The big problem in photonic computing is actually making an optical transistor, i.e. a switch where the presence of photons coming from one source controls whether of photons coming from another source pass. This is harder than electrical transistors because photons are bosons and don't interact with each other, so even theoretically this is hard to imagine.
Papers that claim some progress pop up every once in a while but I haven't seen anything promising yet.
Yes, general photonic computing is mostly “theoretical” at the moment. Still, discussion of theory is important. I wish I could add more to your comment but I’m so far out of my depth that it would be simply misleading (blind leading the blind). I believe there’s theory saying it’s theoretically possible to create efficient photon<->matter interfaces which could achieve transistor-like behavior … but there’s too much I don’t understand to be able to evaluate whether there are inherent limitations which kill the practical application of the proposed theoretical mechanisms.
I think companies have come up with some practical applications of limited photonic “computing” at interface edges but I’ve heard that until we no longer need to convert photonics to electronics it won’t surpass electronics for general computing.
Possibly a strech, but transistors are basically current amplifiers, so their optical equivalent should be... lasers. Indeed lasers are optical amplifiers. Whether or not they can be turned into logic gates as transistors can, I don't know.
Papers that claim some progress pop up every once in a while but I haven't seen anything promising yet.