negative refraction - fcu 20091103ccf.ee.ntu.edu.tw/~ypchiou/photonic_crystals/lhm.pdfpendry et al,...
TRANSCRIPT
Introduction to
Yih-Peng Chiou (邱奕鵬)
Graduate Institute of Photonics and Optoelectronics &Department of Electrical Engineering
National Taiwan University
November 7, 2011
Left-handed Materials
2
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
3
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
4
Review of Electromagnetics
Polarization EP eχε 0=
litysusceptibi electric :eχ
Rao, Elements of Engineering Electromagnetics
5
Some Quantities in EM Waves
Rao, Elements of Engineering Electromagnetics6
Rao, Elements of Engineering Electromagnetics
7
Review of Electromagnetics
Electric displacement
Dispersive
Anisotropic
constant) c(dielectrity permittivi relative :)1( 000
r
re EEPEDε
εεχεε =+=+=
)(ωεε rr =
8
Review of Electromagnetics
Magnetization
01 μχχ BM
m
m
+=
litysusceptibi magnetic :mχ
9Rao, Elements of Engineering Electromagnetics
10Rao, Elements of Engineering Electromagnetics
11
Review of Electromagnetics
Magnetic field intensity
Dispersive:
Anisotropic
ty permeabili relative :
)1( 000
r
rm
BBMBH
μμμχμμ
=+
=−=
)(ωμμ rr =
12
Maxwell’s Equations
22
2
d EEdt
με∇ =Wave Equation:
13
Review of Electromagnetics
Phase velocityvelocity of the propagation of an equal phase surface
Group velocityVelocity of the propagation of a wave packet
Energy velocityVelocity of the propagation of the electromagnetic energy
pv
gv
ev
14
Questions
?
?
and of the same direction (movie)
always positive
pg vv =
HESk ×= //
pv gv
n0>v pi
15
Questions
?
and of the same direction? (movie)
always positive?
pg vv =
HESk ×= //
pv gv
n
?
16
Normally not
Dispersive materials
pg vv = ?
= =p gdv vd
ω ωβ β
17
Questions
?
and of the same direction? (movie)
always positive?
pg vv =
HESk ×= //
pv gv
n
?
18
HESk ×= // ?
K. Iizuka, Elements of Photonics
19
HESk ×= // ?
Not always!
K. Iizuka, Elements of Photonics
Usually not foranisotropic materials
20
Indicatrix Methodof Anisotropy
K. Iizuka, Elements of Photonics
21
refinc θθ ≠
K. Iizuka, Elements of Photonics 22
Questions
?
?
and of the same direction (movie)
always positive
pg vv =
HESk ×= //
pv gv
n ?
?0>v pi ?
Not Always!
24
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
25
Victor G. Veselago, Soviet Physics, 1968 predicted EM wave behaviors in
left-handed materials (LHM) ε <0, μ <0 => n<0
0 0r rn με μ ε
μ ε= ± = ±
26
Some Non-Intuitive Properties of Negative Refraction
A beam incident on an LHM from an RHM refracts to the same side of the normal.
A point source impinging on a flat, parallel slab of LHM would be refocused to a point on the opposite side of the material.
Of suitable index, it can produce a focus with subwavelength resolution beating the normal diffraction limit associated with positive refractive index optics.
Misc. applications: e.g. open cavity.
