Negative refraction in photonic crystals

1. Negative refraction in photonic crystals Mike Kaliteevski Durham University

2. Outine Photonic Crystals: Introduction Negative refraction in left-handed material Non-diffracting beams Electromagnetic wiggler

3. n2 n1 t r Bragg reflector

4. Bragg reflector n1 n1 r n2 d2

5. n2 n2 n1 n1 r d2 d2 Bragg reflector Periodic sequence of the pairs of quarterwave layers is the Bragg reflector. The waves, reflected from different boundaries experience positive interference (enforce each other).

6. Bragg reflector

7. Bloch theorem. Dispersion relations

8. Formation of the photonic band gap in periodic structures   BR BR BR = c/(n1d1+n2d2)

9. Probability of spontaneous emission

10. Probability of spontaneous emission L

11. Microcavity

12. Microcavity Electric field Magnetic field

13. Probability of spontaneous emission L L

14. 2D Photonic crystal

15. 1D photonic crystal

16. 2D photonic crystal

17. 2D photonic crystal

18. Dispersion relations in 2D photonic crystal

19. Plane waves method Wave equation Lattice vector Bloch theorem Reciprocal lattice vector

20. Plane waves method Wave equation Reciprocal lattice vector

21. 2D photonic crystals H E

22. Disperison relations H E

23. Complete PBG

24. Transmissiom of light Modelling Experiment

25. PC spectral filter

26. Defects in photonic crystals m = 1 m = 1 m = 2 m = 2 m = 0 m = 3

27. Photonic crystal waveguide

28. PC Waveguide

29. 3D Photonic crystals OE_15_12982

30. Transmission of light and bandstructure in opals and inverse opals.

31. Photonic microstructures in nature

32. Negative refraction in left-handed material

33. Right - hand materials • Usual electromagnetic word

34. Left - hand materials V.G.Veselago, Electrodinamics of the materials with negative dielectric and magnetic constant (1967) • Inversed Doppler effect • Inversed Vavilov – Cherenkov effect • Negative refraction

35. Refraction Kτ  Kτ

36. Positive refraction Kτ  Kτ

37. Negative refraction Kτ  Kτ

38. Left - hand materials Negative refraction Flat Lense

39. Flat lence n1 n2 n1 D  A n2 =-n1 L

40. Superlence ??? Автор ввел понятие "суперлинза", ...утверждая, что для этого устройства отсутсвует дифракционный предел. Наверное, наиболее убедительное доказательство ошибочности подобного рода утверждений можно найти в ... [ В.Г.Веселаго, УФН, 173 (7) 790 (2003) ] J. B. Pendry , Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 3966 - 3969 (2000) With a conventional lens sharpness of the image is always limited by the wavelength of light. An unconventional alternative to a lens, a slab of negative refractive index material, has the power to focus all Fourier components of a 2D image, even those that do not propagate in a radiative manner. Such “superlenses” ..... Comment: John Michael Williams, Some Problems with Negative Refraction, Phys. Rev. Lett. 87, 249703 (2001) Comment: G. W. 't Hooft, Comment on “Negative Refraction Makes a Perfect Lens”, Phys. Rev. Lett. 87, 249701 (2001) Reply: M. Nieto-Vesperinas and N. Garcia, Nieto-Vesperinas and Garcia Reply:, Phys. Rev. Lett. 91, 099702 (2003)

41. Realization of left-hand materials Metamaterials Photonic crystals

42. Negative refraction in photonic crystals vgr<0 vgr>0 2D hexagonal metallicPC, D=200microns, d = 60 microns

43. Negative refraction in 2D hexagonal photonic crystals

44. Refraction of wave in photonic crystal prism vgr<0 vgr>0

45. Refraction of wave in photonic crystal prism

46. Refraction of wave in photonic crystal prism

47. Refraction of wave in photonic crystal prism

48. Experimental study of negative refraction

49. Experimental study of negative refraction of THzusing QCL

50. Experimental study of negative refraction of THzusing QCL SIGNAL WITHOUT SAMPLE Negatively refracted beam