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. Bragg reflector r n1n1 n2n2 t

4. n1n1 r n1n1 d2d2 n2n2

5. r n1n1 n2n2 n1n1 n2n2 d2d2 d2d2 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.  BR =  c/(n 1 d 1 +n 2 d 2 )  BR   Formation of the photonic band gap in periodic structures

9. Probability of spontaneous emission

10. L

11. Microcavity

12. Electric field Magnetic field

13. Probability of spontaneous emission L L

14. 2D Photonic crystal

15. 1D photonic crystal

16. 2D photonic crystal

18. Dispersion relations in 2D photonic crystal

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

20. Plane waves method Wave equation Reciprocal lattice vector

21. 2D photonic crystals HE

22. Disperison relations H E

23. Complete PBG

24. Transmissiom of light Experiment Modelling

25. PC spectral filter

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

27. Photonic crystal waveguide

28. PC Waveguide

29. OE_15_12982 3D Photonic crystals

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  KτKτ KτKτ

36.  KτKτ KτKτ Positive refraction

37.  KτKτ KτKτ Negative refraction

38. Left - hand materials Negative refraction Flat Lense

39. L n1n1 n2n2  A D Flat lence n1n1 n 2 =-n 1

40. Superlence ??? Comment: John Michael Williams, Some Problems with Negative Refraction, Phys. Rev. Lett. 87, 249703 (2001)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)Phys. Rev. Lett. 87, 249701 (2001) Reply: M. Nieto-Vesperinas and N. Garcia, Nieto- Vesperinas and Garcia Reply:, Phys. Rev. Lett. 91, 099702 (2003)Phys. Rev. Lett. 91, 099702 (2003) J. B. PendryJ. B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 3966 - 3969 (2000) 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) ] 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”.....

41. Realization of left-hand materials Metamaterials Photonic crystals

42. Negative refraction in photonic crystals v gr <0 v gr >0 2D hexagonal metallic PC, D =200 microns, d = 60 microns

43. Negative refraction in 2D hexagonal photonic crystals

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

45. Refraction of wave in photonic crystal prism

48. Experimental study of negative refraction

49. Experimental study of negative refraction of THz using QCL

50. SIGNAL WITHOUT SAMPLE Negatively refracted beam

51. Non-diffracting beams W 

52. L l1l1 l2l2    A D n1n1 n2n2 n1n1

56. Negative refraction in 1D photonic crystals n1 n2 d 1 d 2

57. Problem: Veselago lens based on 1D PC Bragg reflector does not work. Because system is anisotropic: negative effective mass is required for negative refraction, and for 2 nd, 4 th, etc bands m z 0

58. n1n2 d 1 d 2 x z K 0 Field of the wave in the structure

59. Modes in Bragg reflector

60. Amplitude of waves

61. High contrast: n 1 =3.7 n 2 =1 Low contrast: n 1 =1.4 n 2 =1.8

66. Negative refraction

67. Normal channelling

69. Low contrast: n 1 =1.4 n 2 =1.8 Electromagnetic wiggler

70. Electromagnetic wggler

72. Conclusion: One can hardly make Veselago lense based 1D photonic crystal But there are some interesting effects like “electromagnetic snake”, normal channeling, etc.