Absorption spectrum of clusters of spheres from the general solution of Maxwell's equations. II. Optical properties of aggregated metal spheres

Abstract

A very general theory for the infrared absorption spectrum of homogeneous sphere clusters is presented. Maxwell's equations are solved for any arbitrary cluster geometry and for any light (polarized or not) incidence by usual expansion of the various fields. Usual boundary conditions are used but take into account the possible existence of plasmons in the spheres. High-order multipolar (electric and magnetic) interaction effects are included. The problem is cast into the calculation of the microscopic effective dielectric and magnetic susceptibility for the spheres, and that of the appropriate interaction terms. The latter (which constitute the hardest part of the theory in general) are calculated by formulating in a very practical way a recurrence relation for spherical vector wave functions in different reference frames. The extinction cross section is derived for any arbitrary case in order to allow for comparison of experimental data and previous theoretical work. The theory in the absence of any high-order polar effect is applied to the case of metallic clusters, e.g., small sodium spheres. Effects due to size distribution, sphere separation, and sphere magnetic permittivity are analyzed. Different light incidences are considered. A very brief discussion of the experimental status is presented for the case of metallic spheres. New experiments are suggested for which the theory is easily read out. Appendices contain new relations between Legendre functions and "spherical coupling parameters" allowing one to treat up to (${2}^{4}$,${2}^{4}$) polar-order interactions.