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In this paper we evaluate the effect of oxidation on the total power scattered in the far field by a _{2}). Using an effective medium approach to model the Al particle with an outer layer of alumina (Al_{2}O_{3}), we find that the UV peak of total energy scattered in the far field shifts towards longer wavelengths for volume fractions of Al_{2}O_{3} up to _{2}O_{3}, the total intensity of light scattered is significantly reduced.

In recent years a large number of papers in nanophotonics have been investigating the properties of aluminum because it is an abundant and low cost metal with plasmon modes in the visible and the ultraviolet [

In order to evaluate the feasibility of these applications, it is important to consider in what way oxidation of the Al surfaces may affect the performance of this system. In this paper we investigate how the ratio between the power radiated above the substrate, _{2}O_{3}) in the presence of a substrate of either silica (SiO_{2}) or Al. We consider substrates with thickness such that the light reflected by the lower surface is negligible, so that the substrates can be modeled as semi-infinite. The top layer of the Al substrate can also be oxidized, but for sake of simplicity we ignore here this effect, which should not change qualitatively the results presented when the oxidation layers are thin and do not support guided modes. We consider the following two configurations. The first configuration is similar to the standard set-up of a scanning near field optical microscope [

For all cases considered, we use the Bruggerman effective medium approximation [_{2}O_{3} on the far-field scattering of light. The effective dielectric function, _{2}O_{3} can be found, using given values of the permittivity for the two materials [_{2}O_{3}, this theory has reproduced experimental results from Al nanodiscs [_{2} substrates more accurately than the Maxwell-Garnett theory [

The energy radiated above the substrate,

In order to evaluate the aforementioned configurations, we solve Maxwell’s equations for spherical particles above a semi-infinite substrate, with a monochromatic electric dipole source placed, either between or above the particle and the substrate, along the

With this choice of internal and scattered fields, we can form the principal modes as for a single particle in a homogeneous medium [

The procedure described here is general and can be applied to any particle in which the normal is defined at any point on the surface. For the azimuthally symmetric nanostructures considered here, numerical calculations are vastly sped up by forming internal and scattered fields whose tangent components have azimuthal angular dependence

In Figure _{2}O_{3} ranging from _{2}O_{3}. The effect of Al_{2}O_{3} on the refractive index is straightforward: the higher the volume fraction is, the lower the absolute value of the refractive index is. From this, we can expect resonances to be shifted toward longer wavelengths as the volume fraction of Al decreases. The effect of Al_{2}O_{3} on the absorption coefficient is more subtle and changes depending on the volume fraction and the wavelength. At longer wavelengths all volume fractions considered reduce the absorption coefficient with respect to the case of pure Al. However, for Al volume fractions below

Complex dielectric function for Al + Al_{2}O_{3} calculated with the effective medium approach. For the complex permittivity, _{2}O_{3} and

In Figure _{2} substrates. In both cases the UV peak in the scattered energy remains essentially unchanged for Al volume fractions of

Normalised power radiated by spherical particles on top of a substrate, illuminated by an electric dipole. For substrates comprised of (a) Al and (b) SiO_{2}. All curves correspond to the same volume fractions indicated in Figure

In Figure _{2} substrates, and with the dipole source placed in the middle of the gap. In this case the difference between the two substrates is much more significant. The ratio _{2} substrate, the ratio

Normalised power radiated by spherical particles _{2}. All curves correspond to the same volume fractions indicated in Figure

In conclusion, we have presented an effective media study of Al particles with Al_{2}O_{3} oxidation layers on top of, and above, substrates of Al and SiO_{2}. The results can be qualitatively explained by considering how the effective media absorption coefficient and refractive index depend on the volume fractions and the wavelengths. Our investigation of effective media spheres held above an Al substrate indicates that two orders of magnitude enhancement of the far-field radiation in the UV will take place also with oxidized Al particles as long as the volume fraction of Al is not below _{2}O_{3} of

The numerical data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Duncan McArthur is funded by a Leverhulme Trust Research Grant.