Unformatted text preview: Metamaterials = meta = beyond (Greek) Outline Plasmonics Confining light (~1 micron) to the nanometer scale (10nm) 2 orders of magnitude! TransformaIon OpIcs ManipulaIng OpIcal Space Metamaterials MoIvaIon Major breakthroughs are o/en materials related Stone Age, Iron Age, Si Age,...metamaterials People realized the uIlity of naturally occurring materials ScienIsts are now able to engineer new funcIonal nanostructured materials Is it possible to engineer new materials with useful op9cal proper9es Yes! Wonderful things happen when structural dimensions are light and much less What are the smallest possible devices with op9cal func9onality ? ScienIsts have gone from big lenses, to opIcal fibers, to photonic crystals, to... Does the diffracIon set a fundamental limit? Possible soluIon: metal opIcs/plasmonics/metamaterials Plasmonics Metal OpIcs Confining light to the nanometer scale "Plasmonics: Fundamentals and Applications", S. A. Maier, Springer, NY, 2007 PLASMONICS Plasmonics is aiming for synergy between electronics and photonics Plasmonics naturally interfaces with similar size electronic components Plasmonics naturally interfaces with similar operaIng speed photonic networks Electronic / Photonic IntegraIon Merging electronics and photonics at the nanoscale: Surface plasmonbased circuits Surface plasmon polaritons (SPPs): - Electromagnetic interface waves associated with collective oscillations of the surface electron density - By nature subwavelength spatial periods and transverse dimensions perpendicular to the metal surface Plasmonics allows combination Capacity of photonics Miniaturization of electronics PLASMON POLARITONS What is a plasmon ? Compare electron gas in a metal and real gas of molecules Metals are expected to allow for electron density waves: plasmons Bulk plasmon Metals allow for EM wave propagation above the plasma frequency They become transparent! Surface plasmon Dielectric E z Can be subwavelength! D Metal H Note: This is a transverse magnetic (TM) wave I Sometimes called a surface plasmon-polariton (strong coupling to EM field) Solve Maxwell's equations with boundary conditions DISPERSION RELATION FOR SPP Metal H Dielectric: z<0 x We have to prove the existence of solutions that look like: z E Dielectric Hd = ( 0, H yd ,0) exp i ( kxd x + kzd z - t ) Ed = ( Exd ,0, Ezd ) exp i ( kxd x + kzd z - t ) Hm = ( 0, H ym ,0) exp i ( kxm x + kzm z - t )
Em = ( Exm ,0, Ezm ) exp i ( kxm x + kzm z - t ) Metal: z>0 EM wave needs to satisfy: Maxwell's Equations in medium i (i = metal or dielectric): i E = 0
Ex ,m = Ex ,d H = 0 EM wave needs to satisfy the following boundary conditions: H E = - 0 t H = i E t Dzm = Dzd m Ezm = d Ezd H ym = H yd DISPERSION RELATION FOR SPP LOCAL FIELD INTENSITY DEPENDS ON WAVELENGTH Wavelength dependence surface plasmon
z z D << o I I Long wavelength Short wavelength Characteristics plasmon-polariton Applications: Strong localization of the EM field High local field intensities easy to obtain Guiding of light below the diffraction limit (near-field optics) Non-linear optics Sensitive optical studies of surfaces and interfaces Surface enhanced photoluminescence and Raman Bio-sensors Study film growth ...... INCREASING PROPAGATION LENGTH Example of waveguiding structure for SPP: Symmetrical dielectric-metal-dielectric (IMI) structure Propagation length: Confinement: ~ tens of m ~ hundreds of m ~ mm ~ several m D. Sarid, Phys. Rev. Let. 47, 1927 (1981) D. Sarid, Phys. Rev. Lett. 47, 1927 (1981) P. Berini, Physical Review B 61, 10484 (2000) Localized Surface Plasmon Resonance E-field + + + + + - - - - - Surface plasmon = CollecIve electron moIon DemonstraIon of a spaser-based nanolaser, NATURE 2009 TransformaIon OpIcs Controlling the opIcal space of light Coordinate Transforms n2 n1 Analogy to Gravity OpIcal Cloaking Can Objects be Invisible in the Visible Range? OpIcal Cloaking with Metamaterials = 632 nm Nature Photonics (to be published) By courtesy of V. Shalaev (Purdue) Invisibility: An Ancient Dream Perseus' helmet (Greek mythology) Tarnhelm of invisibility (Norse mythology) Cloaking devices (Star Trek, USA) Ring of Gyges ("The Republic", Plato) The 12 Dancing Princesses (Brothers Grimm, Germany) Harry PoKer's cloak (J. K. Rowling, UK) 19 Invisibility in Nature: Chameleon Camouflage hlp://www.youtube.com/watch?v=P3pE19lsG-8&feature=player_detailpage#t=290s 20 Invisibility by TransformaIon of Time-Space Black hole Stealth technique: Invisibility to Radar: Stealth Technology Radar cross-secIon reducIons by absorbing paint / non-metallic frame / shape effect... 22 OpIcal Camouflage (Tachi lab, U. Tokyo) The camera + projector approach From: h:p://www.star.t.u-tokyo.ac.jp
