I am making this an answer because it is too long for comments and in a sense does answer with a reference.
This is a wrong idea of photons that you have:
I don't understand how two photons of the same frequency can have different amplitudes, neither how to produce them.
Two photons of the same frequency have the same "amplitude", since the only thing they have to differ from each other is frequency. Otherwise they are identical. They are the quantum substructure of classical electromagnetism. The macroscopic electric field of a wave consisting of photons does have an amplitude which is statistically built up from the individual photons.
@Lubos Motl has an extensive article of how classical fields are built up from the quantum substructure, and mathematical ability is necessary to understand it. As @dmckee says wave packets come in.
But he also uses the electromagnetic field in a simple example.
The electromagnetic example starts at this paragraph:
However, in the rest of this section, I want to focus on another way how to see classical physics of fields emerge out of large ensembles of photons, one that mimics the thermodynamic limit of statistical physics (even in the context of classical mechanics).