Spectral analysis of the Neumann Poincare operator on touching disks and analysis of plasmon resonance
Younghoon Jung, Mikyoung Lim · arXiv (Cornell University) · 2018
We consider the Neumann Poincare operator on domains generated by two touching disks. There can be two types of such domains, each of which has a cusp point at the touching point of two circles. For each domain we define a Hilbert space on which the Neumann Poincare operator is self-adjoint and continuous. Then we computed the complete spectral resolution of the operator. The Neumann Poincare operator has only the absolutely continuous spectrum on the real line [-1/2,1/2]. As an application, we analyze the localized surface plasmon resonance of a crescent-shaped domain.