Negative World of Metamaterials or How Ambiguity of Square Root Reversed Electromagnetics. Negativan svijet metamaterijala

Transcription

1 Negative World of Metamaterials or How Ambiguity of Square Root Reversed Electromagnetics Negativan svijet metamaterijala ili kako je dvoznačnost kvadratnog korijena okrenula elektromagnetizam naglavačke Silvio Hrabar Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia

2 Outline Mathematics versus Physics and Engineering Electromagnetics of Classical ( Positive ) Materials Are Negative Materials Possible? New Physical Phenomena - Fundamental research Potential Engineering Applications Applied Research Conclusions

3 Mathematics versus Physics and Engineering

4 Mathematics Physics Service? Engineering

5 What is the difference among engineers, physicists and mathematicians?

6

7 Reality Model gives non-physical results Why? Observation Prediction Project Model Is the basic theory correct? Scientist Engineer

8 Mathematics Physics Engineering

9 Electromagnetics of Classical ( Positive ) Materials

10 r The Story of Electricity Ancient Greece Why does amber attract papyrus? Charles Augustin de Coulomb ( ) and concept of Electric field Q 4 Q 5 Q n Q 3 F 02 Q 2 r F = Q Q K R r a 12 Q 0 r Q Q r Q F = K a12 + K a K n a n R02 R03 R0n r Q r Q r Qn r 2 3 F = Q0 K a12 + a13... a 1n = Q R02 R03 R 0n Q r Q Q r 0 r E r r F E = lim Q Q 0 0 0

11 The Story of Magnetism Ancient Greece a strange rock from island of Magnesia Hendrik Antoon Lorentz Q 0 r r r F = Q0E + f ( v, Q0, R02 ) Q 2 r r F r Q ( r r r ) r r = 0 E + v B E B. 02 F QE Concept of B field v r Andre Marie Ampere ( )

12 Wedding of Electricity and Magnetism Electromagnetism (Electromagnetics) Michael Farady ( ) V r B = t Are the E and B Vectors Enough? Yes in principle, but what about the influence of matter? atomic dimensions are on order of m! r D r H r = ε E 1 r = B µ Electric flux density Magnetic field

13 James Clerk Maxwell ( ) r H r E r r E = J + ε t r H = µ t Solution of these equations is a wave!

14 What is EM Harmonic Wave? e( x, t) = Acos( ωt k z) = Re { r r } jωt jk z Ae e Wave vector r k = r 2π a0 λ

15 From Theory towards Applications Heinrich Rudolf Hertz ( ) Nikola Tesla ( ) Guglielmo Marconi ( )

16 . and here we are! E r, H r, ε, µ.

17 Are Negative Materials Possible? (Are some solutions of Maxwell equations meaningless?)

18 What would happen if µ and ε were negative numbers? (Veselago, 1968) A plane wave solution of Maxwell equations: r rr jkr E = Ae r r k = u0ω µε v v v P = E H Forward wave Backward wave E k P Right-handed material E P H H Sign ambiguity k Left-handed material

19 One-dimensional Wave Propagation in Material with µ >0 and ε >0 (forward wave propagation ) E Vp>0 Vg>0 source + 0 X

20 One-dimensional Wave Propagation in Material with µ <0 and ε <0 (backward wave propagation ) E Vp<0 Vg>0 source + 0 X

21 P is opposite to k! This causes reversion of many basic electromagnetic phenomena such as Snell law, Doppler effect e.t.c.

22 Reversion of Snell Law air (ε r=1, µ r=1) Left-handed material Material with Right-handed material Material with ε r<0, µ r <0 ε r>0, µ r>0 φ φ

23 Concave and Convex Lenses using material with µ <0 and ε <0

24 The Concept of Metamaterial a host material scatterer (implant) E P H incoming plane wave a<<λ, the structure behaves as a homogenous material with some new µ and ε metamaterial

25 Classification of Metamaterials Singlenegative materials (SNG) Doublepositive materials (DPS) Doublenegative materials (DNG) Singlenegative materials (SNG)

26 Thin-wire Plasma-like Structure with ε <0 ( Rotman 1962, Pendry 1998) ε reffz ω p = 1 r ω a << λ ε a >>1 r 2 E P 1 real part H 0 f p imaginary part f

27 The Split-ring Resonator Structure with µ<0 (Pendry 1999) µ r real part 0 1 Imaginary part 0 r << λ f 0 f mp f a << λ

28 The first reported Backward-wave Material (Smith et al. 2000) Split-ring resonator SRRs only Thin-wire media SRRs +Wires Wires only k = ω µε SRR s SRR s and Wires wires only : : µ <0 µ >0 ε <0, >0, ε k, becomes k is again positive real number imaginary backward-wave number no no propagation

29 Capacitivelly loaded loops and thin-wire structure (Hrabar, Barbaric; /3)

30 Capacitivelly loaded loops and thin-wire structure (Hrabar, Barbaric 2000; 2/3)

31 Capacitivelly loaded loops and thin-wire structure (Hrabar, Barbaric 2000; 3/3) 0-20 transmission [db] frequency [Ghz] LHM wire medium capacitively loaded loops

