1. Anomalous Refraction and Photonic Crystal Lenses

2. Wave-Environment Interaction in Mesoscopic World Important 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. Famous People
J. B. Pendry

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

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. The Idea of the “Perfect Lens”
First proposed by V. G. Veselago (1968)
“All this was pointed out by Veselago some time ago. The new message in this Letter is that, remarkably, the medium can also cancel 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 that evanescent 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’s “Perfect Lens”
Phys. Rev. Lett. 80, (2000)

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

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, (2002)
“Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous”, P.M. Valanju, R. M. Walser, and A. P. Valanju, PRL 88, (2002)

17. Negative Refraction of Modulated EM Waves APL 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, (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. System Description Slab thickness: d Permittivity and permeability:
Line Source, located at (0, – d/2)
Radiation field from the source:
The radiation field satisfies the Helmholtz equation:

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

25. Fourier Transform
Boundary conditions:

26. Solution of Green’s Function

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

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

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 vs. Group velocity
It can be shown that
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. )

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

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

45. Subwavelength Imaging

46. Subwavelength Focusing by PC

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

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

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

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

51. Negative Refraction?

52. Negative refraction ? (very large incidence angle ) Square lattice, rotated by 45˚

53. Constant Frequency Curve—Triangular lattice
Phys. Rev. B 67, (2003)

54. Negative refraction and left-handed behavior in two-dimensional photonic crystals S. Foteinopoulou and C. M. Soukoulis Phys. Rev. B

55. Constant Frequency Curve
Square Lattice v.s. Triangular Lattice

56. Negative Refraction—Triangular Lattice

57. Negative refraction Triangular lattice, strong reflection

58. Negative refraction Reducing reflection by proper termination of the surfaces

59. Negative Refraction
Beam propagation, proper termination

60. PC Slab Lens – Triangular Lattice (with proper termination of the slab surfaces)

61. Superluminal Phenomenon?

62. Anomalous Reflection

63. Left-Handed Materials Does it really work at the long-wavelength regime?

64. APL, 85, 341 (2004)

65. APL, 85, 1072
(2004)

66. Beyond the Long-wavelength Limit

67. Convex Photonic Crystal Lens (Triangular Lattice)

68. Concave Photonic Crystal Lens (Triangular Lattice)

69. Terraced V shaped PC Lens operating at an NR frequency

70. Calculating the Spot Size and Focal Length
Source field
Distribution Width

71. NR-PC Lens as Wave Coupler

72. Conclusion Subwavelength imaging does not imply negative refraction
Surface termination is important for reducing the reflection
Anomalous refraction, anomalous reflection and strong anisotropy are common features for wave propagation in artificial media beyond the long-wavelength limit
Mesoscopic phenomena can happen in both nanoscale world and macroscopic world, only the relative size between the wavelength and the wave-environment interaction range is important

73. Thanks for Your Attention !