Huygens' Principle geometric derivation and elimination of the wake and backward wave

• Published in: Scientific reports 2021-10, Vol.11 (1), p.20257-20257, Article 20257
• Main Author: Anderson, Forrest L.
• Format: Article
• Language: English
• Subjects: 639/766; 639/766/400; Humanities and Social Sciences; multidisciplinary; Propagation; Science; Science (multidisciplinary); Wave analysis; Wave propagation
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-021-99049-7

Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside of the new wave front combine to form a wake. Also there are two tangential surfaces so wave fronts are propagated in both the forward and backward directions. These problems have not previously been resolved by using a geometrical theory with impulsive wavelets that are in harmony with Huygens' geometrical description. Doing so would provide deeper understanding of and greater intuition into wave propagation, in addition to providing a new model for wave propagation analysis. The interpretation, developed here, of Huygens' geometrical construction shows Huygens' Principle to be correct: as for the wake, the Huygens' wavelets disappear when combined except where they contact their common tangent surfaces, the new propagating wave fronts. As for the backward wave, a source propagates both a forward wave and a backward wave when it is stationary, but it propagates only the forward wave front when it is advancing with a speed equal to the propagation speed of the wave fronts.