Metamaterials: Negative refractive index in ... - Theory.nipne.ro

IFIN_Theor_Phys_Dept_111810<strong>Metamaterials</strong>:<strong>Negative</strong> <strong>refractive</strong> <strong><strong>in</strong>dex</strong> <strong>in</strong>microwave and opticsPhysical pr<strong>in</strong>ciples and perspectivesGeorge NemeşASTiGMAT TM , 1457 Santa Clara St. Ste. 6, Santa Clara, CA 95050gnemes@astigmat-us.comASTiGMAT

Acknowledgments:- Interested attendeesOutl<strong>in</strong>e:1. Goal2. Term<strong>in</strong>ology, def<strong>in</strong>itions, brief history3. <strong>Metamaterials</strong> physics: How can be n < 0?4. Physical properties of metamaterials hav<strong>in</strong>g n < 05. Veselago-Pendry "ideal lens"6. Experimental results (2000-2009)7. Potential applications of utmost <strong>in</strong>terest8. Comments9. ConclusionASTiGMAT

1. GoalIntroduction to the field of metamaterialswith negative <strong>refractive</strong> <strong><strong>in</strong>dex</strong> (n < 0)ASTiGMAT

2. Term<strong>in</strong>ology, def<strong>in</strong>itions, brief history2.1. Term<strong>in</strong>ology- <strong>Negative</strong> <strong>refractive</strong> <strong><strong>in</strong>dex</strong> (NRI) materials- "Left handed materials" (LHM; the vectors E, H, k are oriented us<strong>in</strong>g the"left-handed" rule rather than the regular "right-handed" rule)- <strong>Metamaterials</strong> (MTM; l<strong>in</strong>ear materials, quasi - homogeneous, artificiallymade, with NRI)- Photonic crystals (PhC; sometimes used, partially <strong>in</strong>correct)- Other: double negative materials, s<strong>in</strong>gle negative materialsASTiGMAT

<strong>Metamaterials</strong> and photonic crystals - ma<strong>in</strong> differencea - spatial period(From: V. M. Shalaev, Purdue Univ., Talk at 1 st <strong>Metamaterials</strong> Congress, Rome, 2007)ASTiGMAT

2.2. <strong>Metamaterials</strong>: formal def<strong>in</strong>ition• 2001: Rodger Walser, University of Texas, Aust<strong>in</strong>, <strong>in</strong>troduces(published paper) the term "metamaterial" referr<strong>in</strong>g to artificialcomposites that "...have performances beyond the limitations ofconventional composites".• 2001: Valerie Brown<strong>in</strong>g, Stu Wolf, DARPA (Defense AdvancedResearch Projects Agency), extend the def<strong>in</strong>ition <strong>in</strong> the context of theDARPA <strong>Metamaterials</strong> program :<strong>Metamaterials</strong> are a new class of ordered nanocomposites that exhibitexceptional properties not readily observed <strong>in</strong> nature. These propertiesarise from qualitatively new response functions that are: (1) notobserved <strong>in</strong> the constituent materials and (2) result from the <strong>in</strong>clusion ofartificially fabricated, extr<strong>in</strong>sic, low dimensional <strong>in</strong>homogeneities.ASTiGMAT

More def<strong>in</strong>itionsMeta- denotes position beh<strong>in</strong>d, after, or beyond, and also someth<strong>in</strong>g of a higher orsecond-order k<strong>in</strong>d. . .a) Short and general: Metamaterial is an arrangement of artificial structuralelements, designed to achieve advantageous and unusual properties.b) Long: Metamaterial is an artificial material possess<strong>in</strong>g eng<strong>in</strong>eered effectiveelectromagnetic properties result<strong>in</strong>g from response functions not found <strong>in</strong>constituent materials and not readily observed <strong>in</strong> nature. *c) Narrow: Metamaterial is an artificial material whose effective properties cannotbe determ<strong>in</strong>ed by only material parameters, shape, and concentration of theconstituent <strong>in</strong>clusions.*Based on the def<strong>in</strong>ition of J. Pendry, 2000.(S. Tretyakov, Hels<strong>in</strong>ki University of Technology, SMARAD Centre ofExcellence, September 2006; Director of Metamorphose – European Network ofExcellence)ASTiGMAT

2.3. Brief history2.3.1. Known and "acknowledged" ("modern") history- V. G. Veselago (Lebedev Physics Institute, Moscow) – theoryUFN 92, 517 (1967) (Russian) ε r < 0; μ r < 0 n < 0Sov. Phys. Usp. 10, 509 (1968) (English)- J. B. Pendry et al (Imperial College, London) – theory to obta<strong>in</strong>materials hav<strong>in</strong>g ε r < 0; μ r < 0, not for n < 0Phys. Rev. Lett. 76, 4773 (1996) theory to obta<strong>in</strong> ε r < 0J. Phys. Condens. Matter 10, 4785 (1998) experiment ε r < 0IEEE Trans. MTT 47, 2075 (1999) theory to obta<strong>in</strong> μ r < 0- D. R. Smith et al (UCSD, CA) - experiment n < 0; (f ≈ 5 GHz)Phys. Rev. Lett. 84, 4184 (May 2000)- G. V. Eleftheriades et al; A. A. Ol<strong>in</strong>er; C. Caloz et al – transmission l<strong>in</strong>emodel (nonresonant, wide band structures) (June 2002)IEEE-MTT Symposium; USNC/URSI Nat. Sci. Radio Meet<strong>in</strong>gASTiGMAT

