Normal Modes of a Lattice of Oscillators with Many Resonances and Dipolar Coupling

The normal modes of a lattice of coupled dipoles are studied as a model of the collective excitations of electrons in condensed materials. Two types of oscillations are found in which electrostatic coupling has a dominant influence. One of them is analogous to the oscillation of an electron plasma and has a high dipole moment. Other collective oscillations have a low net dipole moment, owing to destructive interference between out-of-phase components. These two types of oscillation occur in systems with a sufficiently high density of oscillator strength in space and in spectrum. A simple estimate indicates that most condensed materials fulfill this condition.