Determining the non-ideal parallel-plate capacitance of a split-ring resonator gap

Metamaterials in the terahertz range or higher typically have gaps that are far from an ideal parallel plate due to microfabrication limitations on feature size. This work examines the exact solution to the square parallel plate capacitor and finds a valid approximation for capacitance in non-ideal geometries, when the gap size is comparable or larger than the dimensions of the plates.