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Optica Acta International Journal of Optics

The Role of Interference Effects in the Amplification of Light by Stimulated Emission

Alan V. Durrant

Published May 1, 1981• 0 citations
Publisher

Abstract

The mechanisms behind the amplification of light by stimulated emission are investigated using a semiclassical approach. The theory is developed in the plane wave mode picture so as to follow closely the correspondence with the usual quantized field treatment. It is shown that the interference between stimulating and stimulated fields is an essential process for producing the well-known first-order effects, and that interference between stimulated emission fields from different atoms in the sample determines the spatial distribution of the amplification when this is measured locally using a light detector without mode discrimination.

DOI
10.1080/713820607

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The mechanisms behind the amplification of light by stimulated emission are investigated using a semiclassical approach. The theory is developed in the plane wave mode picture so as to follow closely the correspondence with the usual quantized field treatment. It is shown that the interference between stimulating and stimulated fields is an essential process for producing the well-known first-order effects, and that interference between stimulated emission fields from different atoms in the sample determines the spatial distribution of the amplification when this is measured locally using a light detector without mode discrimination.
An investigation is made of the wave problem of the stimulated scattering of light in a pump beam comprising a plane wave and a small (in terms of energy) admixture of fluctuating distortions. The existence of interference maxima and minima in the pump wave causes an appreciable (up to twofold) enhancement of the gain of the scattered wave, the form of which reproduces that of the pump field. This effect is associated with the previously observed reversal of the wavefront in the stimulated scattering of light.
Usually it is assumed that the stimulated emission appears as a consequence of the Bose—Einstein statistics of photons and that to observe this effect at least two excitations have to be initially present in the atom—field system. That is, both the atom and the electromagnetic field have to be excited. In this paper we show that stimulated emission can appear exclusively as a consequence of quantum interference in a system with just a single excitation. Specifically, we consider a single two-level atom which is initially in its lower energy state and it interacts with a single-photon multi-mode wave packet. We show that for a proper choice of the photon-wave packet the atom can exhibit stimulated emission.
The well-known photon correlations of thermal light are now understood to result from the random superposition of independently emitted photons from spontaneous emission. Through random interference the number of photons evolves as a Bose-Einstein distribution rather than the Poisson distribution as one might expect for independent emissions of classical particles. By identifying terms in the density-matrix (\ensuremath{\rho}) equation for a linear amplifier, those terms giving rise to spontaneous emission were earlier distinguished from those causing amplification and absorption. We investigate the role of interference in the evolution of the photon statistics by further identifying terms in the equation for \ensuremath{\rho}${\ifmmode \dot{}\else \.{}\fi{}}_{n}$ solely responsible for quantum interference phenomena. The effects of this random interference on the photon factorial moments are quantified, even for those cases where the final field statistics are not Bose-Einstein. From our analysis we conclude that stimulated emission should be viewed as analogous to time-reversed absorption, rather than either a cascade process or pure constructive interference.
The coherence and directional properties of stimulated and spontaneous emission can be understood without a knowledge of quantum electrodynamics. This paper presents a semiclassical description of the interaction between a free atom and a weak optical field under conditions of either a stimulated emission or a stimulated absorption resonance. It is shown that, under certain conditions, the stimulated or spontaneous radiation fields emitted from a sample of atoms will propagate in the same direction as the incident beam, will be coherent with the incident beam, and will have the correct phase to provide amplification or attenuation.
Recently, the question of the origin of correlations in thermal light has again been debated. The alternative viewpoints suggest that (i) stimulated emission causes the correlations implied by Bose-Einstein statistics and exemplified by the Hanbury Brown-Twiss effect, or (ii) stimulated emission coherently amplifies any initial field, with no change in the nature of photon statistics, apart from the addition of, and interference with, spontaneous-emission noise. It is shown that two essentially different physical models have been considered previously, with many results being only approximate. For these models we obtain the evolution of the photon statistics by deriving exactly the generating function for the diagonal elements of the field density matrix and the quantum characteristic function. The source of Bose-Einstein correlations is seen to be merely the interference in the superposition of random independent fields from a chaotic source, spontaneous emission being one example. Extending the investigation to a nonlinear model, we show that, although there is no longer coherent amplification, it is still not correct to infer that this interaction, which produces the amplification, also leads to Bose-Einstein statistics.
Abstract In terms of quantum interference we demonstrate the physical mechanisms which lead to light amplification without population inversion. The similarities and differences between the two model schemes, namely, A and V-type, are emphasized. A coherent radiation field, on one hand, which drives one of the lasing levels, yields the quantum mechanical two paths via Autler-Townes splittings. On the other hand, the spontaneous emission in this driving transition plays a key role in the asymmetries between the absorption and the stimulated emission in the lasing transition.