Exact geometrical theory of free-space radiative energy transfer

Abstract

An exact theory of free-space radiative energy transfer is given in terms of a generalized specific intensity that is constant along geometrical rays. General and explicit relations are derived for the generalized specific intensity expressed in terms of the field variables. Such relations are also derived for the cross-spectral density function of the field expressed in terms of the generalized specific intensity. For an arbitrary, freely propagated field, the theory is shown to reproduce the exact results of wave theory by transfer equations that are almost identical to the classical ones. The description reduces to the classical theory within a quasi-homogeneous field approximation. Similarly, it reduces to the geometrical-optics energy expressions in that approximation. For two-wave interference, additional ray contributions to the energy transport are found along the interference fringes. These interference rays serve only to describe the effects of the interference on the local energy transport.