Abstract

Huygens' principle that every point on a wavefront can be regarded as a source of spherical wavelets is very useful, but is known to be incomplete because it would also imply backward propagating waves. Huygens (and subsequently Fresnel) simply neglected such waves "ad hoc". Later, Helmholtz and Kirchhoff showed rigorously that the wave from sources inside an arbitrary surface S could be generated by an appropriate set of point and dipole sources on S. For the special case of wavefront (mathematically, a surface approximately normal to the wave propagation on which the wave amplitude changes only slowly), Kirchhoff dropped near-field terms to obtain his diffraction theory, but in so doing lost the intuitive simplicity of Huygens' wavefront sources. I show that we can quantitatively model wave propagation from a wavefront simply by replacing Huygens' point sources by "spatio-temporal dipoles" oriented perpendicular to the wavefront. The spatiotemporal dipole consists of "positive" and "negative" point sources of spherical waves separated (infinitesimally) in space and time; the negative source is delayed relative to the "positive" source by the wave propagation time between the sources. We therefore obtain a wave propagation principle that is both rigorous and intuitive.

© 1990 Optical Society of America