High-Order Hilbert Curves: Fractal Structures with Isotropic, Tailorable Optical Properties
Artikel i vetenskaplig tidskrift, 2015

© 2015 American Chemical Society. Fractals are promising candidates as nonperiodic, nonresonant structures exhibiting a homogeneous, isotropic, and frequency-independent effective optical response. We present a comprehensive optical investigation of a metallic Hilbert curve of fractal order N = 9 in the visible and near-infrared spectral range. Our experiments show that high-order fractal nanostructures exhibit a nearly frequency independent reflectance and an in-plane isotropic optical response. The response can be simulated in the framework of a simple effective medium approximation model with a limited number of parameters. It is shown that high-order Hilbert structures can be considered as a transparent in-plane metal, the dielectric function of which is modified by the filling factor f, hence creating a tunable conductive effective metal with tailorable plasma frequency and variable reflectance without going through an insulator-to-metal transition.


spectroscopic ellipsometry

tunable metal

optical properties

self-similar nanostructures

optical frequencies

Hilbert curve

Bruggeman effective medium approximation




Stefano De Zuani

Universität Stuttgart

T. Reindl


Marcus Rommel

Chalmers, Mikroteknologi och nanovetenskap (MC2), Nanotekniklaboratoriet

Bruno Gompf

Universität Stuttgart

Audrey Berrier

Universität Stuttgart

Martin Dressel

Universität Stuttgart

ACS Photonics

2330-4022 (eISSN)

Vol. 2 12 1719-1724





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