Do anti-photons exist?

Well, they do and don't. Depends on your point of view. Here's the story.

Quantum field theory requires for consistency reasons that every charged particle has its antiparticle. It also tells you what properties will the anti-particle have: it will have the same characteristic from the point of view of space-time (i.e. Poincaré group) which means equal mass and spin. And it will have all charges of opposite sign than a matter particle.

If the particle is not charged then QFT doesn't impose any other constraint and so you don't need antiparticles for photons (since they are not charged). But you can still consider the same operation of keeping mass and spin and swapping charges and since this does nothing to photon, you can decide to identify it with an antiphoton. Your call.

The short answer to "are there anti-photons" is "yes", but the disappointment here is that anti-photons and photons are the same particles. Some particles are their own antiparticles, notably the force carriers like photons, the Z boson, and gluons, which mediate the electromagnetic force, the weak nuclear force, and the strong force, respectively. Particles that are their own antiparticles must be electrically neutral, because an aniparticle has the opposite electrical charge as its partner particle. Other things must also be zero, like the number of quarks. A neutron cannot be its own antiparticle because it is made up of quarks and an antineutron is made up of antiquarks. A $\pi_0$ is made up of a quark and an antiquark and is in fact its own antiparticle also.

You can find lots out about particles at the particle adventure(http://particleadventure.orghttp://pdg.lbl.gov), part of the Particle Data Group's web site( ).