# Introduction to Metamaterials

###### Introduction to Metamaterials
Introduction to Metamaterials Richard D. Averitt Research Themes “Equilibrium  is  when  all  of  the  fast  stuﬀ  has  happened,  and  all  of  the  slow  stuﬀ  hasn’t.”   ­‐Feynman  Metamaterials: a new field D. R. Smith, et al., Phys. Rev. Lett. 84, 4184 (2000) J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. MTT 47, 2075 (1999) The Irresistible Fantasy of the Invisible Man, and Machine New  York  Times,  2007  The Chameleon The Stealth Fighter: Invisible to Radar Very small radar cross section: shape and absorbing paint A camera and a projector From:  http://www.star.t.u­tokyo.ac.jpFantastic 4: The Invisible Woman by  Lee    Kirby  (1961) "...  she  achieves  these  feats  by   bending  all  wavelengths  of  light  in   the  vicinity  around  herself  ...   without  causing  any  visible   distortion.” ­­ Introduction  from   WikipediaThe Invisible Man by H.G. Wells (1897) "...  it  was  an  idea  ...  to  lower  the   refractive  index  of  a  substance,   solid  or  liquid,  to  that  of  air  — so   far  as  all  practical  purposes  are   concerned.” ­­ Chapter  19   "Certain  First  Principles" Key  Concept:    The  Refrac2ve  Index  à  n     Velocity  of  light  in  free  space:  c   In  a  material:  c/n    Mirage: Optical Illusion The  bending  of  light  due  to  the  gradient  in  refractive  index   in  a  desert  mirageTearing  Space:  conformal  map   We  can’t  tear  space:     Mimic  by  shaping   the  refrac2ve  index  n     Wegner,  Linden  in  Physics  Today,  2010  The  New  York  Times;  3­‐D  model  by  Christoph  Hormann  and  Gunnar  Dolling,  Karslruhe  University  Snell’s  Law •  Reflection: θ = θ i r •  Refraction: n sinθ =n sinθ 1 i 2 t The refraction beam is at the other side of the incident normal. NegaUve  RefracUve  Index:  A  long  history   •  A.  Schuster,  An  IntroducUon  to  the  Theory  of  OpUcs,  (1904)          ­‐  Discussed  in  the  context  of  anomalous  dispersion  as  occurs  at  any  absorpUon  band.   •  L.I.  Mandelshtam,  May  5  1944  (last  lecture)   In fac t, the direction of wave propagation is determined by its phase velocity, while energy is transported at the group velocity. Translated by E. F. Keuster PosiUve  RefracUon   X. Huang, W. L. Schaich, Am. J. Phys.72, 1232 (2004) NegaUve  RefracUon   X. Huang, W. L. Schaich, Am. J. Phys.72, 1232 (2004) Sir  John  Pendry  –  leading  theorist  in   the  area:   In  convenUonal  materials,  the  dielectric  response  derives  from  the  consUtuent   atoms.  As  discussed,  negaUve  or  posiUve  ε(ω)  is  possible  over  a  broad  spectral   range.  However,  natural  materials  with  a  resonant  magneUc  permeability  µ(ω)   dont  exist  above  a  few  THz  (e.g.  FerromagneUc  resonance  in  Fe  at  microwave   frequencies,  or    anUferromagneUc  resonance  in  MnF  at  2THz).   2 Pendry,  Contemporary  Physics  Metamaterials: Expanding our Space 25 30 Pendry et al. suggested that an array of ring 35 resonators could respond 40 to the magnetic 45 component light.   50 55 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 Frequency (GHz) J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. MTT 47, 2075 (1999). Transmitted Power (dBm)LCR  circuits   •  A  circuit  with  an  inductor  (L)  and  capacitor  (C)   saUsﬁes  the  same  equaUon  as  the  mass  spring   system  for  simple  harmonic  oscillaUon.   •  If  we  added  a  resistor  (R)  that  we  get  the   damped  oscillator  equaUon.   –  as  for  the  mechanical  oscillator,  the   soluUon  can  be     •  under  damped:      (  γ      2  ω  )   0 •  criUcally  damped:    (  γ    =    2  ω  )     0 •  over  damped:      (  γ        2  ω  )   0 •  We  can  choose  the  values  of  L,  C,  and  R  to   determine  which  kind  of  damping  we  have.  Comparison  between  mass­‐spring  systems  and  LCR  circuits.  γ    is  the  full­‐width  half  maximum  (fwhm)  of  the  power   quality  factor  Q :   absorpUon  curve  Magnetic Metamaterials: Shaping a resonance Dimensions    λ Effective Medium: µ(ω) 1 ω = 0 LCThe first negative index material, meta or otherwise D.  R.  Smith,  W.  J.  Padilla,  et  al,  Phys.  Rev.  Leh.  14,  234  (2000)  Experimental Demonstration of NI Microwave: ease of fabrication R. A. Shelby, D. R. Smith, S. Schultz, Science 84, 4184 (2001) The Electromagnetic Cloak (2006) The Electromagnetic Cloak Experiment Simulation J. B. Pendry, et al., Science 312, 1780 (2006) D. Schurig, et al., Science, 314, 2006. Would you believe......... Cloaking Other Waves: Sound, Water, Earth The Cone of Silence Cloaking Water Waves M.  Farhat,  S.  Enoch,  S.  Guenneau,  and  A.  B.  Movchan,  "Broadband  cylindrical  acoustic   cloak  for  linear  surface  waves  in  a  fluid",  Physical  Review  Letters  101,.134501  (2008).Cloaking Water Waves Metamaterials at BU Terahertz 1 1 THz à 4 meV à 48K à 300 μm à 33 cm •  Terahertz  gap   •  Infrared  and  visible   •  Microwave   Progress  in  sources  and  detectors.     Photonics:     Electronics:  Antenna,  high   Also  need  funcUonal  devices  such   Source:  lasers,  LEDs   speed  transistor  circuits  for   as  ﬁlters,  switches,   Detector:  Photodiodes   microwave  generaUon,   modulators  which  largely  do   FuncUonal:  lens,  polarizer,               detecUon,  control  and   opUcal  switch   not  exist   manipulaUon       ApplicaUons:  opUcal   ApplicaUons:  wireless   ﬁber  communicaUons…   communicaUons,  radar…  Terahertz Region of the EM Spectrum B.B.  Hu,  M.  Nuss,  Opt.  LeQ.  20,  1716  (1995)  THz Metamaterials 1 ω = 36  µm  X  36  µm   0 4  µm  linewidth   LC 2  µm  gap  Experimental Setup: THzTDS Bimaterial Cantilever Based Metamaterials A Mechanical Chameleon The SRRs are 72 µm X 72 µm with Au / Silicon nitride an inplane periodicity of 100 µm cantilever arrays: and an overall dimension of 1 cm X Thermal Actuation 1cm. Phys. Rev. Lett. 103, 147410 (2009) Turning On The Refractive Index Mechanically Control of the EM response at the unit cell level Resonant Detectors Fabricated at 95 and 690 GHz 95  GHz   690  GHz  95 GHz MMBased Thermal Detector: Single Pixel Characterization • R   oom T • A   mbient • Optical Readout   • 15   Hz     Spectrally Selective and Polarization Sensitive Magnetic Metamaterials 3D Standup Metamaterials: Pure Magnetic Excitation at Terahertz Frequencies (a)   (e)   (b)   (f)   (c)   (g)   (d)   Cu  electroplaUng  with  Cu/Ti  seed  layers  3D Standup Metamaterials: Pure Magnetic Excitation at Terahertz Frequencies Create complex materials by combining metamaterials with other materials including transition metal oxides Correlated Electron Matter Metamaterials Competing DOF Subλ “LC” Resonators Mode selec. excitationà Array à effective n(λ) Phase control M. K. Liu, et al, Nature 487, 345 (2012) Field enhancement in the capacitive gaps •  Large field enhancement •  Extreme subλ regime •  Separation of E and H Above Damage Threshold: 4 MV/cm M. K. Liu, et al, Nature 487, 345 (2012)
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