Does Huygens Principle, by itself, explain diffraction?

Question

The Wikipedia article on Huygens–Fresnel principle says that even with the addition of Fresnel, the Huygens/Fresnel principle does not explain diffraction.

...but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures and screens, commonly known as diffraction effects.

My question is: Does Huygens Principle, by itself, explain diffraction?

I think it does: At the edge of openings Huygens wavelets are formed which propagate into the geometric shadow. So is Wikipedia wrong?

Answer 1

In short, no.

Huygens principle provided a simple qualitative explanation for evolving a given wave into its future. However, beyond that it doesn't provide a prescription for how two wavefronts may combine. Based on just wave evolution, one gets deformed but uniform evolution of a wavefront out of a pinhole and not the fringes of diffraction.

As per Fresnel, multiple waves could superimpose as per their phase factors to produce different intensities.

For explaining diffraction, one first produces the multiple wavelets reaching the point of interest from the slit as per Huygens principle. Following this one then evokes Fresnel's idea of interference to combine them all and explain the appearance of fringes.

In fact Fresnel encapsulated this whole idea into a general integral formula that calculates the diffraction in an arbitrary configuration by summing together phase weighted individual contributions.

Its noteworthy that in modern times the explanation of diffraction/interference phenomenon based on destructive/constructive wave superposition is so ubiquitous that one hardly considers the distinction to be of any practical importance.

Answer 2

To my knowledge Huygen did not study diffraction, but refraction and reflection. However, you asked the question whether Huygen's principle describes diffraction. I would argue that this must be answered with a clear YES! This is e.g. in line with Goodman, who writes in his "Fourier optics" book, which is one of the standard texts of this field:

There is a fascinating history associated with the discovery and explanation of diffraction effects. The first accurate report and description of such a phenomenon was made by Grimaldi and was published in the year 1665, shortly after his death. [...]

The initial step in the evolution of a theory that would explain such effects was made by the first proponent of the wave theory of light, Christian Huygens, in the year 1678. [...]

[... Newton ...]

[...] In that year [1804], Thomas Young, an English physician, strengthened the wave theory of light by introducing the critical concept of interference. The idea was a radical one at the time, for it stated that under proper conditions, light could be added to light and produce darkness.

The ideas of Huygens and Young were brought together in 1818 in the famous memoir of Augustin Jean Fresnel. By making some rather arbitrary assumptions about the amplitudes and phases of Huygens' secondary sources, and by allowing the various wavelets to mutually interfere, Fresnel was able to calculate the distribution of light in diffraction patterns with excellent accuracy.

It is a well-known fact in optics, that Huygen's model was not complete. The same is true for Fresnel, Sommerfeld and Rayleigh. They all try to explain diffraction by the superposition of the light inside an aperture. This simplifies the description, but physically it makes sense (at least to me) that it's the boundary of the aperture which is responsible for diffraction. In a latter section (see sec. 3.9) Goodman provides some references where such descriptions can be found. If you are interested, please look it up.