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Dear Colleagues,

Self-similarity and space-filling properties of fractal geometry have been very useful in antenna and microwave engineering to design multiband antennas and arrays, small antennas, and filters. Moreover, since the boom of metamaterials, many designs have also been approached using fractal geometries. In the optical domain, nano-antennas with fractal geometries have also been proposed.

It is interesting to summarize research and developments with fractals in antenna and microwave engineering, and, at the same time, to present the latest advances in the field.

The present Special Issue aims to gather papers in the field of fractal electrodynamics, applications of antennas, and microwave circuits using fractal geometries, metamaterials, and optical antennas with fractal designs. Papers with conceptual/theoretical approaches and experimental designs are welcomed.

Assoc. Prof. Dr. Jaume Anguera
Dr. Aurora Andújar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Fractal antennas
Self-similar antennas
Fractal arrays
Fractal resonators
Fractal filters
Fractal microwave components
Fractal metamaterials
Fractal nano-antennas

Published Papers (3 papers)

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Research

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12 pages, 3627 KiB

Open AccessArticle

Miniaturization of a Koch-Type Fractal Antenna for Wi-Fi Applications

by Dmitrii Tumakov, Dmitry Chikrin and Petr Kokunin

Fractal Fract. 2020, 4(2), 25; https://doi.org/10.3390/fractalfract4020025 - 04 Jun 2020

Cited by 16 | Viewed by 3267

Abstract

Koch-type wire dipole antennas are considered herein. In the case of a first-order prefractal, such antennas differ from a Koch-type dipole by the position of the central vertex of the dipole arm. Earlier, we investigated the dependence of the base frequency for different antenna scales for an arm in the form of a first-order prefractal. In this paper, dipoles for second-order prefractals are considered. The dependence of the base frequency and the reflection coefficient on the dipole wire length and scale is analyzed. It is shown that it is possible to distinguish a family of antennas operating at a given (identical) base frequency. The same length of a Koch-type curve can be obtained with different coordinates of the central vertex. This allows for obtaining numerous antennas with various scales and geometries of the arm. An algorithm for obtaining small antennas for Wi-Fi applications is proposed. Two antennas were obtained: an antenna with the smallest linear dimensions and a minimum antenna for a given reflection coefficient. Full article

(This article belongs to the Special Issue Fractals in Antenna and Microwave Engineering 2019)

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16 pages, 3281 KiB

Open AccessArticle

Fractal, Scale Free Electromagnetic Resonance of a Single Brain Extracted Microtubule Nanowire, a Single Tubulin Protein and a Single Neuron

by Komal Saxena, Pushpendra Singh, Pathik Sahoo, Satyajit Sahu, Subrata Ghosh, Kanad Ray, Daisuke Fujita and Anirban Bandyopadhyay

Fractal Fract. 2020, 4(2), 11; https://doi.org/10.3390/fractalfract4020011 - 06 Apr 2020

Cited by 20 | Viewed by 7383

Abstract

Biomaterials are primarily insulators. For nearly a century, electromagnetic resonance and antenna–receiver properties have been measured and extensively theoretically modeled. The dielectric constituents of biomaterials—if arranged in distinct symmetries, then each vibrational symmetry—would lead to a distinct resonance frequency. While the literature is rich with data on the dielectric resonance of proteins, scale-free relationships of vibrational modes are scarce. Here, we report a self-similar triplet of triplet resonance frequency pattern for the four-4 nm-wide tubulin protein, for the 25-nm-wide microtubule nanowire and 1-μm-wide axon initial segment of a neuron. Thus, preserving the symmetry of vibrations was a fundamental integration feature of the three materials. There was no self-similarity in the physical appearance: the size varied by 10⁶ orders, yet, when they vibrated, the ratios of the frequencies changed in such a way that each of the three resonance frequency bands held three more bands inside (triplet of triplet). This suggests that instead of symmetry, self-similarity lies in the principles of symmetry-breaking. This is why three elements, a protein, it’s complex and neuron resonated in 10⁶ orders of different time domains, yet their vibrational frequencies grouped similarly. Our work supports already-existing hypotheses for the scale-free information integration in the brain from molecular scale to the cognition. Full article

(This article belongs to the Special Issue Fractals in Antenna and Microwave Engineering 2019)

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Review

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26 pages, 60950 KiB

Open AccessEditor’s ChoiceReview

Fractal Antennas: An Historical Perspective

by Jaume Anguera, Aurora Andújar, Jeevani Jayasinghe, V. V. S. S. Sameer Chakravarthy, P. S. R. Chowdary, Joan L. Pijoan, Tanweer Ali and Carlo Cattani

Fractal Fract. 2020, 4(1), 3; https://doi.org/10.3390/fractalfract4010003 - 19 Jan 2020

Cited by 56 | Viewed by 11416

Abstract

Fractal geometry has been proven to be useful in several disciplines. In the field of antenna engineering, fractal geometry is useful to design small and multiband antenna and arrays, and high-directive elements. A historic overview of the most significant fractal mathematic pioneers is [...] Read more.

(This article belongs to the Special Issue Fractals in Antenna and Microwave Engineering 2019)

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