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“Homogenization of photonic and phononic crystals” F. Pérez Rodríguez

International Jubilee Seminar “Current Problems in Solid State Physics” November 15-19, 2011, Kharkov, Ukraine. “Homogenization of photonic and phononic crystals” F. Pérez Rodríguez Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apdo. Post. J-48, Puebla, Pue. 72570, M éxico

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“Homogenization of photonic and phononic crystals” F. Pérez Rodríguez

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  1. International Jubilee Seminar “Current Problems in Solid State Physics” November 15-19, 2011, Kharkov, Ukraine “Homogenization of photonic and phononic crystals” F. Pérez Rodríguez Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apdo. Post. J-48, Puebla, Pue. 72570, México E-mail: fperez@ifuap.buap.mx

  2. Plan • Metamateriales fotónicos • Metamateriales fonónicos

  3. Photonic crystal Photonic metamaterial

  4. Refraction index

  5. Photonic metamaterial Pendry and Smith, Phys.Today (2004)

  6. Poynting and wave vectors Positive- index or right-handed material. Negative-index or left- handed material.

  7. fuente kp Sp kװ kn Sn Refracción negativa

  8. Simulation of refraction Pendry and Smith, Phys.Today (2004).

  9. Observation of negative refraction Shelby, Smith and Schultz, Science (2001)

  10. J. Valentine, S. Zhang, T. Zentgraf, et al, Nature, 2008

  11. E. Plum, et al (2009)

  12. Focusing with ordinary and Veselago lenses Pendry and Smith, Phys.Today (2004).

  13. How to “make” the PC uniform? Conventional approach: (Bloch) wavelength >> lattice constant (period) Homogenization or mean-field theory Rapid oscillations of fields are smoothed out:

  14. Theory is very general: • Arbitrary dielectric, metallic, magnetic, and chiral • inclusions. • Arbitrary Bravais lattice. • Inclusions in neighboring cells can be isolated or • in contact.

  15. Material characterization Tensors of the bianisotropic response Particular cases: magnetodielectric and metallomagnetic photonic crystals with isotropic inclusions

  16. Homogenization of Photonic Crystals V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, J. Appl. Phys. 106, 103520 (2009). Maxwell’s Equations at micro-level

  17. A photonic crystal being periodic by definition:

  18. Master equation

  19. Macroscopic fields

  20. Effective parameters Homogenization

  21. Cubic lattice of small spheres Maxwell Garnett

  22. Cubic and Orthorhombic PCs

  23. Cubic and Orthorhombic PCs

  24. Cubic lattices

  25. Cubic lattices

  26. Metallic wires z f = 0.001 r/a = 0.017 p = cμ0a σ

  27. Pendry´s formula

  28. Magnetic wires

  29. High-permeability metals and alloys

  30. Magnetic properties of various grades of iron

  31. High-permeability magnetic wires z 1000+10i 0.1 0.2 0

  32. Left-handed metamaterial y z x

  33. Left-handed metamaterial

  34. Magnetometallic PC

  35. 300+5i 1000+10i

  36. Effective plasma frequency for metal-dielectric superlattices B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, Progress in Electromagnetics Research Letters (PIER Lett.) 22, 165-174 (2011) Effective permittivity Rytov (1956) Metal-dielectric superlattice

  37. Xu et al (2005)

  38. Al-glass f=0.5/10.5 PIER Lett. (2011)

  39. Al-glass

  40. Al-glass f=0.5/100.5

  41. J.A. Reyes-Avendaño, U. Algredo-Badillo, P. Halevi, and F Pérez-Rodríguez, New J. Phys. 13 073041 (2011). Material characterization (conductivity) Nonlocal effective conductivity dyadic:

  42. Nonlocal dielectric response Expansion in small wave vectors (ka<< 1): Magneto-dielectric response Bianisotropic response

  43. 3D crosses of continous wires

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