Plasmon confinement in fractal quantum systems

TL;DR

This paper investigates how fractal geometries like Sierpinski carpets and gaskets influence plasmonic behavior, revealing highly localized modes and dispersion characteristics that could enable quantum-scale light manipulation.

Contribution

It provides the first detailed calculation of dielectric functions for fractal quantum systems, highlighting the unique plasmonic properties of different fractal structures.

Findings

Sierpinski carpet exhibits dispersion similar to regular lattices.

Sierpinski gasket shows highly localized, flat dispersion plasmon modes.

Strong plasmon confinement observed in finitely ramified fractals.

Abstract

Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale.