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Physics and Applications of Negatively Refracting Electromagnetic Materials Steven M. Anlage, Michael Ricci, Nathan Orloff Work Funded by NSF/ECS-0322844 1 Outline What are Negative Index of Refraction Metamaterials? What novel properties do they have? How are they made? What new RF/microwave applications are emerging? Superconducting Metamaterials Caveats / Prospects for the future 2 Why Negative Refraction? n > 0 n >< 0 1 2 r r Hr refractedH H ray normalθ r Snell’s Law 2 k normalθ θ1 r 2 refracted r n1 sin(θ1) = n2 sin(θ2) k ray k incident r r r ray E EE PositiveNegative Index Index of of Refraction Refraction (PIR) (NIR) = =Right Left Handed Medium (RHM)(LHM) n1>0 n2<0>0 n n11>0>0 Two images! NIRPIR // RHMLHM source No real image Flat“Lens” Lens 3 How can we make refractive index n < 0? ”Use “Metamaterials ng materials withArtificially prepared dielectric and conducti negative values of both ε and μ r r r r DE= ε BH= μ ÎonNegative index of refracti! Many optical properties are reversed! Propagating Waves μ RHM Vac RHM Vac LHM n=εμ >0 ε n=εμ <0 Ordinary Negative Propagating Waves!Non-propagating Waves Refraction Refraction LHM 4 Negative Refraction: Consequences Left-Handed or Negative Index of Refraction Metamaterials ε < 0 AND μ < 0 Veselago, 1967 Propagating waves have index of refraction n < 0 ⇒ Phase velocity is opposite to Poynting vector direction Negative refraction in Snell’s Law: n1 sinθ1 = n2 sinθ2 Flat lens with no optical axis Converging Lens → Diverging Lens “Perfect” Lens (Pendry, 2000) and vice-versa Reverse Doppler Effect Reversed Čerenkov Effect Radiation Tension RHM LHM RHM Flat Lens Imaging Point source “perfect image” V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1967) [Eng. Trans.: Sov. Phys. Uspekhi 10, 509 (1968)] 5 How to make a Negative Dielectric Constant ε(ω) “plasma edge” sThe dielectric constant i 2 EM waves ω p attenuated εr () ω=1 − 2 Losses! ω 0 ω neff = electron concentration ωp Propagating n2 e EM waves ω 2 = eff p ε m The plasma frequency for most metals is in the optical 0 eff or UV spectral ranges Strategy to decrease the plasma frequency ⇒ Thin wire lattice Decrease neff and increase meff with a = 5 mm and r = 1 μm, fp = ωp/2π = 8.20 GHz 6 Metamaterial vs Photonic Crystal wavelength λ elementary Create an “effective medium” with Metamaterial units macroscopic ε , μ , n properties a eff eff that are engineered a ~ λ Use constructive and destructive interference to engineer properties r Photonic of light → ω()k Crystal band structure band gaps defect states negative group velocity … 7 How to Make Negative Permeability Magnetic Permeability μ = μrμ0 r r M = χmagnetic H μ= μ0 (1+ χmagnetic ) A closed ring is diamagnetic (Lenz’s Law) Closed conducting ring r increasing H χ < 0 r magnetic but very small M Enhance χmagnetic with a resonance. Add a capacitor to make an LC oscillator Screening current is enhanced and μ < 0 is possible conducting ring Split-ring resonator (SRR) capacitor inductor 8 Some Ways to Make μeff < 0 region of SRR μeff μeff < 0 0 resonance Jelly Roll SRR Resonance ~21 MHz Planar ~mm SRR 9 Resonance ~10 GHz Metamaterials: Realizations One Strategy: Combine metamaterials so that frequency ranges of ε < 0 and μ < 0 overlap to give n < 0 Left-Handed Materials Theory (Veselago, 1967) Experiments: εeff < 0 accomplished by Pendry, et al. (1998) μeff < 0 accomplished by Pendry, et al. (1999) using split-ring resonators (SRR) εeff < 0 AND μeff < 0 done by D. R. Smith, et al., PRL 84, 4184 (2000) using wires and SRRs Applications: Now Emerging! 10 Metamaterials: Realizations Left-Handed Materials, Negative Refraction: Science 292 77 (2001) Teflon Refraction prism experiment from normal a prism LHM prism prism incident beam 10.5 GHz 11 Evanescent Excitations Consider total internal reflection ( θ inc > θ critical ) Optically less-dense material Evanescent signal Optically dense material θinc Beam of finite width Other examples of Evanescent signals: Excitation of a waveguide beyond cutoff High spatial-frequency (k) non-propagating fields near a source (antenna) 12 “Perfect” Flat Lens Imaging n < 0 Flat Lens can be a Perfect Lens: Pendry PRL 85, 3966 (2000) Image 1 source Image 2 n > 0 n < 0 n > 0 RHM LHM RHM High spatial frequency optical information is carried in evanescent fields These waves are lost in normal “far-field” imaging. However, it is possible to recover this information and make “super resolution” images using LHM lenses! n = -1+i0 Source must be in the near- Losses and deviations from field of the lens to gather n = -1 limit the range of the evanescent waves wavevectors that can be amplified! 