Huygens' principle in EM waves

Question

In trying to understand diffraction, I keep coming across Huygens' principle as the why behind diffraction, and I think I understand the principle itself all right. However, I was hoping to find an explanation of why exactly Huygens' principle explains what happens for electromagnetic radiation.

I can visualize it easily with sound - a particular particle is slammed forward into another particle or group of particles. They don't likely hit head-on so that the second particle or group of particles travels in the exact same direction that the first was travelling in, but rather I imagine it more like billiard balls hitting at different angles with the effect of the particles spreading out in all directions. Please correct me if I'm wrong, but that makes sense to me with what Huygen said. I can see how water waves would follow Huygen's principle in a similar way.

But in EM, there isn't a medium and there aren't particles moving, so would the field somehow behave the same way that the particles do in sound or water waves?

I'd hope to get an intuitive explanation, but if I'm completely wrong in my thinking and the only explanation is that of a pure-wave (as in, not thinking about particles at all and focusing on math) analysis then, I'd like to know.

I have a suspicion that this question is related to my query, but it's somewhat above my head, though I am working on understanding it.

Answer 1

In EM the principle of Huygens is equivalent to Kirchhoff's formula generalized to vector fields http://en.wikipedia.org/wiki/Kirchhoff%27s_diffraction_formula which is way of expressing the diffraction field as the sum of elementary spherical waves. According to a classic explanation due to Kottler, or Stratton & Chu: Diffraction Theory of EM Waves, Phys.Rev. 1939., what "makes" the waves diffract at the edge can be viewed as a field of a current that is induced along the edge by the incident field.

Answer 2

You can think of Huygens's principle as a mathematical principle rather than a principle of physics. As in the Other answer, Huygens's principle can be taken to be roughly a restatement of the Kirchoff diffraction integral, and it is applicable whenever the underlying wave field fulfils the Helmholtz equation:

$$(\nabla^2 + k^2)\,\psi=0$$

So it works for light just as well as it works a sound, because the Helmholtz equation is applicable to both phenomena. The difference between the two phenomena's physics is expressed in the way that you derive the Helmholtz equation as a description of the phenomena in each case: once you've gotten the Helmholtz equation it's all mathematics from thereon.

You might find my answer here applicable and useful to your enquiry.

I hope this doesn't sound dismissive of your doubts, because your question is a good one: you are admirably right to question the applicability when the two phenomena's physics seem so different.

Answer 3

Without assuming that secondary sources actually exist, and without assuming any particular type of wave, one can show that the wave function in a region containing no sources, due to primary sources outside that region, is as if the primary sources had been replaced by a distribution of "secondary" sources on the boundary surface of that region. I have tried to show this from first principles in "Consistent derivation of Kirchhoff's integral theorem and diffraction formula and the Maggi-Rubinowicz transformation using high-school math".