High-Order Hilbert Curves: Fractal Structures with Isotropic, Tailorable Optical Properties

Zuani, Stefano De; Reindl, Thomas; Rommel, Marcus; Gompf, Bruno; Berrier, Audrey; Dressel, Martin

doi:10.1021/acsphotonics.5b00363

Cited by 15 publications

(15 citation statements)

References 31 publications

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“…[3] In contrast, μ-SCs are promising for such applications because of their charge-discharge (CD) rate, high power density, and long cycle life. [20,21] Given the potential advantages of fractal designs, many research groups have recently started to work on fractal electrode designs for several applications, such as in characterization of complex irregular surfaces, [22] neural stimulation, [23] high-density CMOS capacitors, [24] optoelectronic devices, [25,26] biosensors, [27] stretchable electronics, [28] and in radio frequency (RF) MEMS capacitors. [20,21] Given the potential advantages of fractal designs, many research groups have recently started to work on fractal electrode designs for several applications, such as in characterization of complex irregular surfaces, [22] neural stimulation, [23] high-density CMOS capacitors, [24] optoelectronic devices, [25,26] biosensors, [27] stretchable electronics, [28] and in radio frequency (RF) MEMS capacitors.…”

Section: Introductionmentioning

confidence: 99%

“…[4] In addition, compared to thin-film batteries, μ-SCs charge most efficiently by drawing the maximum current that the source can supply, irrespective of voltage, thereby making supercapacitors more appropriate www.advelectronicmat.de structure. [20,21] Given the potential advantages of fractal designs, many research groups have recently started to work on fractal electrode designs for several applications, such as in characterization of complex irregular surfaces, [22] neural stimulation, [23] high-density CMOS capacitors, [24] optoelectronic devices, [25,26] biosensors, [27] stretchable electronics, [28] and in radio frequency (RF) MEMS capacitors. [21,29] Fractal designs have also been theoretically predicted to enhance the performance of electrochemi cal systems since they maximize the electrochemically active surface area while minimizing energy lost during the transport of ions within the fractal network.…”

Section: Introductionmentioning

confidence: 99%

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Fractal Electrochemical Microsupercapacitors

Hota

Jiang

Mashraei

et al. 2017

Adv Elect Materials

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The first successful fabrication of microsupercapacitors (μ‐SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO2 thin‐film electrodes as prototypes, μ‐SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ‐SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin‐film RuO2 electrodes. The energy density of the Moore design is 23.2 mWh cm−3 at a volumetric power density of 769 mW cm−3. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm−3 at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ‐SCs that use thin‐film electrodes at no extra processing or fabrication cost.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractal Electrochemical Microsupercapacitors

Hota

Jiang

Mashraei

et al. 2017

Adv Elect Materials

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show abstract

“…The system studied here was the 64 x 64 square lattice Ising model with cyclic boundary conditions in all directions. showed in Fig 6 ( De Zuani et al, 2015;Akıncı, 2014;Jang & Grimson, 2001;Huang, Zhang, Chen, & Du, 2005;Ito & Suzuki, 1987).…”

Section: Probing Fractal Magnetic Domains On Multiple Length Scales Inmentioning

confidence: 94%

“…We present a comprehensive optical investigation of a metallic Hilbert curve of fractal order N = 9 in the visible and near-infrared spectral range. experiments show that high-order fractal nanostructures exhibit a nearly frequency independent reflectance and an in-plane isotropic optical response (De Zuani et al, 2015). 11.…”

Section: Probing Fractal Magnetic Domains On Multiple Length Scales Inmentioning

confidence: 99%

Some Proposition that Links Ferromagnetic Models with Cantorian Set Theory

Gebril¹

2016

APR

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In this paper, we established a link between ferromagnetic models and set theory. Three dimension spins "S X , S y , S z " are considered in Heisenberg model but it is restricted to z_ axis " S z " in Ising mode. By using Brouwer theory, fractal motion of magnetic domains is predicted theoretically in the materials that their magnetism are explained by Ising model. In addition, we achieved that the experimental data of the fractal motion of magnetic domains in the thin films are agreement with the theoretical assumptions that are proposed.