Founders of the modern metamaterials fieldViktor G. Veselago(Prokhorov Inst. ofGeneral Physics,Moscow, Russia)Sir John B. Pendry(Imperial College,London, UK)David R. Smith(Duke Univ., Durham,NC, USA)ASTiGMAT

Veselago: The correct year is 1967 and not 1964Pendry: The goal is different than to verify Veselago’s theory.Shows how to obta<strong>in</strong> ε < 0 and μ < 0, <strong>in</strong>dependentlyFirst experimental proof of Veselago’s theory,synthesis of a material hav<strong>in</strong>g n < 0Proves the possibility that materials with complex n(hav<strong>in</strong>g absorption) can have Re [n] < 0ASTiGMAT

Pendry’s structures to obta<strong>in</strong>:ε < 0 (up, left) - 1996μ < 0 (up, right; both right pictures) - 1999C. Caloz, T. Itoh, Electromagnetic <strong>Metamaterials</strong>: Transmission L<strong>in</strong>e<strong>Theory</strong> and Microwave Applications, Wiley, Hoboken, NJ, 2006ASTiGMAT

2.3.2. Less known history ("old" results, before Veselago’s; <strong>in</strong>complete list)"Everyth<strong>in</strong>g of importance has been said before, by someone who did not discover it".(Alfred North Whitehead, 1916, address to the British Association for the Advancement of Science;mathematician, philosopher, supervised Bertrand Russell mathematical dissertation).- Site: Alexander Moroz; http://www.wave-scatter<strong>in</strong>g.com/negative.html- S. A. Tretyakov, "Research on negative refraction and backward-wave media: A historicalperspective", EPFL Latsis Symposium 2005, Lausanne, Feb.-Mar. 2005- C. Caloz, T. Itoh, Electromagnetic <strong>Metamaterials</strong>: Transmission L<strong>in</strong>e <strong>Theory</strong> and MicrowaveApplications, Wiley, Hoboken, NJ, 2006, Ch. 1- H. Lamb, Proc. London Math. Soc. 1, 473 (1904)(backward waves; mechanical systems)- A. Schuster, An Introduction to the <strong>Theory</strong> of Optics, Edward Arnold,London, 1904, pp. 313-318 (backward eltm. waves)- H. C. Pockl<strong>in</strong>gton, Nature 71, 607 (1905) (phase velocity orientedopposite to the group velocity)- L. I. Mandel’shtam, Jh. Eksp.Teor. Fiz. 15, 476 (1945) (Russian);Complete Works, vol. 5, Academy of Sci. Publ.,Moscow, 1950, pp. 428-467- G. D. Malyuzh<strong>in</strong>ets, Jh. Tekh. Fiz. 21, 940 (1951) (Russian) (v panti II v g)- D. V. Sivukh<strong>in</strong>, Opt. Spektrosk. 3, 308 (1957) (Russian) (n < 0)ASTiGMAT

Examples of "old" resultsWire media <strong>in</strong> the 1960sW. Rotman, IRE Trans. Antenna Propagation10, 82 (1962)Split r<strong>in</strong>gs <strong>in</strong> the 1950sS. A. Schelkunoff et al, Antennas:<strong>Theory</strong> and Practice,Wiley, NY, 1952Backward-wave transmission l<strong>in</strong>esG. D. Malyuzh<strong>in</strong>ets, Jh. Tekh. Fiz. 21, 940 (1951)ASTiGMAT

2.4. Early dynamics of the metamaterials field related to n < 0Number of published paperson materials with n < 0 (untilthe end of 2002)(J. B. Pendry, Opt. Express11, 639 (2003))2003: The field "explodes": annual special sessions at conferences, special issues ofscientific journals, books, a dedicated special journal (2007)Special issues of optical and microwave journals dedicated to the field:- Optics Express 11 (7), Apr. 2003 (www.<strong>in</strong>fobase.org) – electronic journal, free- IEEE Transactions on Antennas and Propagation 51 (10), Oct. 2003- IEEE Transactions on Microwave Technology and Techniques 53 (4), Apr. 2005- New Journal of Physics 7, Aug. 2005 (www.njp.org) – electronic journal, free- J. Opt. Soc. Am B 23, Mar. 2006 (www.<strong>in</strong>fobase.org)- Progress <strong>in</strong> Electromagnetic Research 35 (2002); 41 (2003); 42 (2003); 51 (2005);63 (2006), 70 (2007) (http://ceta.mit.edu/pier/notify.php) – electronic journal, freeASTiGMAT

