1. Simulation and Understanding of Metamaterials Th. Koschny, J. Zhou, C. M. Soukoulis Ames Laboratory and Department of Physics, Iowa State University. Th. Koschny, MURI NIMs Review May 2007, Purdue

2. Outline 1.Retrieval 2.Breaking of Scaling 3.Cut-wire pairs 4.Diamagnetic response of SRR 5.Anisotropic & Chiral metamaterials

3. Homogeneous Effective Medium Retrieval z, n d PRB, 65, 195104 (2002), Opt. Exp. 11, 649 (2003).

4. Effective medium: Periodicity Artifacts Resonance/Anti-resonance “coupling” “cut-off” deformations negative imaginary part PRE, 68, 065602(R) (2003), PRL 95, 203901 (2005). Curves are for our 200THz SRR, 315nm x 330nm x 185nm unit cell Energy loss is positive for causal branch Im(n) > 0 Re(z) > 0 ν

5. Periodic Effective medium description PRB 71, 245105 (2005), PRE 71, 036617 (2005). Dashed lines: Underlying physical resonances Solid lines: Effective response due to periodicity anti-resonance pseudo-resonance “cut-off” at Brillouin zone edge intermediate band gap “cut-off” & shift generic SRR anti- pseudo- resonance

6. Outline 1.Retrieval 2.Breaking of Scaling 3.Cut-wire pairs 4.Diamagnetic response of SRR 5.Anisotropic & Chiral metamaterials

7. Breaking of Scaling Metals are near-perfect conductors, the effective LC-resonator depends on geometry only Going to THz frequencies Idea: geometric scaling Scale: Such that speed of light invariant and densely stacked ringssparse rings linear scaling

8. PRL 95, 223902 (2005), Opt. Lett. 31, 1259-1261 (2006). Upper frequency limit of the SRRs? 55 nm Theory: Experiment:

9. Why saturation of ω m ? Key point: Kinetic energy of the electrons becomes comparable to magnetic energy in small scale structures (a: unit cell size) V: wire effective volume S: wire effective cross-section n e : e - number density Charge-carriers have non-zero mass !!

10. Effective permeability Can be obtained by effective medium retrieval procedure from transmission & reflection or directly via the magnetic moment of the SRR

11. Limits of simple LC picture “magnetic” modes circular current (anti-symmetric) “electric” modes linear current (symmetric) Magnetic coupling or Electric coupling Electric coupling current density (arrows) & charge density (color)

12. Outline 1.Retrieval 2.Breaking of Scaling 3.Cut-wire pairs 4.Diamagnetic response of SRR 5.Anisotropic & Chiral metamaterials

13. Electric mode of coupled electric resonances Magnetic mode of coupled electric resonances Electric resonance

16. Periodic Short-wire Pair arrays Lagarkov & Sarychev, PRB 53, 6318 (1996); Panina et al., PRB 66, 155411 (2002); Shalaev et al., Opt. Lett. 30, 3356 (2005). Opt. Lett. 31, 3620 (2006), Opt. Lett. 30, 3198 (2005). With periodicity:

17. a b APL 88, 221103 (2006)  < 0 and  < 0 magnetic resonanceelectric resonance Opt. Lett. 31, 3620 (2006) The cross-over of the magnetic and electric resonance frequencies is difficult to achieve!

18. “Fishnet” structure Zhang et al., PRL 95, 137404 (2005). With periodicity: Opt. Lett. 31, 1800 (2006). Realization n<0 at 1.5  m, Karlsruhe & ISU

19. Since the first demonstration of an artificial LHM in 2000, there has been rapid development of metamaterials over a broad range of frequencies. A Brief History of Left-handed Metamaterials Iowa State University involved in designing, fabrication and testing of LHMs from GHz to optical frequencies [4,6,7,10,11,13,14]. Open symbol: µ<0Solid symbol: n<0 n<0 for 1.5 µm (ISU & Karlsruhe) Science 312, 892 (2006) n<0 for 780 nm (ISU & Karlsruhe) Opt. Lett. 32, 53 (2007) µ<0 for 6 THz (ISU & Crete) Opt. Lett. 30, 1348 (2005) n<0 for 4 GHz (ISU & Bilkent ) Opt. Lett. 29, 2623 (2004) Science 315, 47 (2007)

20. Outline 1.Retrieval 2.Breaking of Scaling 3.Cut-wire pairs 4.Diamagnetic response of SRR 5.Anisotropic & Chiral metamaterials

21. Magnetic moment around resonance according to μ ( ω ) should return to unity below and above the resonance?

22. Two types of diamagnetic response below resonance B eliminated from area of ring metal above resonance B eliminated from all enclosed area at resonance

23. Diamagnetic & Resonant currents below resonance at resonance (note: scale is 10x larger) L=10 μ m f=300GHz L=10 μ m f=3.2THz we describe metal by Drude model permittivity then current density is available as: Skin-depth

24. good conductor lossy negative “dielectric” Im Re Metals at THz frequencies Drude model permittivity qualitatively good description for Au, Ag, Cu up to optical frequencies Aluminum Copper Gold Silver Skin-depth saturates at optical frequencies ! Ratio Skin-depth/structure size becomes larger !! first ~ ω 1/2 then ~o(1) Drude model parameters from Experimental data: Johnson & Christy, PRB 6, 4370 (1972); El-Kady et al., PRB 62, 15299 (2000). for f < 1THz

25. Diamagnetic response of open and closed SRR ring dependence on the ring width L=10 μ m f~3THz L=100nm f~70THz

26. Outline 1.Retrieval 2.Breaking of Scaling 3.Cut-wire pairs 4.Diamagnetic response of SRR 5.Anisotropic & Chiral metamaterials

27. Short wires: radius=30nm, length=300nm, Drude-model Gold: F=11% Continuous wires: radius=30nm, Drude-model Gold, (130nm) 2 unit cell: F=16% Anisotropic Arrays of Continuous or Short Nanowires Beware: Periodicity artifacts

28. anisotropic negative refraction left-handed negative refraction Note that the hyperbolic dispersion supports propagating modes for arbitrarily high parallel momenta (which would be evanescent in air).

29. Bilayer chiral metamaterials exhibits strong gyrotropy at optical frequencies. Specific rotatory power: Wavelength (nm) 660, 980, 1310 Optical activity ( ° /mm) 600, 670, 2500 Eigenmodes in chiral medium: right circularly polarized (RCP, +) and left circularly polarized (LCP, -), whose wavenumbers and effective indices are: If the chirality parameter is very large, the refractive index for the LCP eigenmode becomes negative. then Constitutive relations V. A. Fedotov, CLEO Europe 2007 50nm Al 50nm dielectric Chiral Metamaterials: large gyrotropy & negative index

30. Experimental results LCP RCP Frequency (GHz) Transmission (dB) Frequency (GHz) Δ (dB) Frequency (GHz) δ (degree) A.V. Rogacheva, et al., PRL 97, 177401 (2006) Simulations, J. Dong et al. Svirko-Zheludev-Osipov Metamaterial (APL 78, 498 (2001)) Circular Dichroism: Experiment & Simulation

31. Thanks for your attention