Abstract

The Bloch-Maxwell equations are usually derived for isolated molecules interacting with an external electromagnetic field. This is justified in the limit of low molecular density, where intermolecular forces may be neglected. The problem which we address in this work is how to extend these equations in a systematic way to incorporate properly intermolecular forces. We thus develop a systematic microscopic basis for the calculation of nonlinear response functions and susceptibilities. Such a theory is essential for relating microscopic, single-molecule, polarizabilities to the macroscopic susceptibilities of optical materials. The local field approximation [1,2] is a mean-field procedure which is widely used in the calculation of molecular susceptibilities at finite densities, when intermolecular forces are important. The local field model provides a simple way to relate the polarizabilities of isolated molecules to the macroscopic susceptibilities. It is clear, however, that this procedure is not rigorous. It fails to take properly into account the correlated dynamics of the interacting many-body system, i.e., correlations among the molecules, as well as correlations between the molecules and the radiation field. Short-range forces (e.g., exchange) are totally neglected in this procedure. Moreover, even the dipoledipole forces are not fully taken into account. The resulting susceptibilities do not depend at all on the wavevectors (apart from the local field contribution) but just on the frequencies. This indicates that processes such as exciton migration and energy transfer and transport (e.g., the Forster transfer) are neglected in this procedure. Such processes are often added phenomelogically in order to interpret transient grating spectroscopy[3], which is a four-wave mixing technique that measures transport processes by following the wavevector dependence of the susceptibilities. The common derivation of the local field approximation cannot be extended to include these processes, since it is intrinsically a mean-field single molecule theory.

© 1988 Optical Society of America