New Aspects of Old Equations: Metamaterials and Beyond (Part 2) 신종화 KAIST 물리학과

Transcription

1 New Aspects of Old Equations: Metamaterials and Beyond (Part 2) 신종화 KAIST 물리학과

2 Metamaterial Near field Configuration in Periodic Structures New Material

3 Material and Metamaterial Material Metamaterial 0.5nm λ ~ 1 μm 100 nm λ ~ 1 μm ε (Permittivity) μ (Permeability) ε μ 3

4 Photonic Crystal and Metamaterial Photonic Crystal Periodic Metamaterial Periodic Dielectric media Metallic elements Bragg reflection Near field configuration Unit cell size ~ wavelength Unit cell size << wavelength 4

5 Electromagnetic Metamaterial D. Schurig et al., Science 10, 5801 (2006) 5

6 Effective Material Parameters (Assuming Maxwellian macroscopic description) Electric property ε = 1 + r P ε E 0 P: Polarization Magnetic property μ r = 1 + M H M: Magnetization 6

7 Effective Parameters in the Quasi static Regime Negligible electromagnetic fields inside metal Electric fields terminated by surface charges Magnetic fields fended off by surface currents Shape and size of metal inclusions determines P and M, hence, ε and μ. 7

8 Electric Property E P E 8

9 Electric Property E P D = ε 0E + Large P large ε P ε E Purely geometrical effect (non dispersive) 9

10 Electric Property (Alternative Explanation) Measurement of ε via capacitance of a parallel plate capacitor C = Q/V = εa/a ε = (Q/V) (a/a) = ρ av /E av Q Q -Q b/2 a ε V 0 /ε r Q Metal V 0 b/a V 0 -Q -Q ε r = a/b (purely geometric) 10

11 Magnetic Property M H H 11

12 Magnetic Property H M B = μ0 H + Negative M μ < μ 0 ( M) μ H Purely geometrical efffect (non dispersive) 12

13 Magnetic Property (Alternative Explanation) Measurement of μ via inductance L = Φ/I = μn 2 A/l μ = (Φ/I)(l/N 2 A) μ r Φ 0 (B/A)Φ Φ 0 0 I I Cross section area A: total B: air region μ r = B/A (purely geometric) 13

14 Cube Array Large ε ε r ~ a b b Small μ a μ ~ 2b r Moderate n a (2 2 2 unit cells) n = ε r μ r ~ 2 14

15 Broadband, Independent Control Is it possible? of ε and μ Metal inclusions always large ε, small μ? 15

16 Broadband, Independent Control of ε and μ Differences in the boundary conditions for E and H fields Allow an independent control of electrical and magnetic responses via the engineering of geometry 16

17 Isotropic High Index Structures (One unit cell of crystal) J. Shin, J.-T. Shen, and S. Fan, Three-dimensional metamaterials with an ultra-high effective refractive index over broad bandwidth, Phys. Rev. Lett. 102, (2009) 17

18 Electric property E P P The area and separation of faces normal to E field is important. 18

19 Magnetic property H MP M μ1 0. 1μ 0 μ2 0. 5μ0 The average area of current loops (volume enclosed by faces parallel to H field) is important. 19

20 Enhancement of the index ε 2 ε 3 (Fringing field effect) μ2 0. 5μ0 μ μ0 20

21 Comparison of Structures ε r = μ r = n =

22 Numerical Verification 22

23 Numerical Verification Fabry Perot resonance frequencies Index Minimum transmission c Impedance με μ ε 23

24 Numerical Verification ε = 20ε 0 μ = 0.10μ n = ε = 18.3ε n = μ = 0.97μ 0 24

25 So far Geometrical design of unit cell (Nearly ) Independent control of ε and μ over a broad wavelength range. So, what can we do with it? 25

26 Invisibility Cloak? Cloak Video #1

27 Just a video trick. Invisibility Cloak?

28 Invisibility Cloak? Cloak Video #2

29 Optical camouflage. Invisibility Cloak?

30 Invisibility Cloak? Optical camouflage Good engineering problem but not much new physics in it. (Animals have done it for millions of years!)

31 Physics based Invisibility Cloak? Visibility Mainly from absorption and scattering of light (exceptions: fluorescence, other light emitter, etc.)

32 X ray: absorption Visibility

33 Radar: scattering Visibility

34 Sonar: scattering Visibility

35 Physics based Invisibility Cloak? Visibility Mainly from absorption and scattering of light Invisibility No absorption, no scattering But, how?

