Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics

TL;DR

This paper introduces an analytical method using fractional calculus to model and enhance electric fields in nanoplasmonic structures, linking fractional geometry with wave propagation in metal-dielectric nanostructures.

Contribution

It presents a novel analytical approach connecting fractional geometry with wave propagation, enabling explicit expressions for electric field enhancement in nanoplasmonics.

Findings

Derived analytical expressions for electric field enhancement

Established a link between fractional geometry and wave behavior

Provided a new framework for nanoplasmonic analysis

Abstract

We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation. The method is based on fractional calculus and permits to obtain analytical expressions for the electric field enhancement.