Absorption and scattering of light by a dimer of metal nanospheres: comparison of dipole and multipole approaches

Recently, the polarizability tensor of metal bispheres located near a plane metal substrate was analytically derived in dipole approximation and was used to calculate the extinction spectra of silver dimers (Pinchuk and Schatz 2005 Nanotechnology 16 2209). To evaluate the accuracy of dipole approximation for this problem, we compare the optical properties of silver and gold dimers, embedded in a homogeneous dielectric medium, by using electrostatic and electrodynamic dipole approximations and an exact electrodynamic multipole solution. For longitudinal TM-excitation (the electric field is directed along the bisphere axis), the dipole and multipole absorption and scattering spectra differ dramatically, whereas for transversal TE-excitation the dipolar approximation gives acceptable results. The physical origin of the inaccuracies of the dipole electrostatic solution is related to the highly inhomogeneous electric-field distribution near the contact point of the spheres. Thus, we have to include several multipole orders even in the electrostatic solution for dimer particles that are, individually, well within dipole approximation. Although we do not consider the effects of a plane metal substrate, we believe that the multipole interaction of constituent dimer spheres can also be important in this case. The T-matrix plasmon resonance spectral shifts for randomly oriented 42 nm gold bispheres with various separations are in satisfactory agreement with the experimental measurements by Reinhard et al (2005 Nano Lett. 5 2246), whereas the electrostatic dipole approximation gives too underestimated shifts.