36 No Absorption, No Scattering? Make the light to circle around the object. Ray optics picture

37 Periscopes? Only in one direction, at the right distance. Mirrors visible.

38 Lifeguard Problem 38

39 Lifeguard Problem 39

40 Lifeguard Problem 40

41 Lifeguard Problem 41

42 Invisibility Cloak Using Graded Index Lens? 42

43 Anisotropic, Inhomogeneous Medium It Works! 43

44 Two Pictures Topological interpretation Material interpretation D. Schurig et al., Opt. Express 14, 9794 (2006) 44

45 Transformation Optics Optical blackhole, wormhole, waveguide, A. Greenleaf et al., Phys. Rev. Lett 99, (2007) 45

46 Metamaterials Beyond ε and μ 46

47 Photo: stock.xchng ID

48 Photo: stock.xchng ID sjtoh 48

49 Interweaving Conductor Metamaterial (ICM) Best described by a non Maxwellian effective medium A V V =, S UA =. t t J. Shin, J.-T. Shen, and S. Fan, Three-dimensional electromagnetic metamaterials that homogenize to uniform non-maxwellian media, Phys. Rev. B 76, (2007) 49

50 Quasi static Mode P P? 50

51 Constraints of Maxwellian Model Assuming Local Parameters Cubic symmetry of the structure ε1 0 0 μ1 0 0 ε = 0 ε 0, μ = 0 μ ε μ 1 zero or two propagating modes modes are isotropic modes are degenerate 51

52 Two Network Example Single mode 52

53 Scalar Field in Full 3D Electric field, z = 0 plane. Full symmetry in the field: imply a non degenerate state No polarization dependency in full three dimension 53

54 N Network Example To be replaced 54

55 Bandstructure N 1 modes (N = 4, in this case) Non degenerate despite the full cubic symmetry of the system 55

56 Bandstructure N 1 modes (N = 4, in this case) Density of state enhancement over a very broad frequency range 56

57 Four Network FCC Example 57

58 Bandstructure k z Γ R k y Triply degenerate in [1 1 1] direction Iso frequency surfaces Anisotropic even with pyritohedral symmetry k x 58

59 Effective Analytic Theory 2 V = S ( U V), t 2 V V 1 V = 2. M VN V i : Spatially varying voltage of i th network E 2 x S, U: Electric Eand magnetic response tensors 1 ( 1 = ε μ E), E= E. 2 y Spatially t homogeneous Analogous to ε 1 and μ 1 Ez 59

60 Effective Analytic Theory 2 V = S ( U V), t 2 V I = = SQ, UA. S, U : Determined by the capacitance and inductance between networks. Dimenion of S and U Number of modes. Symmetry of S and U Anisotropy of modes. Eigenvalues of S U equation Degeneracy of modes. 60

61 Verification of the Model k z k y k x 61

62 Metamaterial (Summary) Deep subwavelength metallic unit cell Designable near field configuration Artificial materials with novel optical properties 62

63 Duality, Babinet s Principle 63

64 Field Localization and Field Enhancement Related, but not the same Localized but not enhanced case: subwavelength hole Metal Substrate 64

65 Electric Field Enhancement Applications: Nonlinear devices, emission enhancements, optical tweezing, etc. Occurs in metal structures with a sharp tip or narrow gap r r, a << wavelength e.g., SNOM tip, bow tie antenna, metal slits a 65

66 Example: Metal Slit Narrow (~ 70 nm) slit on a thin gold film 66

67 Example: Metal Slit Narrow (~ 70 nm) slit on a thin gold film Large (~ 1,000) electric field enhancement in THz regime. M.A. Seo, Nature Photon. 22, 152 (2009) 67

68 What about magnetic fields? 68

69 Babinet s Principle (Simplest Version) S (Infinitesimally thin, absorbing screen) Field source F S 69

70 Babinet s Principle (Simplest Version) S (Infinitesimally thin, absorbing screen) Field source F S* 70

71 Babinet s Principle (Simplest Version) (Field behind S) + (Field behind S*) = Field without any screen S (Infinitesimally thin, absorbing screen) Field source F S F S + F S* = F o F S* R. Harrington, Time Harmonic Electromagnetic Fields 71

72 Babinet s Principle (with Booker s Extension) (Field behind S) + (Field behind S*) = Field without any screen J PEC (E S, H S ) S (Infinitesimally thin, PEC screen) PMC E S + E S* = E o H S + H S* = H o J (E S*, H S* ) R. Harrington, Time Harmonic Electromagnetic Fields 72

73 Babinet s Principle (with Booker s Extension) (Field behind S) + (Field behind S*) = Field without any screen J PEC (E S, H S ) S (Infinitesimally thin, PEC screen) PEC E S + H S* = E o H S E S* = H o M (H S*, -E S* ) η 1 R. Harrington, Time Harmonic Electromagnetic Fields 73

74 Example: Metal Slit vs. Metal Wire Metal slit Metal wire 74

75 Example: Metal Slit vs. Metal Wire If PEC is assumed, the enhancement factor is almost the same. Sukmo Koo et al. Phys. Rev. Lett. 103, (2009) Jonghwa Shin, Geometry induced Magnetic Field Enhancement 75

76 Breakdown of Babinet s Principle Violation of the fundamental assumptions Perfect electric conductor lossy metal (Finite permittivity, non zero skin depth) Infinitesimally thin measurable thickness No exact complementary magnetic structure for a given electric structure Different enhancement factors Jonghwa Shin, Geometry induced Magnetic Field Enhancement 76

77 Example: Metal Slit vs. Metal Wire With realistic metal parameters, enhancement reduces by orders of magnitudes. Need to study the effects of finite ε! Graduate studies Jonghwa Shin, Geometry induced Magnetic Field Enhancement 77