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From Photonic Crystals to Seismic Metamaterials: A Review via Phononic Crystals and Acoustic Metamaterials

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Abstract

The advancement in electromagnetic metamaterials, which commenced three decades ago, experienced a rapid transformation into acoustic and elastic systems in the forms of phononic crystals and acoustic/elastic metamaterials. Since its early discovery, numerous wave phenomena alongside the possible engineering applications have been highlighted. The existing and emerging fields of metamaterials are far more extensive, ranging from optics to acoustic, and all the way to the elastic systems. Numerous fantastic dynamic properties in optics and acoustic/elastic systems have been reported to date, which cannot be found in naturally occurring materials. The present review tends to discuss the historical context, current progresses and possible future outcomes of metamaterials. The fascinating phenomena observed in optics/electromagnetic metamaterials have been explained and linked with acoustic and elastic counterparts. The idea of perfect lens that is governed by negative permittivity and negative permeability via left-handed materials with negative refractive index properties and the transformation optics for invisibility cloaks and optical rainbow effect alongside the hyperbolic metamaterials are reviewed and discussed. Furthermore, the associated transformation into acoustic and elastic focusing effects via graded index metamaterials, acoustic/elastic invisibility cloaks, transformational acoustics, and seismology and metawedges resembling optical rainbow effects and the likes are explained. The present state of the art has been examined and the physics involved in the governing of those peculiar wave mechanisms has been highlighted. Starting from photonic crystals, phononic crystals and acoustic metamaterials, the present state of the art research in some subfields of acoustic metamaterials has been outlined, such as metasurfaces, topological phononic crystals and seismic metamaterials, the three exciting and emerging research topics. The substantial challenges involved in these realms are characterised and the possible future outcome is further evaluated. This review article may assist researchers and engineers to grasp the idea of metamaterials in not only photonic and phononic crystal systems, but also the counterpart subfields.

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Fig. 1

Source: Scopus)

Fig. 2
Fig. 3

taken from electron micrographs of the fabricated structure (bottom). (A) a bump without a cloak. (B) A bump with a cloak. Figure reprinted with permission from Ergin et al. [38] © 2010, AAAS

Fig. 4

reproduced with permission from Xu et al. [77] © 2019, APS

Fig. 5

reproduced with permission from Urzhumov et al. [100] © 2010, APS

Fig. 6

reproduced with permission from Zhang et al. [47] © 2019, APS

Fig. 7
Fig. 8

© 2019, Wiley; (b, d) Smith et al. [137] © 2004, AIP; (c) Liu et al. [128] © 2007, AAAS

Fig. 9

© 2012, APS; (b) Poddubny et al. [142] © 2012, APS; (c) Chshelokova et al. [143] © 2012, AIP; (d) Siddiqui et al. [144] © 2011, Elsevier; (e) Ishii et al. [130] © 2013 Wiley

Fig. 10

reproduced with permission from Smith et al. [33] © 2000, APS. (b) Locally resonant sonic material: lead sphere coated unit cell along with band structure and transmission study curves. Locally resonant subwavelength bandgaps can be seen. Figure reproduced with permission from Liu et al. [160] © 2000, AAAS

Fig. 11

© 2009, Elsevier

Fig. 12

reproduced with permission from Hussein et al. [199] © 2013, Elsevier

Fig. 13

reproduced with permission from Acar et al. [212] © 2013, Elsevier and Yuksel et al. [214] © 2015, Elsevier

Fig. 14

reproduced with permission from Shen et al. [230] © 2014, APS

Fig. 15

© 2018, AIP

Fig.16

© 2019, Elsevier

Fig. 17

reproduced with permission from Zhou et al. [240] © 2020, Elsevier

Fig. 18

reproduced with permission from Ma et al. [277] © 2018, PNAS

Fig. 19

reproduced with permission from Li et al. [61] © 2019, Elsevier

Fig. 20

reproduced with permission from Babae et al. [278] © 2013, Wiley. (d) Programmable Hierarchical Kirigami. Figure obtained from Ning et al. [299] © 2020, Wiley

Fig. 21

reproduced with permission from Li Tiantian et al. [318] © 2017, Nature

Fig. 22.

reproduced with permission from Zhang et al. [336] © 2018, APS

Fig. 23

reproduced with permission from Zhou et al. [54] © 2019, Elsevier

Fig. 24

reproduced with permission from Pal et al. [359] © 2019, IOP

Fig. 25

reproduced with permission from Zhang et al. [336] © 2018, APS

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reproduced with permission from Huo et al. [361] © 2017, Nature

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reproduced with permission from Lee et al. [371] © 2019, APS

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reproduced with permission from Oudich et al. [380] © 2019, APS

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© 2018, Nature

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reproduced with permission from Xia et al. [343] © 2018, Wiley

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reproduced with permission from Lee et al. [403] © 2018, Elsevier

Fig. 32

reproduced with permission from Jacopo M et al. [395] © 2020, IOP

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reproduced with permission from Cao et al. [418] © 2020, APS

Fig. 34

reproduced with permission from Brule et al. [413] © 2014, APS

Fig. 35

reproduced with permission from Palermo et al. [434] © 2016, Nature

Fig. 36

reproduced with permission from Colombi et al. [9] © 2016, Nature

Fig. 37

reproduced with permission from Polermo et al. [445] © 2018, APS

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Data Availability

All data, models or code generated or used in this review article are available from the corresponding author by request.

Abbreviations

AMM:

Acoustic metamaterial

BG:

Bandgap

CMM:

Contemporary metamaterial

DL:

Deep learning

EM:

Electromagnetic

EMM:

Electromagnetic metamaterial

ENZ:

Epsilon near zero

FDTD:

Finite difference time domain

HMM:

Hyperbolic metamaterial

IA:

Inertial amplification

LHM:

Left-handed materials/media

LR:

Local resonance

MM:

Metamaterials

ML:

Machine learning

MS:

Metasurface

OC:

Optical cloaking

ORT:

Optical rainbow trapping

PBG:

Photonic bandgap

PC:

Photonic crystal

PnC:

Phononic crystal

PL:

Perfect lens

PWE:

Plane wave expansion

QHE:

Quantum hall effect

QSHE:

Quantum spin hall effect

QVHE:

Quantum valley hall effect

SAW:

Surface acoustic wave

SMM:

Seismic metamaterial

TA:

Transformation acoustics

THz:

Terahertz

TI:

Topological insulator

TO:

Transformation optics

TMM:

Topological phononic crystal/metamaterial.

TS:

Transformation seismology

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Acknowledgements

The work described in this paper was supported by General Research Grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. CityU 11216318) and City University of Hong Kong (Project No. 7005273)

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  1. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, People’s Republic of China

    Muhammad & C. W. Lim

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Muhammad: Conceptualization, Methodology, Investigation, Data compilation, Writing-original draft, Validation. C. W. Lim: Funding acquisition, Writing-review & editing, Project administration, Resources, Supervision.

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Muhammad, Lim, C.W. From Photonic Crystals to Seismic Metamaterials: A Review via Phononic Crystals and Acoustic Metamaterials. Arch Computat Methods Eng 29, 1137–1198 (2022). https://doi.org/10.1007/s11831-021-09612-8

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