Specially dedicated journal- <strong>Metamaterials</strong>, Elsevier, 2007 (No. 1, March)The Journal <strong>Metamaterials</strong> is associated with theMetamorphose Network of Excellence (Europe)Coord<strong>in</strong>at<strong>in</strong>g Editor: Mikhail Lap<strong>in</strong>ePublisher: ElsevierASTiGMAT

Published books (2005-2009):- G.V. Eleftheriades, K.G. Balma<strong>in</strong>, <strong>Negative</strong>-Refraction <strong>Metamaterials</strong>:Fundamental Pr<strong>in</strong>ciples and Applications, Wiley, Canada, 2005- C. Caloz, T. Itoh, Electromagnetic <strong>Metamaterials</strong>: Transmission L<strong>in</strong>e <strong>Theory</strong>and Microwave Applications, Wiley, Hoboken, NJ, 2006- N. Engheta, R.W. Ziolkowski, Eds., Electromagnetic <strong>Metamaterials</strong>:Physics and Eng<strong>in</strong>eer<strong>in</strong>g Explorations, Wiley, 2006- V.M. Shalaev, A.K. Sarychev, Electrodynamics of <strong>Metamaterials</strong>, WorldScientific, S<strong>in</strong>gapore, 2007.- J.-P. Berenger, Perfectly Matched Layer (PML) for ComputationalElectromagnetics, Synthesis lectures on Computational ElectromagneticsSeries, Morgan&Claypool Publishers, 2007.- R. Marqués, F. Martín, M. Sorolla, <strong>Metamaterials</strong> with <strong>Negative</strong> Parameters:<strong>Theory</strong>, Design and Microwave Applications, Wiley Series <strong>in</strong> Microwave andOptical Eng<strong>in</strong>eer<strong>in</strong>g, Wiley, Hoboken, NJ, 2008.- L. Solymar, E. Shamon<strong>in</strong>a, Waves <strong>in</strong> <strong>Metamaterials</strong>, Oxford Univ. Press, NY, 2009.- B.A. Munk, <strong>Metamaterials</strong>: Critique and Alternatives, Wiley, Hoboken, NJ, 2009.- Y. Hao, R. Mittra, FDTD Model<strong>in</strong>g of <strong>Metamaterials</strong>: <strong>Theory</strong> and Applications,Artech House, Norwood, MA, 2009.ASTiGMAT

Metamorphose-organized conferences on <strong>Metamaterials</strong>1 st International Congress On Advanced Electromagnetic Materials <strong>in</strong>Microwaves and Optics, Rome, Italy, 22-26 October 2007 (<strong>Metamaterials</strong>'07)(Proceed<strong>in</strong>gs - free, from:http://www.metamorphose-vi.org/<strong><strong>in</strong>dex</strong>.php?Itemid=193&id=110&option=com_content&task=view)2 nd International Congress on Advanced Electromagnetic Materials <strong>in</strong>Microwaves and Optics, Pamplona, Spa<strong>in</strong>, September 21-26, 2008.3 rd International Congress on Advanced Electromagnetic Materials <strong>in</strong>Microwaves and Optics, London, UK, Aug. 30th-Sept. 4th, 2009.4 th <strong>Metamaterials</strong>'2010 Congress will be held <strong>in</strong> Karlsruhe, Germany, onSeptember 13-18, 2010 (The Conference is on September 13-16, and theDoctoral School on September 17-18).ASTiGMAT

Comments- Veselago's theory was experimentally verified <strong>in</strong> the microwavespectrum only <strong>in</strong> 2000 (33 years after it was formulated foroptics), even though the same technology used <strong>in</strong> 2000was available back <strong>in</strong> 1967.- Papers doubt<strong>in</strong>g the existence of n < 0 are published time to time andperhaps will cont<strong>in</strong>ue to be published for some timeASTiGMAT

3. MetaPhysics of metamaterials: How n < 0 is possible?3.1. Necessary conditions to have n < 0- Refractive <strong><strong>in</strong>dex</strong> n to be a quantity with physical mean<strong>in</strong>g (to exist) the material to be homogeneous or quasi-homogeneous (the spatialscale of the periodic <strong>in</strong>homogeneities, p, to be p

- Examples of <strong>in</strong>homogeneous materials for visible light:Particles with sizes 100 nm - 10 μm dispersed <strong>in</strong> homogeneous media:gases, liquids, solids (fog, smog, oil emulsions <strong>in</strong> water, colloidalsystems)- Optical properties of <strong>in</strong>homogeneous materials:Scatter<strong>in</strong>g and diffraction phenomena are predom<strong>in</strong>ant as compared torefraction or reflection phenomena n cannot be def<strong>in</strong>edScatter<strong>in</strong>g takes place at different angles <strong>in</strong>clud<strong>in</strong>g 180 0 (backscatter<strong>in</strong>g)Note: For microwaves (λ ~ 1000 mm - 10 mm), periodic <strong>in</strong>homogeneitieswith sizes p ~ 1 mm do not matter material is ≈ homogeneous n does existASTiGMAT

