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Simulation and Understanding of Metamaterials

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. Outline. Retrieval Breaking of Scaling Cut-wire pairs Diamagnetic response of SRR

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Simulation and Understanding of Metamaterials

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  1. Simulation and Understandingof 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 • Retrieval • Breaking of Scaling • Cut-wire pairs • Diamagnetic response of SRR • Anisotropic & Chiral metamaterials

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

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

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

  6. Outline • Retrieval • Breaking of Scaling • Cut-wire pairs • Diamagnetic response of SRR • Anisotropic & Chiral metamaterials

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

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

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

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

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

  12. Outline • Retrieval • Breaking of Scaling • Cut-wire pairs • Diamagnetic response of SRR • Anisotropic & Chiral metamaterials

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

  14. Periodic Short-wire Pair arrays With periodicity: 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).

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

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

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

  18. Outline • Retrieval • Breaking of Scaling • Cut-wire pairs • Diamagnetic response of SRR • Anisotropic & Chiral metamaterials

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

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

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

  22. Drude model parameters from Experimental data: Johnson & Christy, PRB 6, 4370 (1972); El-Kady et al., PRB 62, 15299 (2000). lossy negative “dielectric” Im Re good conductor for f < 1THz Metals at THz frequencies Drude model permittivity qualitatively good description for Au, Ag, Cu up to optical frequencies Silver Skin-depth saturates at optical frequencies ! Gold Ratio Skin-depth/structure size becomes larger !! first ~ω1/2 then ~o(1) Copper Aluminum

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

  24. Outline • Retrieval • Breaking of Scaling • Cut-wire pairs • Diamagnetic response of SRR • Anisotropic & Chiral metamaterials

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

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

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

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

  29. Thanks for your attention

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