The wave of a photon/Introduction
According the Copenhagen interpretation matter exhibits a wave particle duality which states that a quantum exhibits the properties of both particles and waves. Because the nature of a quantum is unknown, it does not mean that the particle or wave are real physical entities. But until a certain limit one can calculated as if it were classical particles or waves, with classical formula.
For quanta with mass, like the electron, the shape of this wave is a solution of the Schrödinger_equation. The result is a small wave packet around the position of the electron, which in distance degreases fast, but never becomes zero. So in principle the wave is present everywhere in the universe, but very small. According quantum mechanics the wave determines the probability of a particle to be observed at that location, by squaring the wave:
For the massless quanta the Schrödinger equation has no solution, so there is no formula for the shape (envelope) of the wave of a photon. Therefore there are no clear descriptions and a lot of opinions about this shape. The general view is that there still is a wave"packet", which length is determined by the source. In time this would be the coherence time, for which typical time scales are mentioned of nanoseconds for atoms, picoseconds for semiconductors or femtoseconds for light from the sun. Also for photons the wave is supposed to determine the probability, calculated with the same formula.
Although there is no formula, the wave of photon shows often with various experiments, especially with the double slit. By interpreting the results it is possible to draw conclusion about its shape. For the convenience of explanation in the following it will look a real physical wave is mentioned, but that is never the case. In all examples the wave is used as a tool to calculate what the experiments show, so will sometimes also show different behaviour then a normal wave.