Optics in the multipole approximation: from atomic systems to solids

Starting from the microscopic light-matter interaction in form of the minim al coupling Hamiltonian, the multipole approximation for the optical respon se of localized electrons in atomic systems is extended to delocalized elec trons in solids. A spatial averaging procedure is used to derive the electr omagnetic sources for macroscopic Maxwell's equations as well as the corres ponding many particle Hamiltonian on a coarse grained length scale. The res ults are illustrated for semiconductor bulk material up to quadrupole momen ts for the interband transitions, where gauge invariant equations of motion for the optical response are obtained. (C) 2000 Elsevier Science B.V. All rights reserved.