DALHM D evelopment and A nalysis of L eft H anded M aterials

1. 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. Typical LHM behavior Resonance and anti-resonance

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

14. LHM Design used by UCSD, Bilkent and ISU LHM SRR Closed LHM T Substrate GaAs eb=12.3 f (GHz) 30 GHz FORTH structure with 600 x 500 x 500 mm3

15. Left-Handed Materials t r1 d r2 w SRR Parameters: r1=2.5 mm, r2=3.6 mm, d=w=0.2mm t=0.9 mm Parameters: ax=9.3 mm ay=9mm az=6.5 mm Nx=15 Ny=15

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

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

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

19. Experiment Theory Bilkent & Forth

20. Retrieval parameters for Bilkent structure Bilkent & Forth

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

29. Closed rings

30. 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 wp of the LHM is much lower than wp of the wires. • There are “phony” LH peaks when wp < wm 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  10 S. Linden & M. Wegener, Karlsruhe

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. 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. 3D Rings & Wires

43. Retrieved Z, n

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

45. e) b) c) d) a) Going to multi-gap structures (1) Reason: requirement for higher symmetry, for use in 3D LH structures • 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: m2(n gaps)~ n m2(1 gap)

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

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

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

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