Can anyone recommend any papers/studies regarding the relationship of the core diameter of photonic bandgap (PBG) and/or inhibited coupling (IC)/Kagome fibers and signal propagation? I cannot seem to find a discussion in comparing core sizes and efficacy in transmission, although I imagine there must be some influence.
I think you are referring to hollow-core fibers here. Regardless of the exact structure, researchers in this field typically heavily rely on numerical simulations, mostly with finite-element methods. Such simulations are certainly useful to compute the guiding properties of a given fiber, but it is difficult to understand the physics or the scaling behavior from these simulations. For your question, it is probably best to look into the pre-computer literature, namely, the Marcatili & Schmeltzer method. There is an excellent paper by Morten Bache about this, and he calls it the poor man's method, but I think this may actually sometimes more useful than the rich man's comsol: https://arxiv.org/pdf/1806.10416.pdf
I also recommend reading the original Ref. 6. There is a relatively simple equation for the scaling behavior of the losses with diameter.
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