32 The SRR behaves as capacitivelly loaded loop (Hrabar, Bartolic, Eres; 2002) Calculated effective permeability 5 4 H H = H i + H s = H i 1 j R + Kωµ 0 jωl S j ωc real part imaginary part 3 2 r Z Z a H I V + o i Z I H s Frequency [GHz]

33 Schelkunoff, Friis Antennas, Theory and Practice, 1952

34 Wire Medium as Transmission Line (Hrabar 2003,2006) E P ω p ε r = 1 ω a << λ 2 I(H) Z V(E) Y H 2 2 x E V 2 ε 0 2 = ω µε E = = ZY V Freespace Wires 0 ε r <0 = ( j ω µ )( j ω ε )E) E ( jωx )( jωy )V 0 series f<f p 0 ε r <0 shunt f>f p 0>ε r >1 1 0 a r >> ε reffz f p 1 real part imaginary par f )l )l )l )l

35 New Physical Phenomena - Fundamental research

36 Experimental Verification of Negative Refraction (Shelby et al. 2001)

37 Experimental Verification of Negative Refraction (Shelby et al. 2001)

38 Experimental Verification of Negative Refraction (Hrabar, Bartolic; /2) 1 2 3

39 Experimental Verification of Negative Refraction (Hrabar, Bartolic; /2) 1 2 3

40 Simulation of Negative Refraction at Planparallel Slab with n=-1 (Ziolkowski; 2003)

41 Verification of BW propagation by measurement of Negative Refraction (Hrabar, Bartolic, Sipus, 2004) d 1 1 b) a) double rings ) x ) x metallic plate absorber E H P a) A case of forward-wave slab (ε>0,µ>0) b) A case of backward-wave slab (ε<0,µ<0)

42 Super Lens with no Resolution Limit (Pendry, 2000) ε r r µ =1 =1 ε r µ =-1 =-1 r ε r µ =1 =1 r source focus Propagating part of Fourier spectrum Evanescent part of Fourier spectrum

43 Experimental verification (Grbic et al /2) Figure taken from G. Eleftheriades (University of Toronto) presentation slides

44 Experimental verification (Grbic et al /2) Figure taken from G. Eleftheriades (University of Toronto) presentation slides

45 Potential Engineering Applications I Guiding of EM energy

46 Classical rectangular waveguide Electrical field distribution (TE case) High-pass behavior Transmission f < f c, Evanescent E field ISOTROPIC DPS MATERIAL 1 Forward waves ε r >0 µ r >0 ε r f/f c f > f c, Propagating E field P, k P, k

47 Miniaturized Waveguide based on Anisotropic Meta-material (Hrabar, Bartolic, Sipus; 2003) d d

48 Miniaturized Waveguide based on Negative Permeability Metamaterial (transversal dimension reduced down to 25%)

49 Miniaturized waveguide (a=15 mm) filled with capacitively loaded rings the transversal width reduced down to 4%! copper ring chip capacitor

50 Potential Engineering Applications II Antennas

51 Does an open-ended SNG-filled miniaturized waveguide radiate into a free space? (Hrabar, Zivkovic; 2005) The simulated radiation (BW mode, k<0) RF feed

52 Experiemental Miniaturized Open-ended MNG Waveguide Radiator (Hrabar, Jankovic 2005) the aperture (0.25 λx 0.25 λ ) coaxial feed the double ring inclusions lattice constant of 6 mm

53 Phenomenon of ultra-refraction ε r1 ε r2 sin sinθ θ 1 = 2 ε ε r 2 r1 Antenna θ 1 θ 2 If medium 2 is air θ 1 θ 2 θ if 2 ε = r sin 1 = 0 θ ( ( )) ε sin θ r1 2 = 0. 1

54 [db] GHz GHz Figures copied from the original article

55 Shortened Horn with ENZ Metamaterial (Hrabar, Bonefacic, Muha, 2008) Simulated magnitude of the y-componnet of electric field of the shortened horn

56 Simulated magnitude of the y-componnet of electric field of the shortened horn with ENZ slab

57 Comparison of prototyped shortened horns (length of 33% of the length of optimal horn) (length of 52% of the length of optimal horn)

58

59 Potential Engineering Applications III Resonators

60 Sub-wavelength Resonator (Engheta, 2001) slab 1 ε µ 1>0 1 >0 slab 2 ε µ 2<0 2 <0 P 1 P 2 k 1 k 2 metallic plate metallic plate The resonance frequency depends on d 2 /d 1 instead of d 2 +d 1 which would hold in ordinary materials

61 Experimental verification of Engheta s resonator (Hrabar et al., 2004) slab 1 slab 2 ε 1 ε >0 µ 1 µ 2<0 >0 2 <0 waveguide part (backward-wave line) coupling loop coaxial part (forward-wave line) the slot P 2 P 1 k 2 k 1 metallic plate metallic plate N connector the inclusion N connector 0 x (f=350 MHz) overall length ~ λ/30

