Anomalous Refraction and Photonic Crystal Lenses

1. Anomalous Refraction and Photonic Crystal Lenses

2. Wave-Environment Interaction inMesoscopic WorldImportant Features • Wave coherence is important • Complex boundaries or many scatterers • Wavelength ~ Mean scattering distance (Mean free path) • Scattering strength (coupling constant) cannot be too small • Multiple scattering (the bare waves are repeatedly scattered) • The renormalized wave can be very different from the bare waves • The actual size is irrelevant, the relative size is the key parameter. So “Mesoscopic” does not imply “Nanoscale” • Similar phenomena can happen in quantum and classical (electromagnetic and acoustic) systems • Wave equations + Boundary conditions = Physics

3. J. B. Pendry Famous People

4. Photonic crystals as optical components P. Halevi et.al. Appl. Phys. Lett. 75, 2725 (1999) See also Phys. Rev. Lett. 82, 719 (1999)

5. Bikash C. Gupta and Zhen Ye, Phys. Rev. B 67, 153109 (2003) Focusing of electromagnetic waves by periodic arrays of dielectric cylinders

6. Long Wavelength Limit

7. Negative Refraction

8. Permittivity, Permeability Reflection, and Refraction

9. Principle of the Negative Refraction

10. Left-Handed Materials D. R. Smith et. al., Physics Today, 17, May (2000). Phys. Rev. Lett. 84, 4184 (2000) ; Science, 292, 77 (2001)

11. The Building Blocks of LHM + Electric Dipoles Magnetic Dipoles

12. First proposed byV. G. Veselago (1968) s f2 f1 The Idea of the “Perfect Lens” “All this was pointed out by Veselago some time ago. The new message in this Letter is that, remarkably, the medium can alsocancel the decay of evanescent waves. The challenge here is that such waves decay in amplitude, not in phase, as they propagate away from the object plane. Therefore to focus them we need to amplify them rather than to correct their phase. We shall show thatevanescent waves emerge from the far side of the medium enhanced in amplitude by the transmission process.” J. B. Pendry, Phys. Rev. Lett. 80, 3966 (2000)

13. J. B. Pendry, Phys. Rev. Lett. 80, 3966 (2000) J. B. Pendry’s “Perfect Lens”

14. Surface-Plasmon-Polaritons (SPP) SPP exists whenε<0 or μ<0 in theblueregion

15. Subwavelength Focusing Effect Surface-Plasmon-Polariton (SPP)

16. Is it Possible? • “Left-Handed Materials Do Not Make a Perfect Lens”, N. Garcia and M. Nieto-Vesperinas, PRL 88, 207403 (2002) • “Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous”, P.M. Valanju, R. M. Walser, and A. P. Valanju, PRL 88, 187401 (2002)

17. Negative Refractionof Modulated EM WavesAPL 81, 2713 (2002)

18. Simple Explanation

19. Gaussian Beam

20. Refraction of a Wave Packet

21. Perfect Lens ? • Negative Refraction Makes a Perfect Lens J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). • Left-Handed Materials Do Not Make a Perfect Lens N. Garcia et al., Phys. Rev. Lett. 88, 207403 (2002) • Perfect lenses made with left-handed materials: Alice’s mirror? Daniel Maystre and Stefan Enoch, J. Opt. Soc. Am. A, 21, 122 (2004)

22. Perfect Lens ?

23. Radiation field from the source: The radiation field satisfies the Helmholtz equation: System Description Slab thickness: d Permittivity and permeability: Line Source, located at (0, – d/2)

24. Green’s function: Total E field: Calculation of the Electric Field

25. Boundary conditions: Fourier Transform

26. Solution of Green’s Function

27. Ideal lens: 0 I II III IV V 0 0 0 0 I I I I II II II II III III III III IV IV IV IV V V V V Divergenceless condition: p1 p2 p1 p1 p1 p2 p2 p2 Thickness Limitation on an Ideal LHM Lens Phase matching problem: p1 and p2

28. Source No solution can exist in this blank region Virtual images Realizable vs. Unrealizable situations

29. Absorptive Lens (I)

30. Absorptive Lens (II)

31. Subwavelength Focusing

34. Field Strength --- Type I

35. Field Strength --- Type II

36. Field Strength --- Type III

37. Two Cases of Imaging

38. Uncertainty Principle vs. Subwavelength Focusing

40. Energy velocity : Group velocity : It can be shown that Energy velocity vs. Group velocity Wave energy flows along the normal direction of the constant frequency curve (surface)

41. Snell’s Law—The Generalized Form

42. Negative Refraction by Calcite ( Yau et.al. ) http://arxiv.org/abs/cond-mat/0312125

43. Negative Refraction by PC “Refraction in Media with a Negative Refractive Index” S. Foteinopoulou, E. N. Economou, C.M. Soukoulis Phys. Rev. Lett. 90, 107402 (2003)

44. Costas M. Soukoulis et. al., Nature 423, 604, 5 June 2003 Negative Refraction --- Experiment

45. Subwavelength Imaging

46. Subwavelength Focusing by PC

47. All-angle negative refraction without negative effective index Chiyan Luo, Steven G. Johnson, and J. D. Joannopoulos, J. B. Pendry, Phys. Rev. B 65, 201104 (2002) See also: Phys. Rev. Lett. 90, 107402 (2003) Phys. Rev. B. 67 235107 (2003) Phys. Rev. B. 68 045115 (2003)

48. Does subwavelength focusing need negative refraction? L. S Chen, C. H. Kuo, and Z. Ye, Phys. Rev. E 69, 066612 (2004) Z. Y. Li and L. L. Lin, Phys. Rev. B 68, 245110 (2003) S. He, Z. Ruan, L. Chen, and J. Shen, Phys. Rev. B 70, 115113 (2004)

49. Negative refraction or partial band gap effect ? Square lattice, rotated by 45˚ (I) Phys. Rev. E 70, 056608 (2004)  

50. Negative refraction or partial band gap effect? Square lattice, rotated by 45˚ (II) Phys. Rev. B 70, 113101 (2004)