Electromagnetic field distribution in a nanolayer of a photoresist during focusing of a surface plasmon wave on the nanopoint of a scanning metal microtip

A generalized mirror reflection method of electrostatics is formulated and proven for a point charge next to a plane-layered structure, and the case of a point charge next to a film is considered in detail. This method is then generalized to the case of an arbitrary system of charges. It is shown in detail how to apply the obtained method to find the focal distribution of the electric field in the vicinity of the nanopoint of a metal microtip next to a plane-layered structure, which is obtained by convergence (focusing) of a surface plasmon wave towards the nanopoint. The penetration of a focused field into a photoresist film located on the surface of a dielectric or metal half-space is discussed. The generality of the proposed theoretical method is demonstrated by solving the problem of finding the temperature field in the vicinity of a heated paraboloidal tip near a heat-conducting film and a half-space.