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Physical Review A

Quantum theory of amplified total internal reflection due to evanescent-mode coupling

Chang-Woo Lee, Kyungbum Kim, Jaewoo Noh, Wonho Jhe

Published Oct 13, 2000• 9 citations
Publisher

Abstract

We present a quantum theory of the amplification of light undergoing a total internal reflection. We show that the light amplification is due to the stimulated emission of evanescent-mode photon from the active region of the interface. Our theoretical results are in good agreement with experimental observations and provide deeper understanding of the quantum-mechanical characteristics of the evanescent wave. A corresponding triplet-mode laser theory is also presented.

DOI
10.1103/physreva.62.053805

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We present a quantum theory of the amplification of light undergoing a total internal reflection. We show that the light amplification is due to the stimulated emission of evanescent-mode photon from the active region of the interface. Our theoretical results are in good agreement with experimental observations and provide deeper understanding of the quantum-mechanical characteristics of the evanescent wave. A corresponding triplet-mode laser theory is also presented.
An exact analogy between wave mechanics in quantum theory and the scalar wave treatment of optics emerges from the marriage of Newtonian formulation of geometrical optics [1] and the ``formal quantum theory of light rays'' [2]. Here the incidence of a ray of light on the interface between two media is treated as the incidence of a wavefunction on a potential barrier. This leads to the coefficient of reflection identical to Fresnel's formula for s-polarised light [3], although there is no concept of the polarisation of light in this model. In the present work, we apply this model to the total internal reflection of light and evanescent waves. We also deduce a one-to-one correspondence between the transmission coefficient in wave mechanics and frustrated total internal reflection for all angles of incidence. Further, we demonstrate that this model can also be used to derive the Goos-Hänchen shift for s-polarised light. This work augments the discussion on these topics found in the standard texts in optics [4].
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.
The reflection of metastable argon atoms from evanescent waves produced by total internal reflection and surface-plasmon excitation is investigated. We study the departure from ideal specular reflection by comparing our experimental results with a Monte Carlo simulation of the reflection process. The observed broadening of the reflection beam was found to be caused predominantly by fluctuations of the diple force. We show that the surface plasmon produces significant enhancement of the evanescent-wave intensity without degrading the quality of reflection. In addition, the number of spontaneous emissions occurring during the reflection process was investigated by comparing the reflectivity of evanescent-wave mirrors based on open and closed transitions in argon. An open-transition mirror selectively reflects atoms which do not undergo spontaneous emission. For a large detuning, the average number of spontaneous emissions for reflected atoms was 0.11.