13 Experimental Evidence for Super-Resolution Imaging “n=-1” photonic crystal source Source Image Line cut through image λ 13.7 GHz FWHM = λ/5 9.3 GHz with lens image size ~ source size < λ w/o lens Parimi (2003) Losses and deviations from n = -1 limit the image quality Cubukcu (2003) 14 Metamaterials: Novel Applications Thin SubWavelength Cavity Resonators (Engheta, 2002) For a resonance in the z-direction: New possibility – ero net phase windingz p2π k=0 n 1 ( d 1 − n 2) 2 d= integer p z p = 0 “zeroth order resonance” th 0 resonance condition independent of d1 + d2 RHM LHM and depends only on d1/d2 n >0 n <0 d n 1 2 1 = 2 d2 n1 Conducting planes 15 Implementation of an LHM Compact Resonator Microstrip Resonators RHM Transmission Lines RHM/LHM/RHM Conventional RHM LHM Transmission Line (Dual structure) Both resonate at 1.2 GHz RHM/LHM/RHM resonator is 86% smaller Scher, et al., 2004 16 Negative Index Microwave Circuits Dual Transmission Lines with NIR concepts are leading to a new class of microwave devices Compact couplers, resonators, antennas, phase shifters have been demonstrated 1.9 GHz 0th-order resonator T. Itoh, et al., UCLA 17 Metamaterials: Novel Antennas Directional Antenna with n ~ 0 A point source embedded in a metamaterial with n~0 will produce a directed beam nearly normal to the metamaterial/vacuum interface. From [Enoch2002]. RHM Super-Efficient Electrically-small Dipole Antenna (ℓ << λ) LHM Small dipole 3 RHM antenna X ⎛ λ ⎞ 3 Ant= +⎜ ⎟ X ⎛ λ ⎞ Ant= − RRad ⎝ πl ⎠ ⎜ ⎟ RRad ⎝ πl ⎠ LHM shell compensates Im[ZAnt] Factor of 74 improvement in PRad at 10 GHz with λ/1000 antenna Ziolkowski (2003) 18 Scaling LHM (n < 0) Behavior to THz Frequencies… a =120 μm Micro- and Nano-Wire Arrays r =15 μm gold wires ε < 0 for f < ωp/2π = 0.7 THz Wu, et al., 2003 20 nm-thick gold film Nano-Scale Split Ring Resonators μeff < 0 for 81 – 87 THz Linden, et al., 2004 μeff < 0 for 180 THz (1.67 μm) Enkrich, et al., 2005 19 … and on to Infrared and Optical Frequencies Glass μeff Gold εeff wavelength (μm) Jd n < 0 behavior washed out by high losses Im[μ ] ~ 1 m eff TE TM Demonstration of μeff > 1 in optics Impedance Matching εeff Z = Symmetric Antisymmetric μeff electric dipole magnetic dipole mode (670 nm, red) mode (550 nm, green) 20 Grigorenko, et al. Nature 2005 TE TM An Important Limitation: Losses eeff Negative Permittivity 10 Im[ε ] eff Operate just below ω to minimize loss 5 plasma w 2 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ω plasma 0.5 1 1.5 2 wplasma εeff/ ε0= 1 − -5 ω() ω+ i γ Re[ε ] -10 eff 10 ε = -1 + i x Negative5 eff Permeability meff μ = -1 + i x 2 eff d/λ = 0.1 Loss:1 Γ = 1 GHz Transfer Function1.5 0.5 T of a Flat Lens1 x = 10-3 0.1 0.5 -2 0.05 x = 10 x = 10-1f GHz 8 10x = 10120 14 -0.5 0 2.5 5 7.5 10 12.5 15 -1 kx/k0 H L ω0 2= π 10LateralGHz Wavenumber 21 Superconducting Metamaterials Perhaps the only way to demonstrate amplification of evanescent waves (the key new physics) Nb film, ~200 nm thick Nb Wires 0.4” 0.35” What are we doing? 0.9” 1.20” Niobium Wires All-Nb X-band waveguide + couplers Radius~.0125mm 10 Cells (50.8mm) Holey X-Band 22 Negative Index Passband with a Superconducting All-Nb Metamaterial 0 Increasing temperature -20 10 -40 0 -60 -10 -80 -20 10.0 10.4 10.8 -30 SC | (dB) -40 a = 5.08mm NM 21 |S -50 Transmission 0 a = 7.19mm -60 -20 -70 NIR -40 -80 -60 -80 -90 9101112 10 11 12 13 Frequency (GHz) 23 Elementary NIR Material: Single SRR in a 5 x 7 Nb Wire Array 10.76 Q Single SRR -20 10k 10.75 10.74 -30 1k 10.73 f0 (GHz) 10.72 -40 | (dB) 10.71 100 45678 21 T (K) |S -50 ε<0 and μ<0 5.088 K -60 7.047 K 7.494 K -70 7.997 K 10.72 10.73 10.74 10.75 10.76 10.77 24 Frequency (GHz) Caveats and Some Issues to be Addressed Negative Index behavior is limited to finite frequency ranges d(ω ( nω )) Causality constraint: >1 For Im[ε] << 1, Smith, Kroll (2000) dω Dispersion in Re[n(ω)] implies loss: Im[n] > 0 Losses limit frequency range of εeff < 0 and μeff < 0 Decreased range of kx/k0 for evanescent wave amplification Solution: superconductors, active media Scaling to higher frequencies (decrease cell size a) Metal losses generally scale as 1/a or faster Solution: active media, photonic crystals? 25 Conclusions Negatively Refracting Metamaterials offer opportunities for a new kind of optics Negative Index of Refraction Flat Lens Imaging Amplification of Evanescent Waves “Super Lenses” There are many new Emerging Applications Compact (dual TL) structures with enhanced performance Composite LHM/RHM materials with unique field structures New antenna structures Novel optics / NIR lithography SC metamaterials papers: Appl.
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