Geometrical optics reviewed: A new light on an old subject

Abstract

The traditional view of geometrical optics as the ray-tracing procedure for the design of mirror, prism, and lens systems of uniform optical components, has become enlarged in recent years. This has been brought about by the applications of electromagnetic systems at ever decreasing wavelengths on the one hand, and by new optical components, such as optical fibers and integrated optical elements, on the other. The range of geometrical optics now includes such concepts as optics-in-the-large, wide-angle and aspheric designs, geodesic optics, and the optics of nonuniform media. The introduction of electromagnetic field theory in this area involves effects such as diffraction, fields near caustics, and evanescent fields. These are also being discussed in a ray optical interpretation, usually presented as the first-order term in an asymptotic expansion. The optical processes have, in turn, introduced some new geometrical theorems and matrix methods which have applications in the overall geometrical optics science. This paper sets out to review these methods and, in view of the commonly expressed compatibility between the two aspects, to investigate the applications of the geometrical theory to the electromagnetic field description. Indications are given as to possible methods available for the definition of a geometrical electromagnetic field theory which would contain the geometrical theories of the optical field in a covariant transformation theory of the electromagnetic field. It is shown that this is compatible with current methods being applied to the unity of all physics in which geometrical optics is the first-order approximation occupying a central position.