Birck Nanotechnology Center Metamaterials’2007 Part3: Optical Metamaterials and Applications Vladimir M. Shalaev School of Electrical & Computer Engineering Purdue University, USA Birck Nanotechnology Center Outline ¾ What are metamaterials? ¾ Early electrical metamaterials ¾ Magnetic metamaterials ¾ Negative-index metamaterials ¾ Chiral metamaterials ¾ Nonlinear optics with metamaterials ¾ Super-resolution ¾ Optical Cloaking December 2007 2 Birck Nanotechnology Center What is a metamaterial? Metamaterial is an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties. ---Metamorphose μετα = meta = beyond (Greek) - - A natural material with its A metamaterial with artificially atoms structured “atoms” December 2007 3 Birck Nanotechnology Center Metamaterials: Artificial periodic structures? Lycurgus Cup (4th century “Hot-spots” in fractals AD) Ancient random metamaterial with gold nano particles Shalaev, Nonlinear Optics of Random Media, Springer, 2000; see also papers by Stockman December 2007 4 Birck Nanotechnology Center Photonic crystals vs. Optical metamaterials: connections and differences 01 a a<< . a~ a>> Effective medium Structure dominates. Properties described description using Properties determined using geometrical optics Maxwell equations with by diffraction and and ray tracing , , n, Z interference Example: Example: Example: Optical crystals Photonics crystals Lens system Metamaterials Phased array radar Shadows X-ray diffraction optics December 2007 5 Birck Nanotechnology Center Natural Crystals ... have lattice constants much smaller than light wavelengths: a <<λ … are treated as homogeneous media with parameters ε, μ, n, Z (tensors in anisotropic crystals) … have a positive refractive index: n > 1 … show no magnetic response at optical wavelengths: μ =1 December 2007 6 Birck Nanotechnology Center Photonic crystals ... have lattice constants comparable to light wavelengths: a ~ λ … can be artificial or natural … have properties governed by the diffraction of the periodic structures … may exhibit a bandgap for photons … typically are not well described using effective parameters ε, μ, n, Z … often behave like but they are not true metamaterials December 2007 7 Birck Nanotechnology Center Materials & Metamaterials ε, μ diagram: December 2007 8 Birck Nanotechnology Center Natural Optical Materials Air Water Crystals metals Semiconductors December 2007 9 Birck Nanotechnology Center Outline ¾ What are metamaterials? ¾ Early electrical metamaterials ¾ Magnetic metamaterials ¾ Negative-index metamaterials ¾ Chiral metamaterials ¾ Nonlinear optics with metamaterials ¾ Super-resolution ¾ Optical cloaking December 2007 10 Birck Nanotechnology Center Early Example of Meta-Atoms Twisted jute elements Artificial chiral molecules J. C. Bose, Proceeding of Royal Soc. London, 1898 December 2007 11 Birck Nanotechnology Center Early Electric Metamaterial: Artificial Dielectrics Periodic metal-dielectric plates with effective index of less than 1 W. E. Kock, Proc. IRE, Vol. 34, 1946 December 2007 12 Birck Nanotechnology Center Noble metal: ε < 1 in nature Drude model for permittivity: Silver parameters: ε0 = 5.0 2 ω ω = 9.216 eV