The scattering of light. III. External scattering from a finite molecular fluid

Abstract

We calculate the external incoherent scattering from a finite molecular fluid exposed to a weak, external, coherent electromagnetic field. The scattered field is detected outside the fluid and the system models a real scattering experiment in all its aspects. The analysis is based on a classical all order many-body theory developed in two previous papers. The theory is microscopic, i.e. is developed ab initio and in detail in terms of individual scattering processes in vacuo at a strictly molecular level. But it is shown that the collective action of these generates all of the macroscopic features expected in the external scattering: for example, the refractive index, as it was calculated previously from the many-body theory, plays much of its expected macroscopic role. These macroscopic results are reached by showing that the complete scattering process (from a wave incident in vacuo on the fluid to a wave in vacuo scattered from the fluid) separates into three independent collective processes compactly described by a particular quadrilinear form quadratic in a field $ induced in the fluid by any coherent external field, and quadratic in a ‘weight’ field e describing the scattered field in the fluid. The internal fields $ and e couple separately to the external incoming field and to one representing the external scattered field respectively. In each case they account for all collective surface effects. The kernel of the quadrilinear form accounts for all of the internal scattering processes in the fluid. The weight field e and the equations associated with it describe refraction and (multiple) internal reflection of the scattered light at the surface of the medium in all details: these collective surface effects are managed in a very effective way through a new reciprocity principle derived from the microscopic theory and containing a new form of optical extinction theorem for external scattering. The kernel of the quadrilinear form for internal scattering has a natural expansion describing macroscopic single and macroscopic multiple scattering agreeing with phenomenological ideas. The expansion is derived from a relation between the weight field and a propagator for the scattered wave. We show that macroscopic single scattering contains processes displaying ‘backscattering coherence’. This phenomenon has not been recognized in molecular scattering theory before, and back-scattering enhancement very much like that recently observed in scattering from suspensions of dielectric particles, should be observable near a critical point of phase separation. We give explicit formulae for macroscopic single scattering from a dilute gas up to two-body contributions with intermolecular correlations determined by a LennardJones potential. We also show how Einstein’s phenomenological single scattering formula can be derived from certain microscopic scattering processes of all orders. With a minor qualification the formula is valid in a generalized form up to neglect of terms of order six in the polarizability per unit volume.