How does Huygens Principle explain interference? How exactly does Huygens theory about the propagation of wavefronts account for interference?
 A: Every point of a wave front may be
considered the source of secondary
wavelets that spread out in all
directions with a speed equal to the
speed of propagation of the waves.
A: Let us read in detail what the Wikipedia article you linked to tells us:

Huygens' theory served as a fundamental explanation of the wave nature of light interference ... but did not fully resolve all observations such as the low-intensity double-slit experiment first performed by G. I. Taylor in 1909. .. Louis de Broglie proposed his de Broglie hypothesis that the photon is guided by a wave function.

That's odd. Light travels at the highest possible speed and the information across a slit cannot reach the particle in advance. In other words, a wave function for what happens in the future is nonsense. But please note that the wave function is still a useful model for how the particle moves, because we know in advance (empirically) everything about the path with the slit.

The wave function presents a much different explanation of the observed light and dark bands in a double slit experiment. In this conception, the photon follows a path which is a random choice of one of many possible paths. These possible paths form the pattern: in dark areas, no photons are landing, and in bright areas, many photons are landing.

This is a useful model, because interference is a bad explanation (but unfortunately still taught for the bad reason not to overwhelm beginners) for some reasons:

*

*Two photons can’t be in destructive interference because the energy of the two particles can’t vanish. Never we observed radiation with lower frequency (infrared) radiation as a dissipation process from the destructed photons nor a higher frequency radiation as the sum of the two photons.


*Bosons, and photons are bosons, do not interact at this level of energy and density at which we are conducting our experiment. At least not so often that it would affect our double-slit experiment.


*The experiment was further developed and it turns out that single photon experiments over time also show intensity distributions on the screen. The interference explanation must be replaced by another, simpler explanation. De Broglie's wave function is one of them.


*The crux of such experiments is the experiment with only one edge and single photons. Nevertheless the edges appear. Therefore, the best model should be a model that takes into account the interaction between the influenced photon and the properties of the edge. Other players I do not see.

The set of possible photon paths is determined by the surroundings: the photon's originating point (atom), the slit, and the screen. The wave function is a solution to this geometry.

What is obvious for X-ray spectroscopy we have to apply to despicable edges. X-ray spectroscopy is based on the periodicity of the atomic layers of crystals. We should also apply this knowledge to the edges of the slit material. The static electric and magnetic field pattern of the bound electrons on the surface of the slits is influenced by the instrument, and these,periodic in space, fields interact with the photon with its periodic space and time field components.
A: Huygens' principle by itself does not address interference.  His wavelets are shown as apparently positive pulses.  Fresnel later added the idea of instead using sinusoidal wavelets thus allowing for interference since the sinusoidal wavelets have both positive and negative values making additive cancellation possible.  Sometimes now it is referred to as the Huygens-Fresnel principle. However it still has the problem of the wake and the backward wave.  See my Huygens' Principle geometric derivation and elimination of the wake and backward wave, rev2, 3/21/20 ;      DOI: 10.13140/RG.2.2.27684.01927
A: First of all, Huygens's principle is a very basic principle that explains expansion of waves in space and their interference when they meet. Notice, however, that it refers to waves of the same type, e.g. light of the same polarization and frequency. Two waves of the same frequency, but different polarization, can be joined into one (e.g. by a polarization beam-splitter), and won't produce minima and maxima, they will produce a wave with a third direction of polarization.
Also, there exist such things as two-photon interferometry.
But there are cases in which the Huygens' principle, though correct, is not effective, as it is not effective to measure the diameter of New-York meter after meter.  Then, more useful tools have to be developed, according to the configuration examined. An example is diffraction on gratings.
Best regards,
Sofia
