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Physical Review A

Spontaneous emission from a medium with elliptic and hyperbolic dispersion

Zhengjun Liu, Wei Li, Xunya Jiang, Juncheng Cao

Published May 28, 2013• 3 citations
Publisher

Abstract

We analyze the properties of spontaneous emission of a two-level atom in anisotropic media where the geometry of physical dispersion relations is characterized by an ellipsoid or a hyperboloid. Within the framework of quantum optics the rate of spontaneous emission in the above media is explicitly given with the orientation of the dipole transition matrix element taken into account. It indicates that for the ellipsoid case the intensity of the photons coupled into different modes can be tuned by changing the direction of the matrix element relative to the optical axis. For the hyperboloid case it is found that spontaneous emission in the hyperbolic medium (HM) can be dramatically enhanced compared with the case in the background medium. Moreover, in the HM the spontaneous emission exhibits strong directivity and gets the maximum in the asymptote direction.

DOI
10.1103/physreva.87.053836

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We analyze the properties of spontaneous emission of a two-level atom in anisotropic media where the geometry of physical dispersion relations is characterized by an ellipsoid or a hyperboloid. Within the framework of quantum optics the rate of spontaneous emission in the above media is explicitly given with the orientation of the dipole transition matrix element taken into account. It indicates that for the ellipsoid case the intensity of the photons coupled into different modes can be tuned by changing the direction of the matrix element relative to the optical axis. For the hyperboloid case it is found that spontaneous emission in the hyperbolic medium (HM) can be dramatically enhanced compared with the case in the background medium. Moreover, in the HM the spontaneous emission exhibits strong directivity and gets the maximum in the asymptote direction.
Within the frame of quantum optics we analyze the properties of spontaneous emission of two-level atom in media with indefinite permittivity tensor where the geometry of the dispersion relation is characterized by an ellipsoid or a hyperboloid(hyperbolic medium). The decay rate is explicitly given with the orientation of the dipole transition matrix element taken into account. It indicates that for the ellipsoid case the intensity of the photons coupled into different modes can be tuned by changing the direction of the matrix element and for the hyperboloid case it is found that spontaneous emission in hyperbolic medium can be dramatically enhanced compared to the dielectric background. Moreover, spontaneous emission exhibit the strong directivity and get the maximum in the asymptote direction.
We investigate spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. We treat the general case where the atomic dipole matrix element is a complex vector, that is, the atomic dipole can rotate with time in space. We calculate the rates of spontaneous emission into evanescent and radiation modes. We systematically study the angular densities of the rates in the space of wave vectors for the field modes. We show that the asymmetry of the angular density of the spontaneous emission rate under central inversion in the space of in-plane wave vectors occurs when the ellipticity vector of the atomic dipole polarization overlaps with the ellipticity vector of the field mode polarization.
Spontaneous emission from two two-level atoms within an anisotropic photonic crystal is investigated when direct dipole-dipole interaction is taken into account. The radiation properties of the present two atoms system are similar to that of a V-type three-level atom embedded in an anisotropic photonic crystal. The direct dipole-dipole interaction can enhance or depress the spontaneous emission depending on the relative position of the upper levels from the band edge of the photonic crystals. Owing to quantum interference and the dipole-dipole interaction, the spontaneous emission spectra are complicated non-Lorentzian shapes and depend strongly on the relative position of the upper levels from the bandgap and the initial state of the system.
The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies and in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantized electromagnetic field operators to calculate the emission rate in uniaxial media. For the more general case of biaxial media we propose an approximate expression based on interpolation between the limiting cases of uniaxial media. We support our model with numerical simulations which are in strong agreement for typical media configurations and, furthermore, show how local field effects can be taken into account in the model.
In this paper, in order to investigate the quantum effects of the invisibility cloaks, we study the spontaneous emission of an excited two-level atom in the vicinity of these cloaks and compare our results with the spontaneous emission of the aforementioned atom in the absence of these cloak and the vacuum. Here, the desired cloak is modeled by a large number of the spherical thin layers with constant optical parameters whose values radially increase. Since, the spontaneous emission parameter corresponds to the imaginary part of the Green tensor of the physical system, we extend the presented Green tensor for inhomogeneous and isotropic medium to the anisotropic one, and survey the effect of the layers number of the clock and also the orientation of the atomic dipole moment over the spontaneous emission of the two-level atom.