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Journal of Hunan Institute of Science and Technology

Study on the gain of light interacting with the dielectric

Yuexin Liu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Taking the atoms in dielectric as the harmonic oscillator,and building a model of light and dielectric in the circumstance of light radiation approximate with weak signal,the gain of light was solved with the method of quantum mechanics. When the frequency of light radiation is similar with the natural frequency of harmonic oscillator,the conclusion is gotten that if atoms’absorption coefficient k0,then the electromagnetic wave rises in accordance with the regularity of index,and the dielectric gives gain if k0,then the dielectric will absorb radiation.

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Taking the atoms in dielectric as the harmonic oscillator,and building a model of light and dielectric in the circumstance of light radiation approximate with weak signal,the gain of light was solved with the method of quantum mechanics. When the frequency of light radiation is similar with the natural frequency of harmonic oscillator,the conclusion is gotten that if atoms’absorption coefficient k0,then the electromagnetic wave rises in accordance with the regularity of index,and the dielectric gives gain if k0,then the dielectric will absorb radiation.
Abstract The present chapter deals with the macroscopic theory of light-matter interaction. By using the Maxwell’s equations, the wave equation is developed first for free space, and then for a dielectric, and a conductor. The relationship between refractive index and absorption coefficient is then established. The phase and group velocities of the EM wave are defined. The well-known damped harmonic oscillator model is then used to find expressions for real and imaginary parts of the susceptibility. At the end, the two-level atomic system is used to illustrate fundamental processes of light-matter interaction, namely, absorption, spontaneous, and stimulated emissions, and the rates of these processes in terms of Einstein’s A and B coefficients. Absorption, gain, and self-sustained oscillation in a medium with a Fabry–Perot resonator are discussed using the two-level atomic model.
In this work the electromagnetic field in a dielectric medium is quantized in a simple and straightforward way based on the classical expression for the energy density for the case of weak absorption. The quantized field leads to expressions for spontaneous and stimulated emission rates, and gain and absorption coefficients, for the general case of a dispersive dielectric host medium. Local field corrections, when they apply, arise in the same manner as in classical electromagnetic theory. The theory also leads to a radiative level shift dependent on the dispersion of the dielectric, and this shift may be interpreted as a van der Waals interaction between the guest atom and the atoms of the host medium.>
We treat the interaction between an electromagnetic radiation bath and a material system in the semi-classical picture: the radiation is treated according to the Maxwell equations, but the process of emission/absorption is described through the concept of a photon; on the other hand, the material system is modelled according to quantum mechanics, assuming a discrete two-level energy spectrum. This very simple model allows one to elaborate the elementary theory of the absorption/emission coefficients, both for the spontaneous and for the stimulated processes which will be described within the electric dipole approximation. Selection rules for allowed transitions are eventually obtained and the nature of high-order transition is briefly outlined. Finally, a qualitative description of the light amplification by stimulated emission of radiation is presented.
The electromagnetic field in a dispersive dielectric medium is quantized in a straightforward manner based on the classical expression for the field energy away from absorption resonances. Results for spontaneous and stimulated radiative rates, and absorption and gain coefficients, are obtained and compared with other expressions in the literature. Local field corrections, when they exist, are included. A level shift for an atom in a host dielectric medium is obtained and interpreted as the van der Waals interaction between that atom and its neighbours in the host medium.
Atoms and ions containing residual bound electrons do not quite resemble the simple harmonic oscillator model used so successfully in the classical theory of radiation. However, replacing the atoms or ions with sets of harmonic oscillators of a great number of discrete resonance frequencies and having various amplitudes, together with the results of classical radiation theory, go a long way toward a quantitative description of emission or absorption spectra. The set of resonance frequencies is obtained from measured or calculated energy levels using Ritz's combination principle. The amplitudes are associated with matrix elements of appropriate quantum mechanical operators between wave functions of the two energy eigenstates involved at a given frequency. In other words, quantities of the emitters, absorbers, or scatterers are described quantum-mechanically, whereas the electromagnetic field is treated classically. Such semi-classical description of matter-electromagnetic field interactions became unnecessary very early in the development of quantum theory. It will therefore not be discussed in any detail. Instead, we will begin immediately with the combined theory of matter and radiation (Heitler 1954, Dirac 1958, Loudon 1983). Quantum theory of particles and fields There are various ways to also quantize the electromagnetic fields (Cohen-Tannoudji, DuPont-Roc and Grynberg 1989), of which that performed on the combined Hamiltonian equations of motion for the field-matter system is followed here.
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.