# Visualizing diffraction with Huygens' principle

I understand (both intuitively and mathematically) Huygens' principle -- that a wave front can be thought of as a sum of infinitely many spherical wavelets, which are each themselves a source of the wave. However, I've had one burning question with visualizing the consequences of Huygens' principle with diffraction. People often say to think of diffraction using the following visual:

Often the idea with this visual is that because the "sides" of the wave front get cut off, all that remains on the very "outsides" are spherical wavelets that give it this curved shape.

My question is: aren't those spherical wavelets already before, though? What if we think of this visual like this:

In this sense, wasn't the wave front always curved? What specifically is it about going through the slit that does anything other than just (for lack of a more scientific phrasing) "cutting the sides off of" the already curved wave front?

Does the answer have anything to do with the fact that the wave front is much, much longer than the wavelength of the wave, and that the slit's opening width is on an order of magnitude close to that of the wavelength? If this is the answer, why?

• Because of your "cutting off the sides off" of the wavefront that the slit will do, it does not matter that the wave prior to the slits are curved or infinite plane waves, and for simplicity, we tend to think of it as infinitely large plane waves. The wavefront's long length, v.s. wavelength, v.s. slit opening, is not that important to this answer. We just want to explain the observed fact that the waves seem to still propagate at the centre as almost plane waves, but curve outwards nearer the sides. Commented Dec 13, 2023 at 7:14

(Incidentally, physicists tend to be very generous with the word 'principle'. It seems to me: if you call everything a principle then in the end you are diluting the meaning of the word 'principle' down to nothing. I prefer to refer to the concept as Huygens' wavefront hypothesis)

We observe that it is possible to create a beam of light that hardly loses any light in sideways direction. According to a naive interpretation of the wavefront hypothesis the wavelets generated at the sides should result in a lot of energy leaving the beam in sideways direction.

My understanding is that the work has been done, but there is no easy way to communicate how the apparent contradiction can be resolved.

It's not that physicists don't care, I presume, but Huygens' wavefront hypothesis must hold good. Validating it would give a green light, but the physics community is already committed anyway; large areas of physics depend on it.

These are two articles I have found

Optics Letters / Vol. 16, No. 18 / september 15, 1991
David A. B. Miller
Huygens wave propagation principle corrected
Miller uses dipoles instead of point sources.
In the introduction Miller remarks about other treatments: 'The problem is solved mathematically by Kirchhoff's rigorous integration of the wave equation, but the intuitive appeal of Huygens' simple principle is lost.'

Nature scientific reports 2021
Forrest L. Anderson
Huygens’ Principle geometric derivation and elimination of the wake and backward wave

Normally I always quote from a question and answer it specifically. I find that difficult with your question, but nevertheless let me try to explain.

In a pressure wave between two media, the pressure always spreads spherically: If you have a point excitation (stone in a pond), you get a spherical propagation of the oscillating pressure. If you take a long board as excitation, you get a plane wave (as the spherical propagation of infinitesimal points compensate each other), but at the ends of the board you get a spherical propagation again.

With light respectively EM radiation the story looks quite different. Although you don't need modulated EM radiation - i.e. a radio wave - you get a periodic distribution of the transmitted photons behind an edge or a slit or several of them. And that even if you emit the photons individually (then of course only over a longer observation period).

To clarify this again, in the best case you have photons from a monochromatic source and cannot determine any wave property of the radiation. You only know that each emitted photon has an oscillating magnetic and an oscillating electric field component and that it is an indivisible quantum between emission and absorption on the observation screen.

No interaction with each other, as is essential for a mechanical wave in a medium. Only photons, a vacuum (air is not an obstacle for the photon at short distances) and an obstacle with an edge. The edge in turn has surface electrons and researchers generate phonon and other "exotic" energy oscillations in the material of the obstacle.

This is the end of the explanation, as it is forbidden to speculate that the interaction photon - phonon in the material of the edge leads to the periodic distribution of photons on the observation screen.

Huygens's principle can somewhat help picture diffraction, but it doesn't represent what's really happening. Physically there are no wavelets or wave fronts. Huygens principle could be a good analogy for water wave diffraction because there's a medium and other forces involved. However, light diffraction is different. It involves individual particles of light (photons) moving from one point to another, and each one can diffract on its own, independently of the others.