First of all, it's SILICON, not SILICONE. Silicone refers to the rubber-like polymers that include silicone in their chemical structure.
There's "quantum computers", but I suppose those might fit under "optical".
Organic processors were once a thing, though I'm not sure where they are now in terms of development. I remember them involving threatening bacteria with oblivion unless they calculate things for you

GaAs and other "three-five" semiconductors are in use now, but you won't ever see them used for general circuit design, including processors. The materials are more expensive and they're not even necessarily suitable for general-purpose circuits. GaAs designs would be very power-hungry. You'll basically see this stuff in microwave amplifiers (as discrete transistors!) and in highly-efficient solar panels.
Though silicon is still a major part of it, I would take a look at silicon-carbide. I know very little, but it's popped up a lot lately.
I am or at least I was a very green IC designer for MIT Lincoln Laboratory (laid off), so I at least have exposure to the field. They actually developed the 193nm wavelength photolithography systems that EVERYONE uses today. They tried to develop something newer, but apparently extremely high quality optical glass is hard to come-by, so they weren't able to get anything off the ground. Instead companies these days play tricks with their 193nm lithography systems to make them expose objects 10nm and smaller, which people once thought impossible.