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“…Owing to its hierarchical structuring, the Hilbert curve has been employed in the design of broadband electromagnetic components 4 allowing for long electrical lengths and small footprints. Examples include multiband antenna arrays [40], high impedance metasurfaces [41], isotropic broadband metamaterials [42], transparent electrodes [43], and substrates for surface enhanced Raman scattering [44]. Moreover, metallic metasurfaces with Hilbert curve and other fractal designs have been combined with graphene, in order to realize absorbers [45] and photodetectors [46].…”

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confidence: 99%

Self-Affine Graphene Metasurfaces for Tunable Broadband Absorption

Papasimakis

Tsai

2016

Phys. Rev. Applied

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Graphene has emerged as a promising platform for THz metasurfaces supporting electrically tunable deep-subwavelength plasmonic excitations. Here, we introduce a broadband graphene metasurface based on the Hilbert curve, a continuous, space-filling fractal. We demonstrate enhancement of graphene absorption over a broad frequency band (0.5-60 THz) with an average absorption level exceeding 20%. Owing to the continuous nature of the metasurface patterns, both absorption level and bandwidth can be controlled electrically by varying the graphene charge carrier concentration.Keywords: graphene plasmonics, fractal metasurfaces, broadband absorber 2 Structuring materials [1][2][3][4] at the subwavelength scale has led to the emergence of metamaterials [5][6][7], a paradigm shift in the design of artificial electromagnetic materials [8] resulting in technologically important, as well as exotic, applications, including perfect lenses [9], transformation optics and invisibility cloaks [10], and perfect absorbers [11]. The properties of metamaterials largely arise from resonant dispersion; hence material loss restricts the strength [12] and bandwidth of the metamaterial response [13].In particular, with respect to perfect absorbers, various schemes have been suggested in order to achieve strong absorption in gigahertz [14] [25]. However, such methods often result in complex, bulky configurations, with little tunability. Graphene, a monolayer of carbon atoms, provides an appealing alternative: owing to its band structure, graphene supports plasmonic excitations at the deep sub-wavelength scale [26]. Plasmonic resonators can be realized by structuring graphene at the nanoscale [27][28][29], which can then be employed to construct graphene metasurfaces targeting the THz part of the spectrum [30][31][32][33][34]. At the same time the high sensitivity of the electromagnetic properties of graphene to the charge carrier [35] concentration provides means of electrical control of plasmons [36][37][38]. In 3 addition to tunability, graphene as a plasmonic material allows to strongly confine electromagnetic radiation to much smaller physical volumes compared to typical metals.For example, the plasmon wavelength for graphene is about 50 times smaller than the free-space wavelength, while for noble metals this is an order of magnitude smaller [26,29]. Such strong field confinement allows people to realize very complex graphene structures while retaining a subwavelength footprint. Graphene exhibits broadband nonlinearities and high thermal conductivity, whereas its atomic thickness facilitates device integration.Here, we introduce fractal graphene metasurfaces as tunable, broadband THz absorbers of monoatomic thickness (see Fig. 1(a)). We demonstrate multifold enhancement of absorption over an extremely broad frequency band, where average absorption levels exceed 20% from 0.5 to 60 THz in strongly doped graphene. We show that the absorption band is strongly dependent on the charge carrier concentration enabling dynamic electrosta...

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High-Order Hilbert Curves: Fractal Structures with Isotropic, Tailorable Optical Properties

Cited by 15 publications

References 31 publications

Fractal Electrochemical Microsupercapacitors

Fractal Electrochemical Microsupercapacitors

Some Proposition that Links Ferromagnetic Models with Cantorian Set Theory

Self-Affine Graphene Metasurfaces for Tunable Broadband Absorption

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