Split-Ball Resonator

I am trying to find basic theory of split-ball resonator (SBR). Illustrations are attached.

First illustration shows side and top view of SBR where as second one shows a SBR enclosed inside a cavity/shield. I have simulated this structure in HFSS. Its behaviour is similar to split-ring resonator (SRR) but has higher quality factor than SRR.

you can find the theory of split ball resonator in this link,
http://arxiv.org/abs/1309.7106

good luck

Thanks a lot. This paper presents its use in the field of optics and that to nano-scale. I am looking for basic theory for non planar version.