εω()=− ε p p 0 ωω()+Γi Γ=0.0212 eV 50 0 -50 -100 Re(ε), experiment -150 Im(ε), experiment Permittivity of Silver -200 Re(ε), Drude Im(ε), Drude -250 500 1000 1500 2000 Wavelength (nm) Experimental data from Johnson & Christy, PRB, 1972 December 2007 13 Birck Nanotechnology Center Electrical metamaterials: metal wires arrays with tunable plasma frequency 2 ω p εε=+'"1i ε =− 22 2 ω(/)ωεωπσ+ ia0 p r 2πc2 ω 2 = p aar2 ln( / ) A periodic array of thin metal wires with r<<a<<λ acts as a low frequency plasma The effective ε is described with modified ωp Plasma frequency depends on geometry rather than on material properties Pendry, PRL (1996) December 2007 14 Birck Nanotechnology Center Metal-Dielectric Composites and Mixing Rules ⎪⎧εεε& =+cc11 2 2 ⎨ ⎩⎪ε ⊥ =+εε12()cc 12 ε 21 ε ε (ω)− ε (ω) ε (ω)− ε (ω) MG h = f i h MG ()+ 2 h ()ωεωε i ()+ 2 h ()ωεωε ε ee= εε'"+ i e (1)(1)dp−+−−εε d dp 1 ⎪⎧ md ⎪⎫ = ⎨ ⎬ 2(d − 1) ±−+−−+−(1)(1)dpε d dpεεε2 4(1) d ⎩⎭⎪ []mdmd⎪ December 2007 15 Birck Nanotechnology Center Electromagnetic properties of metal wires Depolarization factor: ∞ aa a ds q = ijk Lorentz depolarization factor for a spheroid with aspect ratio α:1:1 i ∫0 2 3/2 2 1/2 2 1/2 1 2(sa+++ijk ) ( sa ) ( sa ) p 0.8 Screening factor: κ =−(1qq ) / 0.6 0.4 p(1:1:1)=1/3 Clausius-Mossotti yields 0.2 shape-dependent EMT: Depolarization factor, ε −−εεε0 -2 -1 0 1 2 ffm eff +−(1 ) d eff =0 10 10 10 10 10 Aspect ratio, α:1:1 εκεmeff++ εκε deff 1 ε =±+εε2 4 κεε ε = [(κεκκε+− 1)f 1] +−+ [ ( 1)f ] eff 2κ { m d } md December 2007 16 Birck Nanotechnology Center Outline ¾ What are metamaterials? ¾ Early electrical metamaterials ¾ Magnetic metamaterials ¾ Negative-index metamaterials ¾ Chiral metamaterials ¾ Nonlinear optics with metamaterials ¾ Super-resolution ¾ Optical cloaking December 2007 17 Birck Nanotechnology Center Absence of Optical Magnetism in Nature (Bohr magneton) Magnetic coupling to an atom: ~ μBe= emcea= /2 = α 0 Electric coupling to an atom: ~ ea0 Magnetic effect / electric effect ≈α2 ≈ (1/137)2 < 10 -4 “… the magnetic permeability µ(ω) ceases to have any physical meaning at relatively low frequencies…there is certainly no meaning in using the magnetic susceptibility from optical frequencies onwards, and in discussion of such phenomena we must put µ=1.” Landau and Lifshitz, ECM, Chapter 79. December 2007 18 M cu a r k r e e n i t t a SRR: the first magnetic metamaterials i n r d i n u g c : e d l o b o p y H A metal ring: weak A bulk metal has no magnetic response magnetism in optics C u t in t th ro e d r u in c g e to re so n a A split ring: n ce magnetic resonance Birck December 2007 Double the ring to Split-ring resonator (SRR) Nanotechnology Center strengthen the resonance H Double SRR: enhanced magnetic resonance Theory: Pendry et al., 1999. Experiment: Smith et al., 2000. 