# Goal of META-MAT

**The purpose of this website (META-MAT.ORG) is to disseminate research results in acoustic, thermal and mechanical metamaterials through the organization of online seminars, symposia, conferences, summer schools and workshops with industry and the academic world.**

### What Are Metamaterials?

In 2001, **R. M. Walser** coined the term “metamaterial,” defining it as a *macroscopic composite with a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation* [WALSER 01]. Since then, the definition has evolved. **M. Wegener** and others have proposed a broader definition: metamaterials are **rationally designed composites** made from tailored building blocks that result in properties beyond those of their individual materials [KADIC 19].

### Foundations of Metamaterials: Key Theories and Researchers

The concept of metamaterials is deeply rooted in **nano-scale science and electromagnetism**. Pioneering work by **V. Veselago** and **J. Pendry** revolutionized how we understand light propagation in complex media, where the **refraction index** can take any value, real or complex [VESELAGO 68, PENDRY 99, PENDRY 00].

Metamaterials can exhibit both **positive and negative refractive indices**, allowing for unprecedented control over wave propagation. These properties align with **passive and active media concepts**, as described by the **Kramers-Kronig relations** [GRALAK 10]. For more complex cases, the refraction index is expressed as a **tensor** representing anisotropic media with sign-shifting phases [MILTON 02, SMITH 04].

### Negative Refraction and Anisotropic Media

A hallmark of negatively refracting media is the **periodic arrangement** of elements much smaller than the wavelength in question. These arrangements create materials with effective properties such as **negative optical index** or **hyperbolic metamaterials** [IOR 13, PODDUBNY 13]. This allows for revolutionary applications, such as **invisibility cloaks**, which work based on the **form invariance of Maxwell’s equations** [PEN 06].

### Applications: From Electromagnetics to Acoustics

The transition from **electromagnetic to acoustic metamaterials** became feasible through the study of **phononic crystals**, which range in size from meters to nanometers. At these scales, the laws of classical mechanics still apply, enabling researchers to create structures with **complete phononic band gaps**, as demonstrated by **Sigalas and Economou** in 1992 [ECONOMOU 93].

One breakthrough in acoustic metamaterials was the discovery that **high-density rods and spheres** exhibit properties such as **negative effective density** at resonance [LIU 00]. The effective density, like the refractive index, can be represented as a **complex-valued matrix**, which is also seen in **mechanical metamaterials** [CHRISTENSEN 15].

### Expanding Beyond Electromagnetism: New Horizons

Interestingly, the principles behind metamaterials extend beyond electromagnetism and acoustics to include **heat, mass, and light diffusion phenomena**. Researchers have uncovered surprising analogies between these fields and wave propagation, expanding the potential applications of metamaterials [GUENNEAU 13, SCHITTNY 13].

References: https://en.wikipedia.org/wiki/Metamaterial

[ACHAOUI 16] Achaoui Y., Ungureanu B., Brûlé S., Enoch S. & Guenneau S., “Seismic wave damping with arrays of inertial resonators”, *Extreme Mechanics Letters*, **8**, 30-37, 2016 (http://dx.doi.org/10.1016/j.eml.2016.02.004).

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[BERTOLDI 17] Bertoldi K., Vitelli V., Christensen J. & van Hecke M., “Flexible mechanical metamaterials”. *Nature Reviews Materials*, **2** (11), 1-11, 2017.

[CAI 10] Cai W. & Shalaev V. M., “Optical metamaterials”, *New York: Springer*, **10** (6011), 2010.

[CHRISTENSEN 15] Christensen J., Kadic M., Kraft O. & Wegener M., “Vibrant times for mechanical metamaterials”, *Mrs Communications*, **5** (3), 453-462, 2015.

[CRASTER 12] Craster R. V. & Guenneau S., “Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking” (Vol. 166). *Springer Science & Business Media*, Eds. 2012.

[CUI 10] Cui T. J., Smith D. R. & Liu R., “Metamaterials” (p. 1). *Spring Street, NY: springer*, 2010.

[ECONOMOU 93] Economou E.N. & Sigalas M.M., “Classical wave propagation in periodic structures: Cermet versus network topology”, *Phys. Rev.* *B*, **48**, 13434-13438, 1993.

[GRALAK 10] Gralak B. & Tip A., “Macroscopic Maxwell’s equations and negative index media”, *Journal of mathematical physics*, **51** (5), 052902, 2010.

