Homogenization Techniques for Periodic Structures

Sébastien Guenneau (1, 2) , Richard Craster (3) , Tryfon Antonakakis (3) , Kirill Cherednichenko (4) , Shane Cooper (4)

1 EPSILON - EPSILON
2 CLARTE - CLARTE
3 Department of Mathematics [Imperial College London]
4 School of Mathematics [Cardiff]

We describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. We contrast the "classical" homogenization, which is well suited for the description of composites as we have known them since their advent until about a decade ago, and the "non-standard" approaches, high-frequency homogenization and high-contrast homogenization, developing in close relation to the study of photonic crystals and metamaterials, which exhibit properties unseen in conventional composite media, such as negative refraction allowing for super-lensing through a flat heterogeneous lens, and cloaking, which considerably reduces the scattering by finite size objects (invisibility) in certain frequency range. These novel electromagnetic paradigms have renewed the interest of physicists and applied mathematicians alike in the theory of gratings.

Domaines: Optique [physics.optics]

Sébastien Guenneau, Richard Craster, Tryfon Antonakakis, Kirill Cherednichenko, Shane Cooper. Homogenization Techniques for Periodic Structures. E. Popov. Gratings: Theory and Numeric Applications, AMU (PUP), pp.11.1-11.31, 2012, 978-2-8539-9860-4. ⟨hal-00785718⟩