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Physical Review A

Frequency shifts of an electric-dipole transition near a partially reflecting surface

R. R. Chance, Alfred Prock, R. Silbey

Published Oct 1, 1975• 95 citations
Publisher

Abstract

The classical theory of dipole radiation is used to calculate the change in frequency of an electric-dipole-allowed transition due to the presence of a nearby reflecting surface. The result is compared to that for a perfect reflector.
DOI
10.1103/physreva.12.1448

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We discuss, from a classical as well as a quantum-mechanical point of view, the effect of the coupling of an excited two-level system with itself due to emission and absorption of electric-dipole radiation, the emitted radiation being reflected by a nearby mirror. Expressions familiar from resonance-scattering theory are found for the shift of the transition frequency and linewidth from their values in the absence of the mirror. This renormalization effect leads to spatial modulation in the transition frequency and width of the excited state due to its resonant interaction with itself via the radiation field reflected from the mirror. This formalism is applied to some recent experiments with monomolecular dye layers. The experimental values of the fluorescence lifetime are in good agreement with the theory for distances from 500 to 6000 \AA{}.
On the basis of a quantum microscopic approach we study the cooperative effects induced by the dipole-dipole interaction in an ensemble of pointlike impurity centers located near a charged perfectly conducting surface. We analyze the simultaneous influence of the modified spatial structure of field modes near the conductive surface and the electric field on the transition spectrum of an excited atom inside an ensemble and on the radiation trapping. We show that the electric field modifies the cooperative Lamb shift, as well as the character of sub- and super-radiant decay. We also demonstrate that electro-optical effects in the presence of a surface are essentially different in comparison with those in free space. The nonmonotonic behavior of electro-optical effects in the presence of a surface with increasing of the electric field has been shown.
In free space, the presence of an atom in its ground state near an excited atom undergoing an electric dipole transition, leads to a modification of the transition rate. This is shown to be modified further if the system of two atoms is located near a macroscopic surface. For small inter-atomic separations, R<< lambda 0 , ( lambda 0 is the reduced electric dipole wavelength) and for distances z,z<< lambda 0 /2 of the system from a perfectly conducting surface, the transition rate for the symmetric state, when both atomic dipoles are oriented perpendicular to the surface, is four times the rate for an isolated single atom. The antisymmetric state is stable. For a configuration in which dipoles are oriented parallel to the surface, both the symmetric and the antisymmetric states are stable. When the behaviour of the same system is investigated near the surface of a semi-infinite electron plasma, serving as a model for a metal, it is found that, in addition to the behaviour in the perfect conductor case, contributions from surface plasmon modes, and other contributions accounting for the finiteness of the plasma frequency are also exhibited.