Quasi-static method and finite element method for obtaining the modifications of the spontaneous emission rate and energy level shift near a plasmonic nanostructure.

We provide numerical demonstrations of the applicability and accuracy of the quasi-static method and the finite-element method in the investigation of the modifications of the spontaneous emission rate and the energy level shift of an emitter placed near a silver-air interface or a silver nano-sphere. The analytical results are presented as a reference. Our calculations show that the finite element method is an accurate and general method.