Electromagnetic field spectrum≈ 800 nm Visible ≈ 400 nmλ 01 km; 100 m; 10 m; 1 m; 100 mm; 10 mm; 1 mm; 100 μm; 10 μm; 1 μm; 100 nm; 10 nm 1 nm-----------------------------------------------------------------------------------------------------------------------------------------------f 0(Hz) 300 k; 3 M; 30 M; 300 M; 3 G; 30 G; 300 G; 3 T; 30 T; 300 T; 3 P; 30 P; 300 PASTiGMAT

3.2. Def<strong>in</strong>ition of n: Maxwell's equations- Electromagnetic field quantities: E(t,r), H(t,r), D(t,r), B(t,r), J(t,r)- Maxwell's equations <strong>in</strong> homogeneous, charge-free materials:(D = εE = ε 0 ε r E; B = μH = μ 0 μ r H; J = σE)∇ x E = - ∂B/∂t∇ x H = J + ∂D/∂t∇ D = 0∇ B = 0ASTiGMAT

3.2. Def<strong>in</strong>ition of n: two possible solutions- Plane wave-type solution: E(t,r) = E 0 exp j(ωt –kr); analogously H(t,r)∇ 2 E + μσ ∂E/∂t + με ∂ 2 E/∂t 2 = 0; analogous for H∇ = – jk; ∂/∂t = jω; ∇ 2 = – k 2 ; ∂ 2 /∂t 2 = – ω 2HEkRHMk x E = + ωμH E, H, k is right-handed for ε > 0; μ > 0k x H = – ωεE E, H, k is left-handed for ε < 0; μ < 0- Solution (perfect, absorption-free dielectric): k 2 = ω 2 εμ = ω 2 /v p2 = ω 2 n 2 /c 2c 2 = 1/(ε 0 μ 0 ) n 2 = ε r μ r ; ε > 0; μ > 0 n > 0 usual caseε = – |ε| = e jπ |ε| < 0; μ = – |μ| = e jπ |μ| < 0; n = e jπ √|ε r μ r | = – |n| < 0- Poynt<strong>in</strong>g vector: S = E x H; For n > 0 k II S; For n < 0 k anti II SkSHELHMSn = ±√ε r μ r VeselagoASTiGMAT

3.3. Possibility that n < 0Plane (ε, μ) (J. B. Pendry, Opt. Express 11, 639 (2003); also Veselago)ε < 0 naturally occurs <strong>in</strong> metals at opticalfrequencies, or <strong>in</strong> plasmas, at <strong>in</strong>fraredfrequencies.μ < 0 naturally occurs <strong>in</strong> ferro- or antiferromagneticresonant systems (low frequencybands, < THz).Quadrants I, III propagation, transmissionQuadrants II, IV evanescent (decay<strong>in</strong>g) field no propagation, no transmissionPendry (1996 -1999) methods to synthesize "solid plasmas" with ε < 0 andmagnetic structures with μ < 0 <strong>in</strong> GHz frequency range Periodic structureswith adjustable geometrical parameters. ε: parallel metallic rods with spatialperiodicity; μ: metallic split r<strong>in</strong>gs = resonant LC circuits at GHz frequencies,periodically positioned <strong>in</strong> space (split-r<strong>in</strong>g resonators, or SRR).ASTiGMAT

3.4. Examples of Pendry periodical structures(a) Metallic rods (ε < 0 for E II z); (b) Split r<strong>in</strong>g resonators (μ < 0 for H II y).In both cases p

Effective relative permittivity, ε reff , and effectiverelative permeability, μ reff- Condition to have the effective material constants ε reff , μ reff : p

Effective relative magnetic permeability (μ reff ) for thesplit-r<strong>in</strong>g resonators structureP<strong>in</strong>k band: frequency <strong>in</strong>terval of<strong>in</strong>terest, μ reff < 0μ reff = 1 – ω pm2 /(ω 2 – ω 0m2 + jωΓ m )In the picture Γ m≈ 0ω 0m- magnetic-type resonant frequency; ω pm- magnetic-type “plasma” frequency(geometry determ<strong>in</strong>es these two quantities bandwidth for μ reff < 0)Note: Similar behavior of ε reff for the periodic structure us<strong>in</strong>g metallic rodsreplac<strong>in</strong>g: μ reff ε reff ; ω pm ω pe(electric-type “plasma”); ω 0m 0ASTiGMAT

3.5. Example of elementary cell ("atom") lead<strong>in</strong>g to n < 0Marcoš, Soukoulis, Phys. Stat. Sol. (a) 197, 595 (2003)Physically 2-D structure (periodical <strong>in</strong> x, y);Electromagnetically 1-D structure (II z, anisotropic); E II y; H II x; k II z;p = several mm; λ 0 ≈ 30 mm; f 0 ≈ 10 GHz; f pe ≈ 20 GHz.ASTiGMAT

