New method to evaluate optical properties of core–shell nanostructures

A new method is presented to calculate, for metallic core–dielectric shell nanostructures, the local refractive index, resonance condition, maximum spectral shift, plasma wavelength, and the sensitivity of the wavelength maximum to variations in the refractive index of the environment. The equations that describe these properties are directly related to the surface plasmon peak position, refractive index of the shell, and to the surrounding medium. The method is based on the approach that a layered core dispersed in a dielectric environment (core–shell model) can be figured out as an uncoated sphere dispersed in a medium with a local refractive index (local refractive index model). Thus, in the Mie theory, the same spectral position of the surface plasmon resonance peak can be obtained by varying the volume fraction of the shell or by varying the local refractive index. The assumed equivalence between plasmon resonance wavelengths enable us to show that the local refractive index depends geometrically on the shell volume fraction. Hence, simple relationships between optical and geometrical properties of these core–shell nanostructures are obtained. Furthermore, good agreement is observed between the new relationships and experimental data corresponding to gold nanoparticles (radius = 7.5 nm) covered with silica shells (with thicknesses up to 29.19 nm), which insured that the equivalence hypothesis is correct.