Isn’t this correction to Huygens Principle a little arbitrary? The article I’m talking about: https://www-ee.stanford.edu/~dabm/146.pdf
In this article, the author solves the main problem with Huygens Principle, which is that you have to ignore the backward wavelets, despite the sources being point sources on the wavefront. This solution is also on Wikipedia prominently as the legitimate correction.
The author solves it by substituting the point sources by a dipole, in which the left source is delayed in such a way that there’s no backward wave, only forward.
I have no doubt that it works mathematically, but physically speaking, isn’t it just another arbitrary correction to the original principle? Like, he just put another source there in conditions that would erase the backward wave. Does this for any of you, however, make sense physically speaking? Why would a dipole be more appropriate in this case than a point source?
I’d appreciate little math, more conceptually speaking.
 A: Here in "Huygens Principle" Kevin Brown gives an interesting historical outlook and explains that the Huygens principle is valid only in the odd number of dimensions.
This however, can be interpreted a bit differently. Perhaps a better interpretation would be that the Huygens principle only establishes any point of the wave as a source of a new wave. This way we could say that the Huygens principle is valid in any number of dimensions, but the retarded wave is canceled only in the odd number of dimensions.
A few interesting examples of how this works. In 3 dimensions the retarded wave is canceled. As a result, we don't hear the echo of our voice reflected from the air (but only as reflections from distant objects). Similarly, a flashlight doesn't blind us, because light does not reflect back from the empty space. However, it would do so in 2 or 4 dimensions.
Another odd-dimensional example is a whip. A wave induced in a long whip is 1-dimensional. Once sent, it does not reflect back. (A half a century ago I used to make a gunshot-like sound with a 30-feet whip to control a herd on a pasture.)
A common example in 2 dimensions is a water surface. Drop a rock in the lake. The rock drowns and triggers a circular wave. While it is expanding in a circle, it does not leave the inside area of the circle quiet. When we turn off a light bulb in 3 dimensions, the darkness is instant. However, on the surface of the lake, the wave in the center of the circle persists for a long time.
The above link also explains that the statement in the article you quote is incorrect that the Kirchhoff solution proves the cancellation of the retarded wave. It does not. It only links the Huygens principle to the Maxwell equations, but these equations do not prohibit the retarded wave.