Idealized hypotheses (<strong>in</strong>itially considered) and the real world1. The electric and the magnetic properties do not <strong>in</strong>teract to each other2. Absorption (losses) <strong>in</strong> the materials is negligible3. Simple geometrical structures, ignor<strong>in</strong>g anisotropy (1-D, 2-D)#1 Not valid careful design to match the negative bands for ε eff , μ eff .#2 and #3 also not valid much research effort necessary new"atomic structures" (geometries), new materials, new pr<strong>in</strong>ciples to getdesired effects (some us<strong>in</strong>g PhC <strong>in</strong>stead of NRI metamaterials).Absorption ε, μ, n - complex quantities: n = n' + jn"; ε = ε' + jε"; μ = μ' + jμ"Useful effects: n'; Losses: n"; Causality: ε" > 0; μ" > 0Factor of merit for negative <strong>refractive</strong> <strong><strong>in</strong>dex</strong>: F = – n'/n"Double-negative materials: n' < 0 because both, ε' < 0, μ' < 0 F largeS<strong>in</strong>gle-negative materials: n' < 0 only because ε' < 0, and μ' > 0 F smallASTiGMAT

Transmission l<strong>in</strong>e approach to MTM with n < 0Eleftheriades group(Univ. Toronto, 2002 and after)Analogy:ε < 0 ⇔ L shuntμ < 0 ⇔ C seriesAdvantage: Wide bandwidthG.V. Eleftheriades, Radio Sci. Bull. 312, 57 (2005)G.V.Eleftheriades, Talk at 1 st <strong>Metamaterials</strong> Congress, Rome, 2007ASTiGMAT

Generalized cell for NRI-transmission l<strong>in</strong>e MTMG.V. Eleftheriades, Talk at 1 st <strong>Metamaterials</strong> Congress, Rome, 2007ASTiGMAT

4. Physical properties of metamaterials with n < 0What physical (optical) effects appear <strong>in</strong> a metamaterial with n < 0as compared to a regular material with n > 0? (Veselago, 1967-1968)- Phase velocity of a wave is opposite to the group velocity of the same wave- <strong>Negative</strong> (reverted) refraction- Light transmission without reflection is possible at the <strong>in</strong>terface of twomaterials with n 1 = n > 0 and n 2 = – n < 0- Reverted Doppler effect (blue shift for the source depart<strong>in</strong>g from the observer)- Reverted Cherenkov effect (the cone of emitted light sh<strong>in</strong>es backwards)- Reverted Goos-Hänchen effect (backward displacement of the TIR, LP beam)- "Lens effect" for the parallel-plane flat with n < 0 (Veselago-Pendry lens)- Other New optics/electrodynamics/physics/new technologiesASTiGMAT

4.1. <strong>Negative</strong> refractionRefraction law (Snell's)n 1 s<strong>in</strong>(θ 1 ) = n 2 s<strong>in</strong>(θ 2 )θ 1 > 0 θ 1 > 0n 1 > 0n 1 > 0n 2 > n 1 > 0θ 2 > 0n 2 < 0|n 2 | > n 1 > 0θ 2 < 0Usual case (positive refraction) <strong>Negative</strong> refraction caseASTiGMAT

Example of negative refraction (simulation)G. Doll<strong>in</strong>g et al, Opt. Express 14, 1842 (2006)ASTiGMAT

4.2. Behavior of convex and concave lensesReverted behavior than <strong>in</strong> the usual case(a) Convex lens divergent effect(b) Concave lens convergent effectNote: Similar behavior does exist <strong>in</strong> the microwave and the X-ray spectrumfor transparent materials with 0 < n < 1 (not n < 0)ASTiGMAT

4.3. Possibility that the reflectance to be zeroSupposedly we have at the <strong>in</strong>terface 1-2:ε 2 = – ε 1 = – |ε| < 0; μ 2 = – μ 1 = – |μ| < 0 n 1 = n > 0; n 2 = – |n| < 0Impedances of the two media: η = √|μ/ε| = η 1 = η 2Reflectances (Fresnel formulae):R p,s = [η 2 cos(θ 2,1 ) – η 1 cos (θ 1,2 )] / [η 2 cos(θ 2,1 ) + η 1 cos(θ 1,2 )]θ 2 = – θ 1 ; η 2 = η 1 R p = 0; R s = 0ASTiGMAT

4.4. Goos-Hänchen shift (effect)- Takes place at total <strong>in</strong>ternal reflection (TIR) with l<strong>in</strong>early polarized beams- It is a small (several λ) longitud<strong>in</strong>al displacement of the beam axis from thepure geometrical optics (ray) description- G-H displacement is greater for <strong>in</strong>cidence angles, i, near the critical anglen 1> 0NormalTIR Interfacen 2> 0n 2< 0|n 2| > n 1Reverted, backwardG-H shift, n 2< 0iOrd<strong>in</strong>ary, forwardG-H shift, n 2> 0Geometrical optics,no G-H shiftASTiGMAT

