1. FET - Open Domain IST-2001-35511 DALHM Development and Analysis of Left Handed Materials FORTH, Crete, Greece Bilkent University, Ankara, Turkey Imperial College, London, England 2nd year Meeting July 29-30, 2004 Crete, Greece

2. Computational Methods Plane wave expansion method (PWE) R. Moussa, S. Foteinopoulou & M. Kafesaki Transfer matrix method (TMM) Th. Koschny, R. Penciu & P. Markos Finite-difference-time-domain-method (FDTD) M. Kafesaki, R. Moussa, & S. Foteinopoulou Effective medium theories E. N. Economou, Th. Koschny Microwave studio T.O.Gundogdu, R. Penciu, M. Kafesaki & Lei Zhang

3. Transfer matrix method to compute scattering amplitudes

4. New discretization scheme: Symmetry is preserved This new symmetric material discretization completely eliminates the problem of the off-diagonal terms in the transfer matrix approach for sufficiently accurate computation. So we have successfully implemented a new discretization scheme that gives no off-diagonal terms.

5. continuum Homogeneous Effective Medium inversion

6. Generic LH related Metamaterials

7. Resonance and anti-resonance Typical LHM behavior

11. Analytic model for the electric and magnetic response of SRRs

12. Analytic model of the electric and magnetic response of LHMs PRL (accepted, 2004)

13. Electric response of LHM Electric and magnetic response of SRR E and M response of LHM Electric response of wires Electric response of cut wires

14. f (GHz) T 30 GHz FORTH structure with 600 x 500 x 500  m 3 Substrate GaAs  b =12.3 LHM Design used by UCSD, Bilkent and ISU LHM SRR Closed LHM

15. Left-Handed Materials SRR Parameters: r 1 =2.5 mm, r 2 =3.6 mm, d=w=0.2 mm t=0.9 mm Parameters: a x =9.3 mm a y =9mm a z =6.5 mm N x =15 N y =15 w t d r1r1 r2r2

16. Transmission data for open and closed SRRs Bilkent & Forth Magnetic resonance disappears for closed SRRs

17. Bilkent & Forth Effective  p of closed SRRs & wires is much lower than  p of the wires.

18. Best LH peak in a left-handed material Losses: -0.3 dB/cm Bilkent & Forth Peak at f=4 GHz =75 mm much larger than size of SRR a=3.6 mm

19. ExperimentTheory Bilkent & Forth

20. Retrieval parameters for Bilkent structure

21. Transmission spectra in the low frequency region for 3 unit cells

22. Transmission spectra in the higher frequency region

23. Transmission S21 in the lower and higher region (1 unit cell)

24. Retrieved n in the lower frequency region

25. Retrieved n in the higher frequency region

26. Retrieved ,  in the lower frequency region

27. Retrieved ,  in the higher region

28. Closed rings

31. Electric and Magnetic Response of SRRs and LHMs Electric and Magnetic Response are independent. One can change the magnetic response without changing the electric response. GHz and THz magnetic response in artificial structures! The SRR has strong electric response. It’s cut-wire like. Effective electric response of LHM is the sum of wire and SRR. Effective  p of the LHM is much lower than  p of the wires. There are “phony” LH peaks when  p <  m PRL (accepted, 2004)

32. Electric coupling to the magnetic resonance APL 84, 2943 (2004)

33. Photonics and Nanostructures (accepted, 2004)

34. Magnetic response at 100 THz, almost optical frequencies S. Linden & M. Wegener, Karlsruhe   10  

36. Magnetic response at 100 THz, almost optical frequencies S. Linden & M. Wegener, Karlsruhe

37. Magnetic response at 100 THz, almost optical frequencies S. Linden & M. Wegener, Karlsruhe

38. 4 cases of different propagation and polarization for single ring cell = 2.5mm gap azimuthal = 0.3mm ring outer side length = 2.2mm ring width = 0.2mm sub thickness =0.25mm

39. Transmission and retrieved parameters k in the plane gives a negative  region, otherwise  remains positive even though a gap appears in the transmission spectra when E field is along the ring gap.

40. Opposed ring can get rid of the effect of electric coupling

41. Sub thickness dependence the closer the separated opposed rings are, the weaker the electric coupling is. Here are shown transmission spectra and  when the thickness are chosen to be 0.25mm, 0.125mm and 0.075mm

42. 3D Rings & Wires cell = 2.5mm in X/Y/Z ring side length = 2.2mm wire width = 0.2mm ring width = 0.2mm opposed ring separation = 0.2mm this structure is symmetric in 3D and also behaves almost the same for different polarizations see black and red curve below.

