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Plasmonics and Metamaterials Nick Fang University of Illinois Plasmonics and Metamaterials Nick Fang University of Illinois ME [email protected] © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 1 Outline • Introduction to Metamaterials • New Physics of Metmaterials – Artificial Plasma – High Frequency Magnetism – Negative Refraction – Cloaking • Outlook ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 2 New Frontiers of Photonics Subdiffraction imaging Sensing Telecom applications Fang et al. , Science, 2005 Van Duyne et al., MRS bulletin, 2005 Invisibility cloaks Metamaterials Logeeswaran et al., Appl. Phys. A, 2007 Chen et al., PRL, 2007 • Materials Today’s top 10 advances in material science over the past 50 years • Discover top 100 science stories of the year 2006 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 3 What are Meta-Materials ? Atomic Crystal Lattice Sub- Meta “Atoms” 1nm 10 nm -100 m ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 4 Metamaterials • Definition by a think-tank futurist: “Metamaterials are new materials designated by manipulating extreme magnitudes of physical conditions during synthesis and manufacture.” • Our Definition: A new class of ordered composites from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities. ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 5 Metamaterial vs Natural Medium Common Natural Metamat’l medium Wave Quantum Waves Classical Waves Propagation Thermal Significant Low? excitation Rotation, Translation Symmetry 230 crystal lattices Topology … Atomic Hard or Soft sphere; nearest “Atoms” can be larger Interaction neighbor dominant than lattice Dopant and Random Controllable Defects And More ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 6 Electromagnetic Metamaterials • When and <0 (from Valerie Browning, DARPA) ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 7 Effective Medium Properties <B> In long wavelength limit(a<<), we take the cell as an macroscopic point: all physical properties are smoothed in the cell volume 11 EriGrdVHriGrdVEH()exp( ) ()exp( ) ii VVCC 11 <H> <E> D DB(riGrdVB )exp( ) ( riGrdV )exp( ) ii VVCC DB The effective and can be defined as ratios of the macroscopic fields: EH ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 8 Plasmonic “Atoms” and “Crystals” Natural metal exhibit negative How to lower the plasma frequency? at Optical Frequency: Consider a sparse wire matrix: 2 • “Diluted” electron density: 2 ne 1, p 2 eff i n p m eff 0 eff • Heavy Mass of Electrons (due to magnetic induction): Natural bulk metal 34 mmeff 10 10 e ! a Applications: Tunable optical high 2r pass filter (visible to THz) Pendry, PRL,1996 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 9 How to Lower the Frequency? •“Diluted” electron density – Lowered filling ratio • Heavy Mass of Electrons – MtifftMagnetic effect PmveA 2 2 2 neff e 2c0 p 2 0meff a ln(a / r) ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 10 Plasmonic Response 3 2 E 1 ) 0 -1 rmittivity ( rmittivity 2 ee P p -2 1 2 -3 -4 The wire medium exhibits <0 below the plasma -5 frequency. 00.511.52 Frequency (/ ) p ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 11 At <0 - Pendry, 1998 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 12 Physics of Surface Plasmon (H. Raether, Surface Plasmons, Springer- dielectric Verlag, 1988) E k z + + + + + + k x H metal y =ckx • EM waves propagating along the interface between two media p with their of opposite si gn. 1/2 • Intensity maximum at interface; exponentially decays away from k 12 x c the interface. 12kx ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 13 Propagation length of SPs If consider the absorption in metal: ' '' 1 1 i1 Then, kx become a complex kx=kx’+ikx’’ 1 ' 2 k ' 1 x ' c 1 1 3 ' 2 '' k '' 1 1 x ' ' 2 c 1 1 2 1 For silver: L=22 m at 514.5nm The propagation length L L=500 m at 1060 nm 1 L 2k '' Potential for Chip Scale x optical interconnects! ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 14 Field enhancement due to SPs The ratio of the electromagnetic energy at two sides of the metal film: 2 H (2 /1) y 2 t01t12 exp(ikz1d1) 2 2 t012 1 r r exp(2ik d ) H y H y0 (0 /1) 01 02 z1 1 k k where zi z k 1 0 2 i k t 1 r rik ik ik kzi kz k i k z 2 3 2 2 2 1 1 T t 4 t e2i 1 2 012 01 2 c 0 rad 1 2 1 2 kx (kx kx ) ' 1(0 1) 0 2 1 2 ' T 1 The maximum enhancement: max 1 ' '' For silver, at =350 nm, T~3X102 0 1 1 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 15 High f Magnetism? 2r a B e- Atom Magnetism in natural materials fa des away a bove 100 GHz ! j Array of Split Ring Resonators (Pendry et al, IEEE MTT, 1999) H0 B - + g - + C - + The strong capacitive coupling betw een ind u ctiv e cu rrent loops leads the magnetic resonance ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 16 Artificial Magnetism H inside the cylinder: H0 k eff = 0 0<<1, No Resonance ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 17 Artificial Magnetism (2) Resonance by Impedance Coupling 1 '()iL iz C FF 11 2(iiz ( )) 22z (1 ) 1i r 0 rr00 2z Resonance, Re())0<0 when F 1 r0 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 18 Split-Ring Resonators 3d z 22 0= 2 r 0 0 MP 1 F R=11, a=25, d=2 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 19 The Swiss Roll Structure Enhanced Coupling by adding more turns, Lower resonant Freq ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 20 Application Example: Open MRI M. C. K. Wiltshire et al., Science 291, 849 (2001). ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 21 Dispersion with Magnetic Resonance 0: resonant frequency (->inf) MP: “Magnetic Plasma” Frequency (=0) ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 22 To Higher Frequency: Resistance Issue Hampered Performance at Hig her Frequency (Sca le Effect) ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 23 Metamaterial for telecom Challenges: Fiber-optic communication systems require devices operating in near-IR [λ = 1312nm/229THz (min. dispersion), 1550nm/193THz (min. attenuation)] 50nm!!! Breakdown of linear scaling and saturation Zhou et al ., PRL , 2005 of resonant response of SRRs at optical freq ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 24 Combining the building blocks 3 2 1 ) 0 y ( 2 tt -1 p 1 -2 2 Permittivi -3 -4 -5 0 0.5 1 1.5 2 Frequency (/ ) 10 p 5 ) ( 2 F 0 1 22 0 Permeability -5 -10 00.511.52 Frequency (/ ) p From these buildi ng bloc ks, a ric h varie ty of metamat eri al structures can be developed. ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 25 LHM with both – and - Merger of SRR and Plasmon Wires: -> LHM Smith et al, PRL, 2000;Science, 2001 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 26 Implications of <0, <0 Direction of Energy Flow: SEH Direc tion of Phase Velocity: kE B Phase and Energy propagation directions are thus antiparallel: kEB|| EH S “Lef t-hddhanded materiil”als” ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 27 Negative Refraction H r For TE Waves E i , t t • Boundary Conditions: nˆ E H E H k k 1:RH 1t 1t 1n 1n 1t 1n 2:LH E2t H2t E2n H2n k2t k2n 11EEnn 22 sgn()n2 sgn(n ) 11H nn 22H 1 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 28 Frequency Dispersion The permittivity and permeability must be causal analytic functions; Kramers -Kronig applies: 1 " x 1 '1 x ' 1 PV dx " PVdx x x 1 1 11 UEH 220 medium 44 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 29 Measurement of Refractive Index ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 30 Measurement of Refractive Index Shelby, Smith et al, Science, 2001 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 31 Rerouting EM Waves Controlling Electromagnetic Fields , J. B.Pendry et al,Science 321,2006 Free space field Distorted field H H E E 0 t q 0 t E E H 0 H t q 0 t ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 32 Metamaterial Cloak 2 R2 (r R1) r r R2 R1 r R1 r R2 R2 R2 R1 R2 R2 R1 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 33 Invisibility cloak • “The cloak would act like you've opened up a hole in space," "All light or other electromagnetic waves are swept around the area, guided by the metamaterial to emerge on the other side as if they had passed through an empty volume of space.“ -David Smith ,Duke University Smith et al, Science 2006 ME 598 © 2006-2009 Nick Fang, University of Illinois.
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