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...Since the late eighteen hundreds we always describe the photon with a mathematical representation which is the sine wave...

I haven't come across a really concise non-technical description of a photon. In essence, a photon is the smallest excitation of the free electromagnetic field. You use them to describe the interaction between matter and the electromagnetic field. Matter can interact with the electromagnetic field to either generate or absorb photons. The classical sine-wave you would find coming from a laser, for example, is a particular way of "stacking" photons known as a coherent mode. These coherent modes behave like the classical light described by Maxwell's equations.The problem is that you can't think of photons as little particles zipping around space. They're excitations of an underlying field that permeates all space and their emission and detection are modeled by probabilities of interactions of matter with the electromagnetic field.

Geezer, you could say that, but I'd be a bit nervous about the description of a photon as being the smallest detectable excitation of an EM field simply because quantum mechanics is all about observations/detections. If it's the smallest unit of the field we can observe, does it make any sense to talk about smaller units of the field?

John Haniotakis asked the Naked Scientists: If we shot a high energy beam of a specific laser against to another beam of the same kind of laser, with the same energy, at the same time, what happens to the light at the collision point? What happens if the same happens in vacuum?