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Quantum theory of the dispersion of the laser light

Miroslav Pardy

Published Dec 16, 2018• 0 citations
Publisher

Abstract

We derive the index of refraction of light from quantum theory of atoms and from the Dirac equation with the plane wave.The result is the integral a part of the mainstream of the quantum optics.The article involves also discussion on the possibility to create the electron-positron pairs during the Čerenkov process with the adequate intex of refraction.

DOI
10.32370/2018_11_1

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We derive the index of refraction of light from quantum theory of atoms and from the Dirac equation with the plane wave.The result is the integral a part of the mainstream of the quantum optics.The article involves also discussion on the possibility to create the electron-positron pairs during the Čerenkov process with the adequate intex of refraction.
In this paper, the energy and momentum operator substitution method derived from the Schrödinger equation is used to list all possible light and matter wave equations, among which the first light wave equation and relativistic approximation equation are proposed for the first time. We expect that we will have some practical application value. The negative sign pairing of energy and momentum operators are important characteristics of this paper. Then the Klein–Gordon equation and Dirac equation are introduced. The process of deriving relativistic energy–momentum relationship by undetermined coefficient method and establishing Dirac equation are mainly introduced. Dirac’s idea of treating negative energy in relativity into positrons is also discussed. Finally, the four-dimensional space-time representation of relativistic wave equation is introduced, which is usually the main representation of quantum electrodynamics and quantum field theory.
Classical dispersion theory Many aspects of the interaction between radiation and matter can be described quite accurately by a classical theory in which the medium is represented by model atoms consisting of positive and negative parts bound by an attraction which depends linearly on their separation. Although quantum theory is necessary to calculate from first principles the magnitude of the parameters involved, in this chapter we shall show that many optical effects can be interpreted physically in terms of this model by the use of classical mechanics. In §13.5 we shall relax the restriction of linearity. Some of the quantum mechanical foundations will be discussed briefly in Chapter 14, but most are outside the scope of this book (see Yariv, 1989; Loudon, 1983). The term dispersion means the dependence of dielectric response (dielectric constant and refractive index) on frequency of the wave field. This will be the topic of the present section. Afterwards we shall see some of the applications of dielectric response to spatial effects. The classical atom Our classical picture of an atom consists of a massive positive nucleus surrounded by a light spherically-symmetrical cloud of electrons with an equal negative charge. We imagine the two as bound together by springs as in Fig. 13.1, so that in equilibrium the centres of mass and charge of the core and electron charge coincide. As a result the static atom has zero dipole moment.
We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a pro-cess similar to the anomalous Doppler effect: Photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions; it can reach up to $\ensuremath{\sim}101010{}^{\ensuremath{-}2}$ photons per pulse. Moreover, it is, in principle, possible to engineer the host medium so as to modify the effective group refractive index. In the presence of ``fast-light'' media, e.g., a with group index smaller than unity, a further $\ensuremath{\sim}101010\ifmmode\times\else\texttimes\fi{}$ enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments, would clearly identify the correlated emission of photon pairs.