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Canadian Journal of Physics

Collective excitation transfer effect in dielectric susceptibility

Haider R. Zaidi

Published Jul 15, 1977• 3 citations
Publisher

Abstract

The combined effect of two collective processes in the resonant dielectric susceptibility is investigated. The first is the coherent excitation transfer process, which gives rise to the Lorentz–Lorenz shift. The second is the many body shielding of the resonant interaction between the atoms. The combined treatment of these effects leads to a qualitatively different behaviour of the susceptibility of a high density gas. The frequency dependence of the susceptibility is obtained from the detailed numerical solution of the self-consistent equations. In the quasi-static limit, an analytical solution is also obtained. In this limit, the result depends upon two parameters: one proportional to the gas density, and the other proportional to the square root of it.

DOI
10.1139/p77-161

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The combined effect of two collective processes in the resonant dielectric susceptibility is investigated. The first is the coherent excitation transfer process, which gives rise to the Lorentz–Lorenz shift. The second is the many body shielding of the resonant interaction between the atoms. The combined treatment of these effects leads to a qualitatively different behaviour of the susceptibility of a high density gas. The frequency dependence of the susceptibility is obtained from the detailed numerical solution of the self-consistent equations. In the quasi-static limit, an analytical solution is also obtained. In this limit, the result depends upon two parameters: one proportional to the gas density, and the other proportional to the square root of it.
A theory is developed for the resonant dielectric susceptibility of a high density gas which consists of two level atoms interacting through the dipole–dipole potential. A many body collision model, which includes the binary as well as the shielding effects, is investigated. The linear response of the dielectric is given by a generalized transport equation. Self-consistent coupled equations are derived for the various collision operators, using the propagator techniques. In the two limiting cases, the results of the binary collision model and those of the shielded interaction model, respectively, are recovered. The equations are simplified by neglecting the nonresonant contributions. Finally, a solution is obtained in the resonance broadening approximation. The resulting expression for the dielectric susceptibility includes the two body collision as well as the many body shielding effects. In particular, it includes the important collective excitation transfer effects. The proposed many body collision model should be appropriate for the resonant, linear response of high density gases.
The resonance broadening of a transition between two excited states of a radiator in a high density gas is investigated. The important many body shielding contributions are included to all orders, and the two body correlations for the close collisions are approximately taken into account. Corrections to the line width and shift at moderately high densities are calculated. The results agree with the experimental data for krypton. The density dependence of the width parameter is examined at very high densities also. It is found that this parameter, after reaching a peak value, decreases with further increase in the density. Moreover, the square root dependence of the line widths on the density is not valid over any extended range of gas densities.
The properties of optically dense materials are influenced by interactions between elementary optical excitations (oscillators). Since such interactions are absent in the dilute limit, the resulting properties are unique to optically dense materials. While linear optical experiments can probe these effects, for example the Lorentz-Lorenz resonance shift, they are often more apparent in nonlinear experiments that are sensitive to coherence. Direct gap semiconductors are typically optically dense close to the fundamental gap and have been extensively studied using ultrafast coherent spectroscopy over the last ten years. However, their coherent optical properties are very complex because of many-body interactions among the extended excitations (electron-hole pairs or excitons). Dense atomic vapors have also been studied, but typically using frequency domain techniques. We present the results of using ultrafast techniques to study both semiconductors and dense atomic vapors. This reveals the similarities and differences of the two systems, yielding insight into the characteristics of each individually.
Intense light incident on a dense-gas--dielectric interface, from the dielectric side, is reflected because of the combined effect of the discontinuities in the index of refraction at the interface and at the transition region in the gas where the degree of atomic saturation changes abruptly. This latter discontinuity gives rise to a self-reflected wave. At low intensities this self-reflected wave is weak, the problem is linear, and the net reflected wave intensity taken as a function of frequency has a simple shape that should allow measurement of the hitherto undetected self-induced frequency shift in a collision-broadened gas at an absorption resonance. Calculations show that in the weak intensity regime, r'', the imaginary part of the reflection coefficient, is quasi-Lorentzian and shifted by an amount comparable to its width. At high light intensity r'' broadens, shifts, and distorts. The distortion, which nonuniformly modulates the Lorentzian shape, comes from an interference of the forward and self-reflected waves. In the wings of the resonance line the self-reflected wave can be neglected, and the shape of r'' although not distorted is shifted from where it would be if there were no local field correction.
A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.
The purpose of this work was to investigate coherence effects in the interaction of two counterpropagating electromagnetic waves with the atoms of a gas, in the case in which one of the waves is weak and frequency modulated, while the other is sufficiently intense to cause saturation. Solving the equations for the density matrix in first-order perturbation theory, the authors obtained in analytic form the real part of the susceptibility integrated over the atom's velocity, expressed in terms of the rate equation model (REM) predictions plus the coherence corrections. The relaxation constants of the levels involved in the transition were kept different in order to allow a wider range of applications of the results. Calculated line shapes related either to the frequency-modulated (FM) sideband or to the ordinary dispersion techniques are presented. The REM approximation and the coherence corrections are shown in detail for an optical line which is of interest for frequency standard investigations.