  We study the dynamics of an infinite regular lattice of classical charged
oscillators. Each individual oscillator is described as a point particle
subject to a harmonic restoring potential, to the retarded electromagnetic
field generated by all the other particles, and to the radiation reaction
expressed according to the Lorentz--Dirac equation. Exact normal mode
solutions, describing the propagation of plane electromagnetic waves through
the lattice, are obtained for the complete linearized system of infinitely many
oscillators. At variance with all the available results, our method is valid
for any values of the frequency, or of the ratio between wavelength and lattice
parameter. A remarkable feature is that the proper inclusion of radiation
reaction in the dynamics of the individual oscillators does not give rise to
any extinction coefficient for the global normal modes of the lattice. The
dispersion relations resulting from our solution are numerically studied for
the case of a simple cubic lattice. New predictions are obtained in this way
about the behavior of the crystal at frequencies near the proper oscillation
frequency of the dipoles.
