# Huygens' principle in EM waves

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.

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