A. V. Chebykin, A. A. Orlov, F. Heisler, K. V. Baryshnikova, P. A. Belov

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The paper deals with theoretical demonstration of Purcell effect in extremely anisotropic metamaterials with elliptical isofrequency surface. This effect is free from association with divergence in density of states unlike the case of hyperbolic metamaterials. It is shown that a large Purcell factor can be observed without excitation of modes with large wave vectors in one direction, and the component of the wave vector normal to the layers is less than k0. For these materials the possibility is given for increasing of the power radiated in the medium, as well as the power radiated from material into free space across the medium border situated transversely to the layers. We have investigated isofrequency contours and the dependence of Purcell factor from the frequency for infinite layered metamaterial structure. In the visible light range strong spatial dispersion gives no possibility to obtain enhancement of spontaneous emission in metamaterial with unit cell which consists of two layers. This effect can be achieved in periodic metal-dielectric layered nanostructures with a unit cell containing two different metallic layers and two dielectric ones. Analysis of the dependences for Purcell factor from the frequency shows that the spontaneous emission is enhanced by a factor of ten or more only for dipole orientation along metamaterial layers, but in the case of the transverse orientation radiation can be enhanced only 2-3 times at most. The results can be used to create a new type of metamaterials with elliptical isofrequency contours, providing a more efficient light emission in the far field.

Keywords: metamaterials, Purcell effect, spontaneous radiation, surface plasmons

Acknowledgements. The work is partially financially supported by the Government of the Russian Federation (grant 074-U01),the Russian Foundation for Basic Research (project 14-02-31720),and the Russian Federation President scholarship (grant СП-2154.2012.1). The authors express their special thanks to an anonymous reviewer for valuable remarks and rendering assistance in paper preparation.

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