All artificial metamaterials have a periodic arrangement of cells or pieces of metamaterial with a period or several periods that are small compared to the wavelength.
Can there be metamaterials with a non-periodic structure?
Vadym Slyusar
The main idea behind periodicity in Metamaterials arrangement such that the mutual coupling between cells plays a key role of changing the characteristic impedance of the unit-cell, also to make a regular multiplied phase shift between electric fields. This is required for metasurfaces.
But we can found a non periodic structures of metamaterial, in which the cell is loaded by terminal impedance, such configurations can be found in Filters, Duplexers, phase shifters and so on...
Yes they can. The area of artificial materials is of course an interesting area of research over 100 years old, essentially your question is one related to homogenisation, if your unit-cell is much smaller than a wavelength your system can be considered homogenised and hence can be described via effective media theory's and described in terms of an effective permittivity and permeability. I would suggest for background looking at Maxwell-Garnett and the Bruggeman approach effective media theory's. Lakhtakia presents a comprehensive review of the early work on effective media theories, and a review of more modern work can be found in the paper by Belov that also discusses the homogenisation of metamaterials including a radiation term.
Selected Papers on Linear Optical Composite Materials, Lakhtakia, A. (Ed.) 1996, SPIE Press
Belov, P. and Simovski,C, Phys. Rev. E, 73 (2005)
D. A. G. Bruggeman, Annalen Der Physik, 24, 1935
J. C. Garnett, Phil Trans R Soc Lond, 203, 1904
Thank you Rebecca Seviour ! I will study publications that were proposed by you. For me will be interesting the relationship between periodic and non-periodic structures and what is a limitation for non-periodic homogenization of metamaterials
Dear Vadym Slyusar,
Yes, they can. The concept of metamaterial is a much more general concept. Metamaterials are artifical structures (periodic, quasi-periodic and non-periodic/aperiodic) that allow to tailor the propagation/scattering of electromagnetic waves. Periodic structures are only a subclass of more general metamaterials. One of the reasons for the popularization of metamaterials based on periodic structures is the fact that a very complex problem can be reduced to the "simple" study of a single element, the so-called unit cell, thanks to the Bloch-Floquet theorem.
Thank you, Antonio Alex-Amor ! You confirmed my assumption. I am pleased that we have a common vision of metamaterials theory.
Yes, periodic structures and even array structures for the metamaterials are dispensable. One or more metamaterial units are widely used in antennas, filters and phase shifters to exhibit exotic properties. Also, the concept of metamaterials emphasizes the exotic electromagnetic properties of metamaterials, rather than materials, types of structures, and arrangements. So, either periodic or non-periodic, resonant or nonresonant structures can constitude metamaterials, what's more, metamaterials in a broad sense are not confined to a structure but are evolving into a design concept, with a focus on new properties rather than types of structures. The review papers related to metamaterials development and applications may help you.
[1] S. Xiao, T. Wang, T. Liu, C. Zhou, X. Jiang, J. Zhang., Active metamaterials and metadevices: A review[J]. Journal of Physics D: Applied Physics, 2020, 53(50): 1-24
[2] X. Fu, T. J. Cui., Recent progress on metamaterials: From effective medium model to real-time information processing system[J]. Progress in Quantum Electronics, 2019, 67(May): 1–38
Thank you Xin Wang .Your answer has expanded my situational awareness regarding the area of metamaterials.
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