Geometric-optical Rays, Poynting's Vector, and Field Momenta
In isotropic media, the rays of geometrical optics are usually obtained from the surfaces of constant phase (i.e., wavefronts) by drawing normals to these surfaces at various points of interest. It is also possible to find the rays from the eikonal equation, which is derived from Maxwell's equations in the limit when the wavelength λ of the light is vanishingly small. Both methods provide a fairly accurate picture of beam propagation and electromagnetic energy transport in situations where the concepts of geometrical optics and ray-tracing are applicable. The ray artifact, however, breaks down near caustics and focal points and in the vicinity of sharp boundaries, where diffraction effects and the vectorial nature of the field can no longer be ignored.
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