DNA-linked metal nanosphere materials: Fourier-transform solutions for the optical response

Methods are developed for modeling the optical properties of aggregates of large numbers of small metal nanospheres in a dielectric medium. Aggregates are modeled as systems of coupled dipoles, with the dipole polarizabilities for the spheres determined using Mie theory. Fast-Fourier-transform (FFT) and conjugate-gradient (CG) techniques are used to solve the electrodynamic equations for both ordered and disordered aggregates. Results are shown to match solutions arrived at by direct methods. The range of validity of the coupled-dipole approximation for modeling DNA-linked colloidal materials is established by comparison with coupled-multipole results. While the methods are applicable only to lattice gas aggregates and aggregates composed of nanospheres on cubic lattices, there are no restrictions as to aggregate shape.