Asymptotic analysis for superfocusing of the electric field in between two nearly touching metallic spheres

Abstract

We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region between the two spheres. The enhanced field can be arbitrary large with the generic blow-up rate $|\epsilon \ln \epsilon {|}^{-1}$ in three dimensional space, where $\epsilon$ is the distance between the spheres. In this paper we derive rigorously an asymptotic formula of the electric field consisting of elementary functions. The asymptotic formula explicitly characterizes superfocusing of the electric field in terms of the spheres radii, the distance between the spheres, and the external field. We illustrate our results with numerical calculations.

References in corpus (2)

• Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers
• Optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions

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• Characterization of Electric Fields for Perfect Conductivity Problems in 3D
• Two types of electric field enhancements by infinitely many circular conductors arranged closely in two parallel line