Focusing of the surface plasmon wave on the nanoapex of a scanning metal microtip near a plane-layered structure

A generalized method of mirror reflections of electrostatics for a point charge located near a flat-layered structure is formulated and proved. The method is generalized to the case of an arbitrary system of charges. It is shown in detail how to apply the obtained method to finding the focal distribution of the electric field in the vicinity of the nanoapex of a metal micropoint located near the flat-layered structure, which is obtained when a surface plasmon TM wave converges to the nanoapex. The penetration of the field into the area of the surface layer of the flat-layered structure (photoresist) with a size of the order of the tip rounding radius is demonstrated.