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Huygens's wave propagation principle corrected
, 1991
"... Huygens's principle that each point on a wave front represents a source of spherical waves is conceptually useful but is incomplete; the backward parts of the wavelets have to be neglected ad hoc, otherwise backward waves are generated. The problem is solved mathematically by Kirchhoff's rigorous in ..."
Abstract

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Huygens's principle that each point on a wave front represents a source of spherical waves is conceptually useful but is incomplete; the backward parts of the wavelets have to be neglected ad hoc, otherwise backward waves are generated. The problem is solved mathematically by Kirchhoff's rigorous integration of the wave equation, but the intuitive appeal of Huygens's simple principle is lost. I show that, by using spatiotemporal dipoles instead of spherical point sources, one can recover a simple principle of scalar wave propagation that is correct whenever the concept of a wave front is meaningful. Huygens's principle ' that every point on a wave front can be considered as a new source of spherical wavelets is a powerful conceptual tool in understanding wave propagation. When combined by Fresnel2 with the principle of interference, this concept explained key phenomena of diffraction. Both Huygens and Fresnel had to neglect backward parts of the wavelets arbitrarily, however. Otherwise, wave propagation in free space cannot be described