Resonances and circuit theory for the interaction of metallic disks and annuli with an electromagnetic field

To understand the nature of the electromagnetic resonances of finite metallic surfaces, we formulate a rigorous and rapidly convergent circuit theory for the interaction of a metallic disk and a metallic annulus with an electromagnetic field. Expressions for the current induced and the resonance condition are derived. A new understanding of the nature of the resonances is obtained. For half of the resonances we find a divergent electric field at the edge of the disk, even though it is smooth in shape. For the disk, we compare with previous results using vector spheroidal wave functions and found good agreement for the resonance condition. Our approach can be generalized to other finite surfaces.