43. Retrieved Z, n

44. n and   there are multiple negative index regions from the retrieval code

45. Going to multi-gap structures (1) (a)better than (b) (wider SRR dip); (c) better than (d) (stronger dip); (e) like the conventional SRR but weaker dip (for large separation) Problem: Increase of  m (  m close to  0 ) Gaps act like capacitors in series:  m 2 (n gaps) ~ n  m 2 (1 gap) Reason: requirement for higher symmetry, for use in 3D LH structures a) b) c) d)e)

46. Going to multi-gap structures (2) Solution: Make the gaps smaller or change the design Improvements?  Up to a point Only the left one

47. Promising multi-gap structures from 1D study a) b)b) (a): Detailed study on progress (in 1D) (b): Not studied in detail yet (c): Good LH T 3D structures a) b)b) c) Best combination: (b)+(c) c)

48. Two-sided SRR Structures: No coupling to Electric Field

49. Two-sided SRRs do not have coupling to electric field

51. Multi-Azimuthal SRR

52. 2-gaps SRR adding another gap at the opposite side of ring helps to inhibit the electric coupling Magnetic properties remain the same

53. testing with different k and polarization

54. 4-gaps SRR introducing 4 cuts at each side of the ring respectively may help to build a near-isotropic structure unit cell = 25mm ring side = 22mm ring width = 2mm azimuthal = 50um sub thickness = 2.5mm

56. Comparison of 1/2/4-gaps SRR all SRR have a total azimuthal length 50  m While keeping the sum of the gap widths the same, the 1, 2 or 4 cuts SRR have different resonance frequencies. 4-cuts SRR has a much higher resonance region than single cut ones. To build a LHM with 4cuts SRR, wires need to be more compact to enhance plasma frequency.

57. LHM composed of 4-cuts SRR and Wires Unit cell dimension = 2.5mm Ring side length = 2.2mm Ring width = 0.2mm Wire width = 0.6mm Ring thickness = 17micron Wire thickness = 50micron Sub thickness = 0.25mm Sub permittivity = 2.2 Deposit permittivity = 9.61

61. T and R of a Metamaterial UCSD and ISU, PRB, 65, 195103 (2002) d

62. z, n Inversion of S-parameters d UCSD and ISU, PRB, 65, 195103 (2002)

63. Refractive index n Permittivity  Permeability  Im n > 0 Re n > 0 Im  < 0 ??? Re  > 0 Im  > 0 Re  < 0 Energy Losses Q in a passive medium are always positive in spite of the fact that Im  < 0 Q(  ) > 0, provided that Im n(  ) > 0 and Re z(  ) > 0

64. 1d single-ring SRR: retrieved Re n(  ) via cHEM inversion for different length of the unit cell: 6x10x9... 6x10x14

65. TMM simulated 1d single-ring SRR: retrieved Re n(  ) via cHEM inversion for different resonance frequencies Emulate small SRR gap: we fill the gap with dielectic, eg.eps=300 Vacuum case as before π/(N z  )

66. TMM simulated 1d single-ring SRR: retrieved eps(  ) and mu(  ) via cHEM inversion for different resonance frequencies Emulate small srr gap: we fill the gap with dielectic, eg. eps=300 Vacuum case as before No negative Im  and Im  are observed !

67. TMM simulated 1d single-ring off-plane LHM: retrieved Re n(  ) and Im n(  ) via cHEM inversion Re n(  ) Im n(  )

68. TMM simulated 1d single-ring off-plane LHM: retrieved  (  ) and  (  ) via cHEM

69. Intermediate summary: continuum homogeneous effective material (cHEM) ● cHEM inversion basically works, we find length-independent(!) effective material behavior  Re n(  ) seems to be cut-off at Brillouing zone.  Discrepancy between n(  ) and z(  ): where is the resonance?  Resonance/anti-resonance coupling.  Negative imaginary parts in  or   Deformed resonances, i.e. unexpected shallow negative   What is all this structure at higher frequencies? but problems:

70. Model: Effective periodic material (PEM)

71. PEM analytic SRR model: retrieved n(  ), z(  ) and eps(  ), mu(  ) via cHEM n(  )z(  ) eps(  ) mu(  )

72. PEM analytic LHM model: retrieved n(  ), z(  ) and eps(  ), mu(  ) via cHEM n(  ) z(  ) eps(  ) mu(  )

73. TMM simulated 1d single-ring SRR: retrieved (cHEM) + calculated (PEM-to-cHEM) n(  ), z(  ) Re n(  ) Im n(  ) Re z(  )Im z(  )

74. TMM simulated 1d single-ring SRR: retrieved core+avrg eps(  ), mu(  ) via lattice P EM inversion eps,mu SRR eps,mu LHM

76. 3D Rings & Wires cell = 2.5mm in X/Y/Z ring side length = 2.2mm wire width = 0.2mm ring width = 0.2mm opposed ring separation = 0.2mm this structure is symmetric in 3D and also behaves almost same for different polarization see black and red curve below. different size for gap azimuthal is chosen, they are 0.3mm, 0.2mm and 0.1mm.

77. Retrieved Z, n

78. Retrieved n and   there are multiple negative index regions from retrieval code