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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Near-field effect and spatial distribution of spontaneous photons near surface

Oleg N. Gadomsky, Konstantin V. Krutitsky

Published May 6, 1996• 4 citations
Publisher

Abstract

The report is devoted to the spontaneous emission of initially excited atom near the surface of semi-infinite dielectric. We predict near field effect in quantum optics which manifests itself to the fullest extent in the near zone with respect to dielectric surface and springs up under consistent description of atomic interaction in the radiation field and under consideration of spatial dielectric structure.

DOI
10.1117/12.239814

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Abstract : Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric constant epsilon(omega). The Einstein coefficient A(m)(e) of an excited state jeme appears to depend on the magnetic quantum number me. A sum rule for A(m)(e) is derived, and from the rotational symmetry with respect to the surface normal it is found that A(m)(e) = A(-m)(e). A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on epsilon(omega), and it is pointed out how information about the substrate, e.g., epsilon(omega), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem. Keywords: Spontaneous decay, Atomic fluorescence, Atom near metal surface, Absorbing dielectric, Einstein coefficient, Magnetic quantum number.

•Oct 1, 1987•0 citations
The report is devoted to the spontaneous emission of initially excited atom near the surface of semi-infinite dielectric. We predict near field effect in quantum optics which manifests itself to the fullest extent in the near zone with respect to dielectric surface and springs up under consistent description of atomic interaction in the radiation field and under consideration of spatial dielectric structure.
We have theoretically investigated the process of spontaneous emission of initially excited two-level atom inside and outside of ultra-thin dielectric film. Dielectric medium is considered as discrete-continuous system of interacting dipoles. For the solution of this boundary problem of quantum optics we use Heisenberg equations for atomic operators. Mode functions of ultra-thin film are calculated by direct solution of integro-differential field equation. Coordinate dependences of excited state life time are analyzed and it is shown that consideration of near-field effect may essentially change spectral properties of the atoms located at small distances from the surface.
The lifetime of an excited atom near an absorbing dielectric surface is calculated from an exact solution of a microscopic Hamiltonian model, which includes the effects of dispersion, local-field correction, and near-field Coulomb interaction. Results for the total decay rate are shown to be in excellent agreement with those based on classical electromagnetic theory and to yield the well-known result for the rate of nonradiative energy transfer in the limit of very small distance from the surface. \textcopyright{} 1996 The American Physical Society.
The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.
Spontaneous-emission properties and resonance fluorescence for a two-level adatom near the surface of a semi-infinite superlattice with quasiperiodic structure are studied by use of surface-dressed optical Bloch equations and Maxwell's equations. Effects of dielectric properties and the geometric structure of this superlattice on spontaneous-decay rate and frequency shift, resonance-fluorescence spectrum, time evolution of adatomic inversion, and fluctuations of the dipole moment for this adatom are discussed and some novel phenomena are discovered.
A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.
Abstract : Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric constant epsilon(omega). The Einstein coefficient A(m)(e) of an excited state jeme appears to depend on the magnetic quantum number me. A sum rule for A(m)(e) is derived, and from the rotational symmetry with respect to the surface normal it is found that A(m)(e) = A(-m)(e). A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on epsilon(omega), and it is pointed out how information about the substrate, e.g., epsilon(omega), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem. Keywords: Spontaneous decay, Atomic fluorescence, Atom near metal surface, Absorbing dielectric, Einstein coefficient, Magnetic quantum number.