DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION(SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-m edium interactive system. On the basis of the postulation, the behavio rs of light transmitting through the medium with refractive index n ar e investigated, the investigation covering the realms of both geometri cal optics and wave optics. The wave equation of light in static trans mission is studied modally, the postulation being employed to derive t he exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the rel ationships concerning the conservation of optical fluid and the dynami c properties are given, and some simple applications of the theories m entioned are presented.