Huygens’ principle corrected

“Time-delayed” (or “spatio-temporal”) dipoles on a wavefront give the correct sources for a corrected Huygens’ principle.

Huygens’ principle, known since at least 1690, gives a first model for the diffraction of waves. The “next” wave (or “phase”) front can be calculated from the previous one by assuming simple point sources of spherical waves at each point on the current wavefront. Taking this principle too literally, however, leads also to the generation of backwards waves that do not exist physically. Later, Fresnel and others introduced so-called “obliquity factors” in an ad hoc fashion to compensate for this while still leaving a usable diffraction model.

After only 300 years, this paper (“Huygens’s wave propagation principle corrected,”) solves this problem, giving a simple and correct version. It shows that using “time-delayed” or “spatio-temporal” dipoles instead of simple point sources gives the correct answer for forward wave propagation while eliminating the unphysical backward waves.

Such a “time-delayed” or “spatio-temporal” dipole consists of a “positive” source and a “negative” source separated by a short (or infinitesimal” distance, with the “negative” source firing at a slight time delay compared to the “positive” source. That time delay corresponds to the time take for the wave to propagate from the position of the “positive” source to the position of the “negative” source. For phase fronts on which the amplitude does not vary rapidly in space, this approach is exact for scalar waves.

D. A. B. Miller, “Huygens’s wave propagation principle corrected,” Optics Lett. 16, 1370‑1372, (1991).