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Acta Physica Sinica

THE NONLINEAR THEORY OF INTERACTION BETWEEN LIGHT AND MATTER DESCRIBED BY q-DEFOR- MED OSCILLATOR MODEL

Guangcan Yang, 广西师范学院物理系,南宁530001

Published Jan 1, 1994• 0 citations
Publisher

Abstract

The nonlinear theory of interaction between light and matter has been established by using q-oscillator as a model for the light field. The formal solution of Schr?di-ngar equation is obtained, and the first crder approximation of emission and absorption probability are acquired by perturbation theory. We also discussed the Rabi problem for resonance condition. When q→1, the theory reduces to the common linear theory.

DOI
10.7498/aps.43.521

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The nonlinear theory of interaction between light and matter has been established by using q-oscillator as a model for the light field. The formal solution of Schr?di-ngar equation is obtained, and the first crder approximation of emission and absorption probability are acquired by perturbation theory. We also discussed the Rabi problem for resonance condition. When q→1, the theory reduces to the common linear theory.
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A detectable nonlinear response between light and matter depends on one of two key ingredients: Either there is a resonance between the light wave and some natural oscillation mode of the material, or the light is sufficiently intense. In this chapter, the authors let the matter variables themselves play active roles and derive coupled nonlinear differential equations for the electric and matter fields. They outline the use of Schrodinger's equation to derive the Bloch equations, which describe the dynamics of the oscillators of matter and help to derive the Maxwell equation for the envelope of an almost monochromatic electromagnetic wave. The authors analyse the case of two distinct co- or counter-propagating waves interacting with a three-level medium where both waves excite separate quantum transitions sharing a common level. They also help to derive an effective two-level atom model that describes two-photon absorption and stimulated Raman scattering.
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.
A treatment of nonlinear optical phenomena beginning with a microscopically correct Hamiltonian containing the Bose operators of the light field and the Fermi operators for the optically active electrons in the medium is presented. Using techniques recently developed, a nonperturbative solution to the Schrodinger equation is possible. No linearization or semiclassical approximations are introduced. Two photon emission and absorption including both the degenerate and nondegenerate cases are considered. Parametric amplification and frequency conversion are investigated as examples of multiphoton processes. Atomic cooperation is shown to enhance the above phenomena. A formal treatment of a model illustrating super and subradiance is included.
Although the primarily phenomenological theory of absorption and refraction of light by matter, based on classical models as presented in Chapter 4, is very useful, it is incomplete and often inadequate. A more complete and accurate picture of electrodynamics is given by the theory of quantum optics, and that is the topic of this chapter. The models developed in this chapter are more detailed and therefore more complicated than the phenomenological models of Chapter 4. The most robust models, which are applied in Part II, are presented in this chapter. The quantum models accurately represent experimental data and allow extrapolation and interpolation of such data. Many practical computer based models concerning optical propagation are based on this theory. The theory of elastic scatter as presented in Chapter 4 is consistent with quantum optics and is not presented again. (However, inelastic scatter must address the quantum nature of the scattering medium.) Quantum optics is not completely covered in this chapter. Entire textbooks are devoted to this diverse and comprehensive topic covering optics (see Refs. 5.1–5.3). The emphasis of this book is on absorption and reflection spectroscopy. Now details of internal structure of the medium impacting light–matter interaction are examined. The classical oscillator model is upgraded by semiclassical radiation theory and a quantum oscillator model is developed. Semiclassical radiation theory is based on a quantized medium coupled to a classical field. It is often applied to laser theory, where near-line-center stimulated emission dominates. The quantum oscillator model again utilizes the quantized medium and classical field, but with more attention to detailed balance between absorption and emission. It satisfies causality and the fundamental symmetry relationships established in Chapter 2. These quantum optics models are more complete formalisms and provide solutions to the shortcomings of classical electrodynamics. Of particular interest to propagation in gaseous media is the line shape in the far wing. To achieve long path lengths, propagation near line center of a resonance must be avoided. Line shape models in quantum optics accurately represent much of the frequency and temperature dependence observed in experimental data.
We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model and, after full field quantization, we derive the Feynman rules from this theory.