Optical polarizability of metal nanopartides and their biospecific conjugates

摘要

We present analytical solutions for polarizability of small metal particles such as nanoshells, nanorods, and bispheres. The optical model of the gold nanoshell conjugates with biopolymers is treated in terms of a multilayered spherical particle with a silica core covered by a gold shell and by two inhomogeneous dielectric shells that simulate effect of primary adsorption of recognizing molecules followed by the target molecules binding. To calculate the optical polarizability of the multilayered particle, we develope a simple analytical method based on a principle of the dipole equivalency of the multilayered conjugate and its homogeneous counterpart. This is used to derive simple relations between the parameters of the local dielectric environment and the gold nanoshelt structure. To calculate the optical polarizability of axially symmetrical metal nanorods, we use the electrostatic limit of the extended boundary conditions method (EBCM) to derive an integral formula for the geometrical depolarization factor. This solution is exemplified by application to the right circular cylinders and s-cylinders with semi-spherical ends. Finally, we derive analytical solutions for the electrodynamic and electrostatic optical polarizabilities of a small metal bisphere by using the discrete dipole approximation (DDA). The electrostatic solution is examined by the comparison of extinction spectra with the exact T-matrix calculations.