19 Birck Nanotechnology Center Artificial magnetic resonators: “Ancient” form and Today’s design SRR for GHz magnetic resonance (Hardy et al., 1981): Modern magnetic units for optical metamagnetism: H E k SRR C-shaped Rod Nanostrip (or nanorod) Pair December 2007 20 Birck Nanotechnology Center Progress in Optical Magnetism Metamaterials Terahertz magnetism a) Yen, et al. ~ 1THz (2-SRR) – 2004 Katsarakis, et al (SRR – 5 layers) - 2005 b) Zhang et al ~50THz (SRR+mirror) - 2005 c) Linden, et al. 100THz (1-SRR) -2004 d) Enkrich, et al. 200THz (u-shaped)-2005 2004-2007 years: from 10 GHz to 500 THZ December 2007 21 Birck Nanotechnology Center Limits of size scaling in SRRs Direct scaling-down the SRR dimensions doesn’t help much… Loss in metal gives kinetic inductance 1 Lsize∝ L ∝ coil kinetic size LLLtotal=+ coil kinetic Csizetotal ∝ 11 1 ω ∝= ∝ Saturation res 2 Ltotal×⋅+⋅⋅ C total (/)() A size B size C size size+ const. Zhou et al, PRL (2005); Klein, et al., OL, 2006 December 2007 22 Birck Nanotechnology Center Magnetic Metamaterial: Nanorod to Nanostrip Dielectric Metal H E k Nanorod pair Nanorod pair array Nanostrip pair • Nanostrip pair has a much stronger magnetic response Lagar’kov, Sarychev PRB (1996) - µ > 0 Podolskiy, Sarychev & Shalaev, JNOPM (2002) - µ < 0 & n < 0 Kildishev et al, JOSA B (2006); Shvets et al JOSA (2006) – strip pairs Svirko, et al, APL (2001) - “crossed” rods for chirality December 2007 23 Birck Nanotechnology Center Visible magnetism: structure and geometries tnmdnmpw==≈35 40 2 b Width varies from 50 nm to 127 nm Purdue group Yuan, et al., Opt. Expr., 2007 – red light Cai, et al., Opt. Expr., 2007 – all the visible December 2007 24 Birck Nanotechnology Center Negative Magnetic Response H E k December 2007 25 Birck Nanotechnology Center Width tunes resonance Resonant TM Non-resonant TE Resonant TM Non-resonant TE Transmission Transmission Reflection Reflection 160 μm 0.9 0.9 0.9 0.9 A 0.8 0.8 A 0.8 B 0.8 0.7 0.7 B 0.7 C 0.7 C 0.6 0.6 0.6 D 0.6 D E 0.5 0.5 E 0.5 F 0.5 0.4 A 0.4 F 0.4 0.4 A B B 0.3 0.3 0.3 0.3 C C Reflection Transmission 0.2 D 0.2 0.2 0.2 D 0.1 E 0.1 0.1 0.1 E F F 0.0 0.0 0.0 0.0 400 500 600 700 800 900 400 500 600 700 800 900 400 500 600 700 800 900 400 500 600 700 800 900 Wavelength (nm) Wavelength (nm) Wavelength (nm) Wavelength (nm) Sample # A B C D E F Cai, et al., Opt. Expr., 15, Width w (nm) 50 69 83 98 118 127 3333 (2007) December 2007 26 Birck Nanotechnology Center Dependence of λm and μ′ on w 800 1.0 Experimental 750 Analytical Permeability 0.5 Permeability ( 700 0.0 650 -0.5 (nm) 600 m -1.0 λ 550 μ ' ) 500 -1.5 450 -2.0 50 60 70 80 90 100 110 120 130 Strip width, w (nm) λm as a function of strip width “w”: experiment vs. theory Negligible saturation effect on size-scaling (as opposed to SRRs) December 2007 27 Birck Nanotechnology Center Outline ¾ What are metamaterials? ¾ Early electrical metamaterials ¾ Magnetic metamaterials ¾ Negative-index metamaterials ¾ Chiral metamaterials ¾ Nonlinear optics with metamaterials ¾ Super-resolution ¾ Optical cloaking December 2007 28 Birck Nanotechnology Center Negative refractive index: A historical review … energy can be carried forward at the group velocity but in a direction that is anti-parallel to the phase velocity… Schuster, 1904 Negative refraction and backward propagation of waves Sir Arthur Schuster Sir Horace Lamb Mandel’stam, 1945 L. I. Mandel’stam Left-handed materials: the electrodynamics of substances with simultaneously negative values of ε and μ Veselago, 1968 Pendry, the one who whipped up the V.