23 Cloaking ! Invisibility Cloaking is more than invisibility or camouflage Camouflage: an adapta9on to the surrounding environment Cloaking: No need to adapt to a par9cular environment, with the ul9mate goal of transparency -- no scaRering; no shade Criteria for an ideal cloak Macroscopic, no limit to subwavelength size or near field region Independent of object to be cloaked Minimized absorp9on and scaRering Broadband ... TransformaIon of Maxwell's equaIons Straight field line in Cartesian coordinate Distorted field line in distorted coordinate Spa9al profile of ! & ! tensors determines the distor9on of coordinate Seeking for profile of ! & ! to make light avoid par9cular region in space -- op9cal cloaking Pendry et al., Science, 2006 Designing Space for Light Fermat: ndl = 0 n = (r)(r) "curving" op[cal space Straight field line in Cartesian coordinate Distorted field line in distorted coordinate Spa9al profile of ! & ! tensors determines the distor9on of coordinates Seeking for profile of ! & ! to make light avoid par9cular region in space -- op9cal cloaking Pendry et al., Science, 2006 Leonhard, Science, 2006 Greenleaf et al (2003) L. S. Dolin, Izv. VUZ, 1961 A Similarity in Mother Nature The bending of light due to the gradient in refrac[ve index in a desert mirage Pendry et al., 2006 27 Cloaking All distor9on effects can be hidden in and tensors. Maxwell's equa9ons look like the Cartesian case. It is possible to arrange light rays path to avoid the certain part of the space An object placed there will be invisible to the external observer this is the sense of op9cal cloaking ElectromagneIc Cloaking by TransformaIon OpIcs An ideal cloak requires a closed surface with: Cloaking capability for macroscopic objects No leakage field inside the cloak No perturba[on of field outside the cloak No dependence on shape of a cloaked object hKp://www.youtube.com/watch?v=z0-kUEiLWPU&feature=related Schurig et al., Science, 2006 Leonhardt, Science, 2006 (Quasi-staIc) Cloaking of small parIcles: Alu and Engheta, PRE, 72, 016623, 2005 Milton & Nicorovici, Proc. R. Soc. A, 2006 Nicorovici, McPhedran and Milton, PRB, 1994 General math. requirements and microwave demonstraIons b a b Cloaking Based on Coordinate TransformaIon z r r b-a r + a b r-a r = r = r r = = r -a 2 b r -a z = z = b-a r hRp://www.youtube.com/watch?v=Ja_fuZyHDuk&feature=related Schurig et al., Science, 2006 30 Experimental DemonstraIon at Microwave Frequency Ideal case Structure of the cloak Reduced parameter set Experimental data Schurig et al., Science, 2006 How about OpIcal Frequencies?
Scaling the microwave cloak design? Intrinsic limits to the scaling of SRR size High loss in resonant structures 2 H E k r -a r b r -a r = r = , = = , z = z = r r -a b-a r
2 b r -a z = b-a r r = r -a r -a r = r To maintain the dispersion relation z = constant z r = constant (for in-plane k) = 1 z 2 b = b-a 2 2 b r -a r = b-a r No magneIsm required! A constant permixvity of a dielectric; > 1 Gradient in r direcIon only; !r changing from 0 to 1. Cai, et al., Nature Photonics, 1, 224 (2007) Cloaking Performance: Field Mapping Movies
Example: Non-magne9c cloak @ 632.8nm with silver wires in silica Cloak OFF Cloak ON Towards Experimental RealizaIon We need a design that is ... ! Less complicated in fabrica9on Compa9bility with mature fabrica9on techniques like direct deposi9on and direct etching ! BeRer loss features Loss might be ul9mate limi9ng issue for cloaking r = 0.1 r = 0.03 34 OpIcal Mimicry Progress Towards True Invisibility on May.17, 2009, under Science www.codingfuture.com Theory: J. Li, J. Pendry GHz: Smith et al (Duke) OpIcal: Zhang et al (Berkeley) Lipson et al (Cornel) Carpet Cloak ValenIne, Nature Mat., 8, 568 (2009) The Op9cal Black Hole: Broadband Omnidirec9onal Light Absorber Mimicing the properNes of a cosmological black hole, whose intense gravity bends the surrounding space-Nme, causing any nearby ma:er or radiaNon to follow the warped space-Nme and spiral inwards. OpIcal Black Hole All-dielectric Real materials (e.g. semiconductors) Narimanov, Kildishev Trapping and ManipulaIng Light Narimanov, Kildishev Analogy to Gravity ...
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- The Republic, Wavelength, Surface plasmon resonance, plasmon