[GUENNEAU 13] Guenneau S. & Puvirajesinghe T.M., “Fick’s second law transformed: one path to cloaking in mass diffusion”, *Journal of The Royal Society Interface*, **10** (83), 20130106, 2013.

[IOR 13] Iorch I.V., Mukhin I.S., Shadrivov I.V., Belov P.A. & Kivshar Y.S., “Hyperbolic metamaterials based on multilayer graphene structures”, *Phys. Rev.* *B*,** 87**, 075416-6, 2013.

[KADIC 19] Kadic M., Milton G. W., van Hecke M. & Wegener M., “3D metamaterials”. *Nature Reviews Physics*, **1** (3), 198-210, 2019.

[LIU 00] Liu Z., Zhang X., Mao Y., Zhu Y., Yang Z., Chan C. T. & Sheng P. “Locally Resonant Sonic Materials”, *Science*, **289**, 1734, 2000.

[MILTON 02] Milton G.W., “The Theory of Composites” *(Cambridge Monographs on Applied and Computational Mathematics). Cambridge: Cambridge University Press*, 2002, doi:10.1017/CBO9780511613357

[MILTON 06a] Milton G.W., Briane M. & Willis J.R., “On cloaking for elasticity and physical equations with a transformation invariant form”, *New Journal of Physics*, **8** (10), 248, 2006.

[MILTON 06b] Milton G.W. & Nicorovici N.A.P., “On the cloaking effects associated with anomalous localized resonance”, *Proceedings of the Royal Society A, ***462**, 3027-3059, 2006.

[MILTON 07] Milton G.W. & Willis J.R., “On modifications of Newton’s second law and linear continuum elastodynamics”, *Proceedings of the Royal Society A*, **463**, 855-880, 2007.

[MINIACI 16] Miniaci M., Krushynska A., Movchan A. B., Bosia F. & Pugno N. M., “Spider web-inspired metamaterials”, *Appl. Phys. Lett.* 109, 071905, 2016.

[NICOLET 94] Nicolet A., Remacle J.F., Meys B., Genon A., Legros W., “Transformation methods in computational electromagnetics”,* Journal of Applied Physics*, **75**, 10, 6036-6038, 1994.

[OBRIEN 02] O’brien S. & Pendry J.B., “Photonic band-gap effects in dielecrtric composites”, *J. Phys. Cond. Matt.* **14**, 4035-4044, 2002.

[PENDRY 99] Pendry J.B., Holden A.J., Robbins D.J. & Stewart W.J., “Magnetism from conductors and enhanced nonlinear phenomena”, *IEEE Transactions on Microwave Theory and Techniques* **47** (11): 2075, 1999.

[PENDRY 00] Pendry J. B., “Negative refraction makes a perfect lens”, *Phys. Rev. Lett.* **85**, 3966-3969, 2000.

[PENDRY 06] Pendry J.B., Schurig D. & Smith D.R., “Controlling Electromagnetic Fields”, *Science* **312** (5781): 1789-1782, 2006.

[PODDUBNY 13] Poddubny A., Iorsh I., Belov P. & Kivshar, Y., “Hyperbolic metamaterials”. *Nature photonics*, **7** (12), 948, 2013.

[SCHITTNY 13] Schittny R., Kadic M., Guenneau S. & Wegener M., “Experiments on transformation thermodynamics: molding the flow of hea”, *Physical review letters*, **110** (19), 195901, 2013.

[SCHITTNY 14] Schittny R., Kadic M., Bückmann T. & Wegener M., “Invisibility cloaking in a diffusive light scattering medium”, *Science ***345** (6195), 427-429, 2014.

[SMITH 04] Smith D. R., Pendry J. B. & Wiltshire M. C., “Metamaterials and negative refractive index”. *Science*, **305** (5685), 788-792, 2004.

[VESELAGO 68] Veselago V.G., “The Electrodynamics of substances with simultaneously negative values of ε and μ”, *Soviet Physics Uspekhi* **10** (4), 509-514, 1968.

[WALSER 01] Walser R.M., “Electromagnetic metamaterials”, paper presented at the *International Society for Optical Engineering (SPIE)*, **4467**, pp. 1-165, 2001.

[WILLIS 81] Willis J.R., “Variational and related methods for the overall properties of composites”, *Advances in applied mechanics*, **21**, 1-78, 1981.

[ZHELUDEV 12] Zheludev N. I. & Kivshar Y. S., “From metamaterials to metadevices”. *Nature materials*, **11** (11), 917-924, 2012.