Absorption spectrum of clusters of spheres from the general solution of Maxwell's equations. The long-wavelength limit

A theory is presented to calculate the infrared absorption spectrum of $N$ dielectric spheres of arbitrary sizes, embedded in a dielectric matrix. The Laplace equation is solved exactly for this system, and general solutions take into account interactions at all multipolar orders. Phase factors are introduced when retardation effects become important. Absorption and absorbed power spectra are calculated for two (different or identical) spheres and for an infinite linear chain of identical spheres for different field directions. The theory is applied to MgO spheres. It is found that the Fröhlich mode for a single sphere splits into several resonant modes, and that quadrupolar-order interactions and incident field direction have drastic effects on the predicted infrared spectrum. Experimental consequences regarding damping-factor effects and the position of the modes are discussed.