Contrary to the prior commenter, there is definitely significant engineering going toward this, but it's not clear or likely that photonic computing will supplant electronic computing (at least not anytime soon), but rather most seem to think of it as an accelerator for highly parallel tasks. Two major ways people are thinking of achieving this are using lithium niobate devices which mediate nonlinear optical effects via light-matter interaction, and silicon photonic devices with electrically tunable elements. In the past there was a lot of work with III-V semiconductors (GaAs/InAs/GaN/AlN etc) but that seems to have leveled off in favor of lithium niobate.
Photonics has definitely proved itself in communications and linear computing, but still has a way to in terms of general (nonlinear) compute.