the formation, development, and major subjects of nonlinear optics and photonics. The semiclassical theory treats the light as a classical electromagnetic field governed by Maxwell equations, while the optical medium is a molecular system governed by quantum mechanics; the key parameters for this theory are various-order nonlinear susceptibilities. The quantum theory of radiation treats light as an ensemble of photons and the medium as a molecular system, both of which are described by quantum mechanics, and the key aspect is the concept of the so-called intermediate state represented by a virtual energy state level. The semiclassical theory gives a concise quantitative description of various nonlinear multi-wave mixing effects as well as those nonlinear processes related to the induced refractive-index changes. In contrast, the quantum theory of radiation can provide a conceptual interpretation for almost all known nonlinear optical effects and phenomena.

Oxford University Press eBooks•Oct 30, 2014•0 citations
It is pointed out that induced radiation effects cannot be purely quantum in nature and that they must be present in the classical theory of radiation processes. The classical theory is usually built on the example of the harmonic oscillator. Several effects arising from the interaction of the oscillators with the field disappear when harmonic oscillators are considered. This is particularly true when one is concerned with radiation processes induced by the field. In addition, the interaction between the field and the radiation of nonlinear oscillators (their frequencies depend on the energy) was not previously considered from the standpoint of the classical theory. Because of these reasons and because of the interest in the problem of quantum generators the question of the role of induced radiation in classicai theory was examined. The theory is described, and some specific properties of the classical system are contrasted with those of the quantum system. The description includes a discussion of spontaneous radiation processes and both harmonic and anharmonic oscillators are considered. The limiting transition from quantum to classical theory is discussed, and a detailed comparison of the two more » theories is made. An ensemble of oscillators distributed in energy is discussed in the classical theory. It is shown, for certaln determined conditions, that classical systems do not absorb but rather enhance incident radiation. (TTT) « less
A classical model for the interaction of molecular systems with infrared radiation is presented. It differs from the usual ’’semiclassical theory of radiation and matter’’ in that the molecular system is treated by classical rather than quantum mechanics, and the radiation field is described, as in Jaynes’ neoclassical theory, as classical (mechanical) harmonic oscillators rather than as a classical field (i.e., via Maxwell’s equations). The classical Hamiltonian for the composite system—molecules, radiation, and their interaction—is thus that of a completely mechanical system, and its classical dynamics is determined by computing the classical trajectories of the system. Quantum mechanical interference and tunneling effects can be built into the description within the framework of the classical S-matrix theory. Even within the strictly classical limit of the model, it is shown that all dynamical effects in the interaction of radiation and matter are obtained; in the perturbative limit, for example, it is shown that absorption and induced emission, and even spontaneous emission, which is often difficult to obtain in other classical or semiclassical models, appear in a completely straightforward manner.
This chapter describes the formation, development, and major subjects of nonlinear optics and photonics. The semiclassical theory treats the light as a classical electromagnetic field governed by Maxwell equations, while the optical medium is a molecular system governed by quantum mechanics; the key parameters for this theory are various-order nonlinear susceptibilities. The quantum theory of radiation treats light as an ensemble of photons and the medium as a molecular system, both of which are described by quantum mechanics, and the key aspect is the concept of the so-called intermediate state represented by a virtual energy state level. The semiclassical theory gives a concise quantitative description of various nonlinear multi-wave mixing effects as well as those nonlinear processes related to the induced refractive-index changes. In contrast, the quantum theory of radiation can provide a conceptual interpretation for almost all known nonlinear optical effects and phenomena.