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Physical Review A

Spontaneous emission in an absorptive and inhomogeneous cavity

Kazuki Koshino, Akira Shimizu

Published Jun 1, 1996• 10 citations
Publisher

Abstract

We consider the spontaneous emission (SE) of radiation by an atom in a one-dimensional cavity which consists of two medium regions and a vacuum region between them. The medium regions are composed of a bulk dielectric material which has a continuous absorption spectrum. We quantize the electromagnetic field as well as the polarization fields of the material, and polaritons composed of infinite number of fields are obtained. Using the polariton solutions, we then study the SE for an atom in such an absorptive and inhomogeneous cavity. The SE rate is shown to depend strongly on the position of the atom, the length l of the vacuum region, and the complex refractive index \ensuremath{\eta}+i\ensuremath{\kappa}. It is found in particular that the position dependence of the SE rate disappears for some particular values of l, in either of the vacuum or medium region. We also find that unlike the three-dimensional case the SE rate in a homogeneous cavity depends on both \ensuremath{\eta} and \ensuremath{\kappa}. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.4468

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We consider the spontaneous emission (SE) of radiation by an atom in a one-dimensional cavity which consists of two medium regions and a vacuum region between them. The medium regions are composed of a bulk dielectric material which has a continuous absorption spectrum. We quantize the electromagnetic field as well as the polarization fields of the material, and polaritons composed of infinite number of fields are obtained. Using the polariton solutions, we then study the SE for an atom in such an absorptive and inhomogeneous cavity. The SE rate is shown to depend strongly on the position of the atom, the length l of the vacuum region, and the complex refractive index \ensuremath{\eta}+i\ensuremath{\kappa}. It is found in particular that the position dependence of the SE rate disappears for some particular values of l, in either of the vacuum or medium region. We also find that unlike the three-dimensional case the SE rate in a homogeneous cavity depends on both \ensuremath{\eta} and \ensuremath{\kappa}. \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.
We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.
Abstract The electromagnetic field is quantized on the basis of the complete set of spatial modes of a plane dielectric slab of arbitrary thickness and refractive index but infinite transverse dimensions, located in otherwise empty three-dimensional space. The vacuum field fluctuations and spontaneous emission rates are evaluated as functions of position both inside and outside the slab. The source-field operator is derived for emission by atoms inside the slab, in the direction perpendicular to its surfaces. Particular attention is given to the possibility of suppressing spontaneous emission by placing atoms in, or close to, a dielectric slab.
Starting from first principles we simulate numerically the dynamics of a system of two-level atoms interacting with a multimode electromagnetic field in a one-dimensional cavity. In particular, we investigate the spontaneous emission of an excited two-level atom in the cavity. We show how the decay depends on the mode spectrum and on the position of the atom in the cavity. We study how the spontaneous emission is modified when the initially excited atom is surrounded by a material medium modeled as a system of two-level atoms. We also study the propagation of photon wave packets emitted by the atom within the material media. Our microscopic model provides us with a deeper understanding of the atom-field interaction and offers us a framework for a systematic investigation of the transition from a microscopic to a macroscopic (phenomenological) description of the spontaneous decay in material media (e.g., dielectrics).
We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.