5. Veselago-Pendry "ideal lens"Ideal lens: plan-parallel plate withε r = –1; μ r = –1, placed <strong>in</strong> air (vacuum)Veselago (1967-1968)Pendry (2000)Pendry: The spatial resolution of theimage made by the lens is given by theevanescent field (that vanishes <strong>in</strong>vacuum after (1-2)λ).The lens material "amplifies" theevanescent field perfect spatialresolution (~ λ/100 - λ/1000)ASTiGMAT

"Ideal lens" - simplified description of super-resolution(J. B. Pendry, D. R. Smith, Phys. Today,June 2004, pp. 37-43)(a) Image through classical lens, formed by the propagat<strong>in</strong>g field. The spatial resolution Δ is limited byk trM≈ ω 2 /c 2 , because k z= (ω 2 /c 2 –k trM2) 1/2 needs to be real to account for propagation Δ ≈ λ.(b) Attenuation of the evanescent field <strong>in</strong> the medium with n > 0 (classical lens <strong>in</strong> air or vacuum). The f<strong>in</strong>estructure of the object (small x, y) is revealed <strong>in</strong> the very large values of k trM(by the Fourier transformtheorem), mak<strong>in</strong>g the field to be evanescent (k trM> ω/c) k z= j(k trM– ω 2 /c 2 ) 1/2 . The <strong>in</strong>formation on thevery f<strong>in</strong>e structure of the object does not exist at the imag<strong>in</strong>e.(c) Image through the “ideal lens” obta<strong>in</strong>ed with propagat<strong>in</strong>g field Δ ≈ λ (identical to the case (a)).(d) Image through the “ideal lens” obta<strong>in</strong>ed with evanescent field amplified by the “ideal lens” Theoretical spatial resolution at the image: Δ ≈ 0 (near perfect, i.e., Δ ~ λ/100 - λ/1000).ASTiGMAT

"Ideal lens" and positive n - negative n optical media ("optics - antioptics")Generalization of the ideal lens(J. B. Pendry, D. R. Smith, Phys. Today,June 2004, p. 37)(a) Alternate sections with n = 1 andn = −1, equal thickness d focus<strong>in</strong>g(b) Group and phase velocity <strong>in</strong> eachsection(c) Focus<strong>in</strong>g with two complex sections,with "mirror-like" properties of n(d) Intuitive explanation of case (c):total optical path length = 0Note: Cancel<strong>in</strong>g of a positive optical path length can be done also with classicallenses and free spaces (Sudarshan et al; Nemeş): "negative space" systemASTiGMAT

Partial conclusion and comments- Only the "classical" phenomena and configurations were considered- <strong>Negative</strong> refraction does not necessarily mean n < 0Photonic Crystals (PhC) can have negative refraction, though theydo not have n < 0 (they do not have a well-def<strong>in</strong>ed n eff at all)- PhC have low loss - can be used to obta<strong>in</strong> similar effects to those of MTM- Other approaches toward n < 0 Chirality (handedness) of structures(Chiral object - asymmetric to its mirror image)- New structures closer to isotropic MTM are conceived- Alternat<strong>in</strong>g layers of positive and negative <strong><strong>in</strong>dex</strong> MTM new properties(discrete or cont<strong>in</strong>uous transition considered)ASTiGMAT

6. Experimental results (2000-2009)- First experiments (2000-2002) – microwaves (5 GHz - 20 GHz)- Later on (2002-2005) – hundreds GHz, THz, hundreds THz (near<strong>in</strong>frared, NIR)- Recent (2006 - 2009) – NIR and visible- New results and new trends (2006 - 2009):- F<strong>in</strong>d<strong>in</strong>g new configurations for desired effects- F<strong>in</strong>d<strong>in</strong>g useful applications <strong>in</strong> microwaves- Race to obta<strong>in</strong> and extend visible work<strong>in</strong>g systems and applicationsASTiGMAT

First experiments (2000-2001)1-D Metamaterial with n < 0 <strong>in</strong> microwaves (f ≈ 5 GHz)(D.R. Smith et al, Phys. Rev. Lett. 84, 4184 (2000))ASTiGMAT

First experiments2-D Metamaterial with n < 0 <strong>in</strong> microwaves(R. A. Shelby et al, Science, 292, 77 (2001);J. B. Pendry, D. R. Smith, Phys. Today, June 2004pp. 37-43); p = 5 mm; λ ~ 30 mm; f ~ 10 GHz(a) Resonant structure: split-r<strong>in</strong>gs and metallic rods(wires, visible <strong>in</strong> the back of the vertical holders)(b) Spectral band where ε r < 0 şi μ r < 0(c) Transmitted power spectrum: only metallic rods(green); only split-r<strong>in</strong>gs (blue); both (red) transmission = propagationASTiGMAT

