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

Near-field effect in quantum optics of surface: spontaneous emission in ultrathin dielectric film

Oleg N. Gadomsky, Konstantin V. Krutitsky

Published Sep 26, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.287683

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 26, 1997•0 citations
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.
In nonlinear resonance optics, the boundary-value problem of the interaction of steady quasiresonant optical radiation with an ultrathin film is solved within the framework of a model of a discretely continuous film of atoms in which the point of observation is surrounded by discretely distributed atoms forming a truncated Lorentz sphere. Outside the sphere the distribution of atoms is continuous. A closed system, formed by an integral field equation and modified Bloch equations, is used to calculate the microscopic field inside the film and thus the dynamic detuning from a resonance, which takes account of the near-field effect, i.e. of the discretely continuous distribution of atoms in the film. A significant dependence of the effect on the nature of the symmetry of the distribution of atoms in the film is demonstrated.
As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain.
Boundary problem of quantum optics for spontaneous emission of atom embedded in one-dimensional chain of discrete dipoles is solved. The role of boundary effects caused by violation of translational symmetry in atomic spatial distribution is investigated. Life time of excited state and frequency shift of atomic transition are calculated. It is shown that these spectral characteristics significantly depend on atomic position in the chain. Angular distribution of spontaneous photons is also investigated. Theoretical analysis is based on the system of Heisenberg equations for atomic and field operators. For the calculation of the mode functions it is employed as the method of integro-differential equations.
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.
The role of near field effect is investigated in the boundary value problem of nonlinear resonant optics at the interaction of steady quasiresonant optical radiation with the film of two-level atoms. Dynamical detuning from resonance, nonlinear index of refraction, reflected and refracted waves are analyzed on the basis of solution of closed system of integral field equation and optical Bloch equations with account for discrete-continuous distribution of two-level atoms. An essential dependence of near field effect upon type of symmetry of atomic distribution is shown.