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Is there any theoretical limitation on the size of the diameter of an Plastic optical fiber? I would like to transmit visible sunlight through it. I see bundles of small cores available but wouldn't it be more efficient to make a very large single core?

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Light gets "trapped" in an optical fiber when the light travels such that the angle of incidence when hitting the surface is low enough that the optical index change causes the light to "bend" back into the fiber. This is known as total internal reflection. Basically with larger fibers you'll get light bleeding out. Thin fibers work over long distance because the losses are so low. The larger a fiber the larger the loss you'll see, so the less useful it is.

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