We analyze dispersion properties of metal-dielectric nanostructured metamaterials. We demonstrate that, in a sharp contrast to the results for the corresponding effective medium, the structure demonstrates strong optical nonlocality due to excitation of surface plasmon polaritons that can be engineered by changing a ratio between the thicknesses of metal and dielectric layers. In particular, this nonlocality allows the existence of an additional extraordinary wave that manifests itself in the splitting of the TM-polarized beam scattered at an air-metamaterial interface.

We study layered metal-dielectric structures, which can be considered as a simple example of nanostructured metamaterials. We analyze the dispersion properties of such structures and demonstrate that they show strong optical nonlocality due to excitation of surface plasmon polaritons. We derive a model of a nonlocal effective medium for describing the effects of strong spatial dispersion in the multilayered metal-dielectric metamaterials. We obtain analytical expressions for the components of the effective permittivity tensor which depend on the wave vector and reveal that spatial dispersion effects exist in both directions across and along the layers.

We study the spontaneous emission of a dipole emitter imbedded into a layered metal-dielectric metamaterial. We demonstrate ultra-high values of the Purcell factor in such structures due to a high density of states with hyperbolic isofrequency surfaces. We reveal that the traditional effective-medium approach greatly underestimates the value of the Purcell factor due to the presence of an effective nonlocality, and we present an analytical model which agrees well with numerical calculations. c 2011 Optical Society of America OCIS codes: 160.1190, 160.3918.Spontaneous emission rate of a light source can be tuned by engineering its environment. A ratio of the decay rate in the media as compared to that in vacuum is usually termed as the Purcell factor [1], and the possibility of a controllable change of of the radiative lifetime has been demonstrated in various optical systems, including photonic crystals and plasmonic nanostructures [2][3][4].In metamaterials the Purcell factor can be greatly enhanced, with two possible mechanisms of achieving high values of the Purcell factors. In the first case, we should place a dipole emitter into a metamaterial that is described as an uniform hyperbolic medium. Such hyperbolic media are uniaxial media characterized by the permittivity tensor of the diagonal form with the principal components being of the opposite signs [5, 6]. The density of photonic states in such a system diverges. As a result, a huge Purcell factor can be reached, and its values being determined either by losses and inhomogeneity of the medium [6] or by a spatial extent of the source [7]. The second mechanism of achieving high Purcell factors employs the excitation of surface plasmon polaritons (SPPs) at the metal-dielectric interfaces inside a metamaterial [4, 8].In this Letter, we study the spontaneous emission of a dipole emitter imbedded into a layered metal-dielectric metamaterial (see Fig. 1) and reveal the possibility for ultrahigh values of the Purcell factor due to a high density of states with hyperbolic isofrequency surfaces. In particular, we demonstrate the dramatic dependence of the Purcell factor near the SPP resonance on the ratio of the layer thicknesses and the dipole orientation, so that the Purcell factor can have either maximum or minimum at the plasmon frequency for high and low metal filling factors, respectively. This revealed mechanism of the enhancement of the Purcell factor has an interface nature, and thus it can not be described within any traditional homogenization approach. However, here we present an analytical model which agrees well with our numerical results.The hyperbolic medium at certain frequency ranges can be realized by layered metal-dielectric nanostructures. Through conventional effective-medium approach a metal-dielectric nanostructure formed by pairs of layers with permittivities ε 1 , ε 2 , and thicknesses d 1 , d 2 (see Fig. 1) can be modeled as an uniaxial anisotropic medium with permittivity tensor of the form:

We consider multilayered metal-dielectric metamaterials composed of alternating nanolayers of two types and calculate the components of their effective dielectric permittivity tensors as functions of both frequency and wave vector. We demonstrate that such structures can be described as strongly nonlocal uniaxial effective media, and we analyze how the nonlocal permittivity tensor components are related to other manifestations of strong spatial dispersion in such structures, and how the resonance of permittivity depends on the propagation direction.

With the growth of computational power, representations of large datasets are becoming more and more common instruments in the toolboxes of chemoinformaticians. Every scientist in the field can find the method of choice for a particular task. However, there is no universal reference representation of the chemical space currently available and expert knowledge is required.

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We theoretically demonstrate the strong Purcell effect in ε-near-zero ultra-anisotropic uniaxial metamaterials with elliptic isofrequency surface. Contrary to the hyperbolic metamaterials, the effect does not rely on the diverging density of states and evanescent waves. As a result, both the radiative decay rate and the far-field emission power are enhanced. The effect can be realized in the periodic layered metal-dielectric nanostructures with complex unit cell containing two different metallic layers.

We study surface modes at an interface separating two different layered metal-dielectric metamaterials. We demonstrate that, in a sharp contrast to the effective-medium approach predicting a single interface mode with the surface-plasmon dispersion, the transfer-matrix method reveals the existence of three types of localized interface modes, including a backward interface mode. These results confirm that metal-dielectric nanostructured metamaterials can demonstrate strong optical nonlocality due to the excitation of surface plasmon polaritons. V