I was wondering if a photon is divisible.
If you look at a photon as a particle, then you may be able to split it (in theory).
Is it possible and how do you split it?
The photon cannot be split as one can split a nucleus. As it has zero mass it cannot decay. But it can interact with another particle lose part of its energy and thus change wavelength. It can be transmuted.
Have a look at the compton scattering entry in wikipedia.
Edit: Intrigued by the other answers I searched and found that within special crystals "splits" can happen, if one defines as a split that there can come out two photons whose energy adds up to the original energy of the photon. So in a collective crystal photon interaction there exists such a probability.
The answer somewhat depends on how you define "splitting" of a particle with a zero rest mass. Since it can never be stopped, there is always kinetic energy in a photon which can be converted into other particles. If this counts as "splitting" then the photon can be split e.g., into more photons in a parametric down-conversion. or even into pairs of massive particles and antiparticles if there is enough energy. However, if such excess energy conversion into matter does not count as splitting, then the answer is no. In this (rather loose) sense once can say that a photon is "pure energy".
QED predicts that a photon can split into two photons of lower energy, in a strong magnetic field. This is believed to happen in the magnetospheres of the most magnetized neutron stars, called magnetars. See Baring 2008 and references therein.