Many-body optics. III. The optical extinction theorem and ϵl(k,ω)

Abstract

For Pt. II see abstr. A3075 of 1970. It is shown that the optical modes which were investigated in the earlier paper I (abstr. A37680 of 1968), which are either longitudinal or transverse, and which satisfy the dispersion relations of I, are acceptable solutions of the optical integral equation for a locally isotropic molecular fluid at normal temperatures. Acceptable solutions must satisfy the optical Extinction Theorem. In simplest geometry the longitudinal modes prove to be normal modes; but the transverse modes are modes forced by incident light. The linear response of the system to light is calculated: it is shown that the existence of a surface to the system is essential to the existence of such a response. Light couples to the system through the surface. It is shown that there are additional longitudinal modes which can be forced by incident free charge. In simplest geometry the extinction theorem now becomes irrelevant. It is then possible to express the longitudinal dipole response in terms of a (k, omega )-dependent longitudinal dielectric constant epsilon l(k, omega ): an explicit formula for epsilon l(k, omega ) in terms of cluster integrals for the fluid is obtained to all orders in intermolecular correlation but exhibition of the details of that correlation is deferred until later. The zeros of epsilon l(k, omega ) yield the dispersion relation for the longitudinal normal modes in the same simplest geometry. Only in the complex dielectric constant approximation does epsilon l(k, omega ) coincide with the square of the transverse refractive index mt2( omega ).