First experiments<strong>Negative</strong> refraction <strong>in</strong> microwaves (J. B.Pendry, D. R. Smith, Phys. Today,June 2004, pp. 37-43)(a) Prism with n < 0, simulation(b) Prism with n > 0, teflon, simulation(c) Experiment, prism, metamaterial n < 0(d) Experiment, teflon prismASTiGMAT

Progress, microwavesMetamaterial prism formicrowaves(C. Soukoulis, OPN, June2006, pp. 16-21)ASTiGMAT

Progress, microwavesExperiment to verify the transmission and the negative refraction(C. Soukoulis, OPN, June 2006, pp. 16-21)ASTiGMAT

Progress, microwavesVeselago-Pendry lens for microwaves,n = –1, spatial resolution < λ(C. Soukoulis, OPN, June 2006, pp. 16-21)ASTiGMAT

Progress: from microwaves toward optical spectrumExample of metamaterials with n < 0 made by planar lithography technique(C. Soukoulis, OPN, June 2006, pp. 16-21)Different structures (left to right): SRR; Parallel metallic slabs; Mesh-typeASTiGMAT

Experiments, microwaves: focus<strong>in</strong>g plano-concave lensVodo et al, APL 86, 201108 (2005)ASTiGMAT

Progress: from microwaves toward optical spectrum(C. Soukoulis, OPN, June 2006, pp. 16-21)ASTiGMAT

Progress: microwaves toward optical spectrum(C. M. Soukoulis, OPN, June 2006, pp. 17-21)Note: These are other structures than SRRASTiGMAT

Progress: from microwaves toward optical spectrumMagnetic metamaterial for mid-<strong>in</strong>frared (λ ≈ 4.6 μm)(S. Zhang et al, PRL 94, 37402 (2005))ASTiGMAT

Progress: mid-near <strong>in</strong>fraredDistance between holes: 838 nm;Holes diameter: 360 nmThicknesses Au/Al 2O 3/Au: 30/60/30 nmn < 0 at λ = 2 μm(S. Zhang et al, PRL 95, 137404 (2005))ASTiGMAT

Progress: near <strong>in</strong>frared (toward visible)n = – 0.3 ; λ = 1.5 μm(V.M. Shalaev et al, Opt. Lett. 30, 3356 (2005))ASTiGMAT

Progress: visible (2006)n < 0; λ ≈ 0.47 μmASTiGMAT

Progress: visible (2007)ASTiGMAT

Other recent issues (2006-2009)Us<strong>in</strong>g new configurations to achieve isotropy (2D)D.O. Guney et al, Opt. Lett. 34, 508 (2009)(Note: HEM = homogeneous effective medium)ASTiGMAT

Swiss cross configuration (2009)New structure and resultsλ = 1400 nm(C. Helgert et al, Opt. Lett. 34, 704 (2009))ASTiGMAT

Photonic Crystals- PhC are artificial materials with periodically modulated <strong>refractive</strong> <strong><strong>in</strong>dex</strong><strong>in</strong> (1-D), 2-D, 3-D. The spatial period p ~ λ.ASTiGMAT

Mother Nature and PhCQuasi-periodical micro-structures performs as pass and stop bands forlight of certa<strong>in</strong> wavelengths different colorsPhC structure of butterly w<strong>in</strong>gs and of opal<strong>Negative</strong> refraction <strong>in</strong> the eye of some <strong>in</strong>sects and somelobsters (D.G. Stavenga, J. Eur. Opt. Soc.- RP 1, 06010 (2006))(A. Lakhtakia et al, OPN 18, 27 (2007))ASTiGMAT

Photonic crystal (PhC) approachPhC is different than MTM - uses diffraction, scatter<strong>in</strong>gPhC has frequency (wavelength) band gapsSmaller losses than MTM(Pictures from: C. Lopez, Si PhC, OPN 20, 28 (2009))ASTiGMAT

7. High-<strong>in</strong>terest potential applications7.1. Imag<strong>in</strong>g with spatial resolution

7.1. Toward imag<strong>in</strong>g with spatial resolution

Another slab (Veselago-Pendry-type) lens(G.V. Eleftheriades, Talk at 1 st <strong>Metamaterials</strong> Congress, Rome, 2007)ASTiGMAT

New concept for super-resolution lens ("wire medium" lens)Convert<strong>in</strong>g the evanescent field <strong>in</strong>to propagat<strong>in</strong>g wavesSpatial resolution: λ/15 <strong>in</strong> microwavesP.A. Belov et al, Phys. Rev. B 73, 033108 (2006)Similar results obta<strong>in</strong>ed by the same group <strong>in</strong> THz regimeλ/20 @ 5 THz; λ/10 @ 30 THz(Pictures courtesy P. Belov, Talk at Queen Mary Univ. of London, UK, 2006)ASTiGMAT

