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].

Tensegrity Metamaterials (University of Salerno)

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].

Nanophononic metamaterials: Thermal conductivity reduction by “millions” of local resonances (Ann and H.J. Smead Department of Aerospace Engineering Sciences, Department of Physics, University of Colorado Boulder, USA)

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).

[ALU 05] Alù A. & Engheta N., “Achieving transparency with plasmonic and metamaterial coatings”, Physical Review E, 72 (1), 016623, 2005.

[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.