Accurate description of the optical response of a multilayered spherical system in the long wavelength approximation

Abstract

The optical response of a multilayered spherical system of unlimited number of layers (a ``matryoshka'') in the long wavelength limit can be accounted for from the knowledge of the static multipole polarizability of the system to first-order accuracy. However, for systems of ultrasmall dimensions or systems with sizes not-too-small compared to the wavelength, this ordinary quasistatic long wavelength approximation (LWA) becomes inaccurate. Here we introduce two significant modifications of the LWA for such a nanomatryoshka in each of the two limits: the nonlocal optical response for ultrasmall systems $(l10\text{ }\text{nm})$, and the ``finite-wavelength corrections'' for systems $\ensuremath{\sim}100\text{ }\text{nm}$. This is accomplished by employing the previous work for a single-layer shell, in combination with a certain effective-medium approach formulated recently in the literature. Numerical calculations for the extinction cross sections for such a system of different dimensions are provided as illustrations for these effects. This formulation thus provides significant improvements on the ordinary LWA, yielding enough accuracy for the description of the optical response of these nanoshell systems over an appreciable range of sizes, without resorting to more involved quantum mechanical or fully electrodynamic calculations.