62 Potential Engineering Applications IV Going optical!

63 Going Optical - Approach I Scaling Down the Size of Inclusions Figure taken from V. Shalaev (Purdue University ) presentation slides

64 Going Optical Approach II Make Use of Surface Plasmons The Lycurgus Cup (glass; British Museum; 4 th century A. D.)

65 Going Optical A Soft Approach Make Use of Surface Plasmons Permittivity of silver

66 From Plasmonic Spheres to Nano-circuit Elements in Optical Domain (Alu, Engheta; 2005) Nano-transmission-lines Forward-wave Nano-antenna Nano-circuit Backward-wave

67 New Idea - Scaled RF Replicas of Plasmonic Structures

68 Prototyping of RF replicas of plasmonic spheres (Hrabar, Eres; Kumric, 2007) Simulated E-field distribution of ideal plasmonic nanosphere Best s spherical resonator

69 Prototyping of Plasmonicc spheres diameter = 5.8 cm

70 L Measurement of E-field phase distribution along four-sphere chains (RF replicas of plasmonic WG) Measuring points 1 20 Phase[degrees] solid: simulated; dashed: measured FW T 1 20 Measuring points Phase[degrees] Measuring point solid: simulated; dashed: measured BW Measuring point

71 Prototyping of RF analog of plasmonic circular cluster (Hrabar, Muha, Zaluski, Mlakar, 2010)

72 Figure taken from N. Engheta (University of Pennsylvania) presentation slides

73 Figure taken from N. Engheta (University of Pennsylvania) presentation slides

74 Figure taken from N. Engheta (University of Pennsylvania) presentation slides

75 Scaled prototype of optical D-dot wire (Muha, Hrabar et al. 2011)

76 Near-field Superlens Figure taken from V. Shalaev (Purdue University ) presentation slides

77 Experimentally achieved images N. Fang, H. Lee, C. Sun, X. Zhang, Science 308, 534, (2005). written object (top) optical image (center) optical image without super- lens

78 Potential Engineering Applications V Is it feasible to be invisible?

79 Figure taken from V. Shalaev (Purdue University ) presentation slides

80 Transformation Electromagnetics (Dollin 1961, Pendry 2006) Experimental verification already reported

81 First Experimental Results (Schurig 2006) Simulations Measurements

82 Figure taken from V. Shalaev (Purdue University ) presentation slides Problem 1 All these structures are again extremely narrowband!

83 Problem 2 All these structures have significant loss! Figure taken from V. Shalaev (Purdue University ) presentation slides

84 Dispersion models of passive materials (metamaterials) with ε r <1 or µ r <1 Drude model ε reffz 1 0 real part imaginary part f p f 0 Lorentz model µ r real part 1 part 0 f 0 f mp f Imaginary Both of these models are highly dispersive for 0< ε r <1 (or 0< µ r <1)

85 Resonance is always present in passive metamaterials WHY? ) dielectric E URL: Walter Fendt, September 9, 1998

86 Can one go around the dispersion-energy limitations? W = W e + W m = 1 ε 0 2 ( ωε ) ω r E µ 0 ( ωµ ) ω r H 2 ( ωε r ) ( ωµ r ) > 0, ω ω > 0. W<0,??? The only way is to use active medium (i.e. to introduce active elements)!

87 Active medium should introduce assisting negative restoring force! F as One would need a negative spring or a negative mass URL: Walter Fendt, September 9, 1998

88 Going Active - Non-Foster reactive elements (negative C and negative L) jx X C X L f -jx X C X L Z in = V I in in = V I l l = Z l

89 New idea : Introduction of negative capacitance into TL (Hrabar et al, APS 2008) Positive capacitance Negative capacitance C = C 1 + C 2 C e = C+ + C = C+ C ε ε ε ε 0 ε 1 ε e = + = < < 0 0

90 Experimental RF Active ENZ TL with Three Unit Cells (l = 1 m), (Hrabar et.al 2011) Z 0 Realistic C Realistic C Realistic C )x=λ/30 )x=λ/30 )x=λ/30

91 Measurement of effective permittivity of ENZ Active TL with Three Unit Cells (Hrabar et.al 2011) ENZ switched OFF ENZ switched ON

92 Potential Engineering Applications VI Going nano?

93 Graphene-based One-atom-thick Metamaterials Figures taken from N. Engheta (University of Pennsylvania) presentation slides

94 Graphene-based Metamaterials Figures taken from N. Engheta (University of Pennsylvania) presentation slides

95 What s next? Nanotechnolgy + metamaterials (plasmonics,,photonics, lasing, gain materials, superluminal materials, graphene, nano-spheres and nanofilms) Gravity, matter, acoustics + metamaterials (black hole metamaterials, seismic metamaterials, acoustic lenses)

96 Conclusions Metamaterials offer new exciting physical phenomena, which are very often counterintuitive! In author s opinion, this area is not in its infant phase any more and applications, that make use of new intriguing phenomena are expected to come in coming years! It is an interdisciplinary field which needs extensive collaboration of different worlds (math, physics, engineering, at least!)