7.1. Toward imag<strong>in</strong>g with spatial resolution

7.2. Toward objects' camouflage (<strong>in</strong>visibility; cloak<strong>in</strong>g)- Problem: partial or total camouflage?Partial <strong>in</strong>visibility – perhaps easier to obta<strong>in</strong>Total <strong>in</strong>visibility – perhaps more usefulASTiGMAT

Example of partial camouflage, obta<strong>in</strong>ed by techniquesdifferent than us<strong>in</strong>g metamaterialsSite Prof. Susumu Tachi, Japanwww.projects.star.t.utokyo.ac.jp/projects/MEDIA/xv/oc.htmloc-okugai3.mpgMirror.mpgOc-s.mpgBone2.mpgASTiGMAT

Example of microwave (not visible) camouflageStealth fighter – "black" (low cross-section) <strong>in</strong> microwaves, yet visibleASTiGMAT

Total <strong>in</strong>visibility by us<strong>in</strong>g geometrical transforms (theory)and metamaterials (theory and experiment)Pr<strong>in</strong>ciple: Surround the object desired to be <strong>in</strong>visible by a metamaterial speciallydesigned to distort the light ray paths through the metamaterial (red l<strong>in</strong>es below)by-pass<strong>in</strong>g the object, and then to restore them after the object exactly as theywere before by-pass<strong>in</strong>g the object (same positions and slopes) <strong>in</strong>visible objectSite Prof. Ulf Leonhard, St. Andrews Univ., UKhttp://www.standrews.ac.uk/~ulf/<strong>in</strong>visibility.htmlASTiGMAT

Results: <strong>in</strong>visibility us<strong>in</strong>g metamaterialsTheoretical concept illustrated for non-specialists(ray paths <strong>in</strong> black - upper picture;<strong>in</strong> red - lower picture)J.B. Pendry et al, Science Express, 25 May 2006ASTiGMAT

Results: <strong>in</strong>visibility us<strong>in</strong>g MTM. SimulationsCloak<strong>in</strong>g of a sphere of ≈ 0.2 m <strong>in</strong> diameter by a "shell" of metamaterialASTiGMAT

Invisibility: First experimental result, microwaves- First experimental (partial) success : Science Express, 19 Oct. 2006(D.R. Smith group, Duke Univ., NC, USA)A photo of the “metamaterial” cloak,Released to Reuters on October 19, 2006,which deflects microwave beams so theyflow around a "hidden" object <strong>in</strong>side withlittle distortion, mak<strong>in</strong>g it appear almost asif noth<strong>in</strong>g were there at all.Metamaterial for microwaves, "swiss roll" configuration,first camouflage experiment, microwavesASTiGMAT

New (2008) cloak<strong>in</strong>g experiments, visible (500 nm)Design and simulations Results. (a)-device; (b)-cloaked areaI.I. Smolyan<strong>in</strong>ov et al, Opt. Lett. 33, 1342 (2008)ASTiGMAT

Cloak<strong>in</strong>g: new theoretical simulations, arbitrary-shaped objectNicolet et al, Opt. Lett. 33, 1585 (2008)ASTiGMAT

New (2009) reported cloak<strong>in</strong>g experiment <strong>in</strong> microwavesP. Alitalo, S. Tretyakov, Materials Today 12, 22 (2009)ASTiGMAT

8. CommentsTo start the <strong>in</strong>volvement <strong>in</strong> the MTM field implies simultaneously tackl<strong>in</strong>g:1. <strong>Theory</strong>- Understand<strong>in</strong>g specific phenomena <strong>in</strong>volved- Design of structures behav<strong>in</strong>g as MTM- Simulations- Develop<strong>in</strong>g new ideas2. Technology- Obta<strong>in</strong><strong>in</strong>g the designed structures (various techniques for micro- andnano- structur<strong>in</strong>g)3. <strong>Theory</strong> and experiments- Measurement of physical parameters of <strong>in</strong>terest (n, transmission bands, etc)ASTiGMAT

9. Conclusion- MTM is a fasc<strong>in</strong>at<strong>in</strong>g "new" field, with > 100 years of theoretical historyand about 10 years of practical experiments Physics, eng<strong>in</strong>eer<strong>in</strong>g.Mother Nature designed PhC and perhaps also MTM much earlier.- Periodic structures <strong>in</strong> different materials give rise to new, unexpectedbehavior, desired or not, <strong>in</strong> the microwave, THz, and optical spectrum.- MTM and PhC are complementary, and sometimes <strong>in</strong>tertw<strong>in</strong><strong>in</strong>g concepts.The difference consists <strong>in</strong> the scale of spatial periodicity versus λ.- Many microwave applications use already MTM concepts.- Major expected applications:Super-resolution opticsCloak<strong>in</strong>g at microwave and optical frequencies- The dynamics of the field is fast and the money <strong>in</strong>volved is huge.ASTiGMAT