One of the reasons why Mie's theory has remained important for so long is that it is the only simple, exact solution to Maxwell's equations that is relevant to particles. In this paper, we highlight recent advances in theoretical research in this area, emphasizing especially the linear optical properties (extinction, absorption, Rayleigh scattering, and Raman scattering) of isolated silver particles of arbitrary shape with sizes up to a few hundred nanometers. Mie's solution remains of great interest to this day, 5 but the modern generation of metal nanoparticle science, including applications to medical diagnostics 6 and nanooptics, 7 has provided new challenges for theory. 1 It was therefore one of the great triumphs of classical physics when in 1908, Mie presented a solution to Maxwell's equations 2-4 that describes the extinction spectra (extinction = scattering + absorption) of spherical particles of arbitrary size. These properties have been of interest for centuries, and scientific research on metal nanoparticles dates at least to Michael Faraday. Gold colloidal nanoparticles are responsible for the brilliant reds seen in stained glass windows. Included is a description of the qualitative features of dipole and quadrupole plasmon resonances for spherical particles a discussion of analytical and numerical methods for calculating extinction and scattering cross-sections, local fields, and other optical properties for nonspherical particles and a survey of applications to problems of recent interest involving triangular silver particles and related shapes.

In this feature article, we describe recent progress in the theory of nanoparticle optical properties, particularly methods for solving Maxwell's equations for light scattering from particles of arbitrary shape in a complex environment. More recently, new lithographic techniques as well as improvements to classical wet chemistry methods have made it possible to synthesize noble metal nanoparticles with a wide range of sizes, shapes, and dielectric environments. The optical properties of metal nanoparticles have long been of interest in physical chemistry, starting with Faraday's investigations of colloidal gold in the middle 1800s.

George steel tor johnson