27
θinc θrefl
θtrans
metamaterial
Free space
Snell’s Law
28
Refocusing and Open Cavity
29
Self-imaging
30
Simulation
Finite-Difference Time-Domain MethodUsing Dispersive ModelingDispersive PML
Taflove, Computational Electrodynamics –The Finite Difference Time Domain Method, Artech House, 2000
Normal NIM NIM-slab
31
Normal incident
Division points in one wavelength = 20;n = -1;
32
Oblique incident
Division points in one wavelength = 20;n = -1;The angle of incidence = 20 degree;
Division points in one wavelength = 40;n = -2;The angle of incidence = 20 degree;
33
Negative refraction index prism
Division points in one wavelength = 20;n = 2;
Division points in one wavelength = 20;n = -1;
34
Sub-diffraction limited focusing
35
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
36
Victor G. Veselago, Soviet Physics, 1968 predicted EM wave behaviors in
left-handed materials (LHM) ε <0, μ <0 => n<0
0 0r rn με μ ε
μ ε= ± = ±
37
j ze β−
2= nπβλ
38
39
Permittivity, Permeability Reflection, and Refraction
μηε
=
2 1
2 1+η ηη η
−Γ =
40
Negative Permittivity (Permeability)
Polarization
Harmonically bounded oscillationPolarization out of φ of applied field (ω<ωo)Near resonance freq.Polarization overcome applied field
EP eχε 0=
litysusceptibi electric :eχ
41
Extremely low frequencyplasmons in metallic mesostructure
Periodic array ofmetal thin wires (TW)tunable in the GHz range
Pendry et al, PRL 76, 4773, 1996
lossless
42
Magnetism from conductorsand enhanced nonlinear phenomena
Periodic array of metalsplit-ring resonator (SRR)tunable in the GHz range
Pendry et al, MTT 47, 2075, 1999
lossless
43
The Building Blocks of LHM
2
2( ) 1 pωε ω
ω= −
2
2 20
( ) 1 Fωμ ωω ω
= −−
Electric DipolesElectric Dipoles Magnetic DipolesMagnetic Dipoles+
44
Real partAlways small than 1
Imaginary partAlways positive
Drude modelΓ = 1e8 s-1
f0 = 30 GHzωp = 2πsqrt(2) f0
-1
f0
It will intersect at 0 whenfrequency equals to
ωp = 266 GHz
Real partAlways small than 1
Imaginary partAlways positive
Drude modelΓ = 1e8 s-1
f0 = 30 GHzωp = 2πsqrt(7) f0
-6
f0
It will intersect at 0 whenfrequency equals to
ωp = 498 GHz
))(
1()(2
0e
pe
iΓ+−=
ωωω
εωε
))(
1()(2
0m
pm
iΓ+−=
ωωω
μωμ
Drude model:
45
Drude-Lorentz Model
J. B. Pendry et al., IEEE/MTT 47, 2075(1999)
Array of wire elements
Split−ring resonator (SRR)
46
Split rings and metal strips
Rings and strips on opposite sides of a fiber glass circuit board
Cell dimension: 5mmInput: X-band (8~12 GHz)
~30 mm @ 10GHz
D. R. Smith et. al., Science, 292, 77 (2001)
47
Left-Handed Materials for Real
D. R. Smith et. al., Physics Today, 17, May (2000).
Phys. Rev. Lett. 84, 4184 (2000) ; Science, 292, 77 (2001)48
49
Metamaterial
50
LHM Measurement
51
25.6 deg n = 1.41
18.4 deg. n = -1.0
52
ω: magnetic/electronic plasma/resonance frequencies
Total internal reflection?
53OptExp200304, v11, p640, Kolinko
Refraction from a wedge
54
Stepped pattern
55 56
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
57
Some Other Behaviors of LHM
Sub-diffraction limited focusingInterchange of convergence and divergence effects in convex and concave lenses, respectively, when the lens is made LHMReversal of Doppler effectReversal of Vavilov-Cerenkov radiationReversal of the boundary conditions relating the normal components of the electric and magnetic fields at the interface between a conventional/righthanded (RH) medium and a LH mediumNegative space Magic transformation => invisible cloaks
58
Sub-diffraction limited focusing
59
f = R/(n − 1)
60
Negative index focusing lens
61
Reverse Doppler Effect in LHM
In RHM, EM waves undergo blue shift when they are reflected from a approaching object, or red shift from a leaving object
In LHM, it is reversed
cnvcnvff
/1/1' 0 +
−=
(LHM)
(RHM)
(LHM)
(RHM)n < 0
cnvcnvff
/1/1' 0 −
+=
62
Reverse Cerenkov Radiation
63
Boundary Conditions
antiparallel
antiparallel
64
Localized Surface Wave
65 66
Negative Space
67 68U. Leonhardt et al., Science 323, 110 -112 (2009)
Invisible Cloak
Coordinate transformation
69
J. B. Pendry et al., Science 312, 1780 -1782 (2006)
70
Realization of Invisible Cloak
D. Schurig et al., Science 314, 977 -980 (2006)
71D. Schurig et al., Science 314, 977 -980 (2006) 72D. Schurig et al., Science 314, 977 -980 (2006)
simulation
(reduced material properties)
73U. Leonhardt et al., Science 323, 110 -112 (2009)
Wider Operating Frequency
74
U. Leonhardt et al., Science 323, 110 -112 (2009)
3D cloaking
Wider Operating Frequency
75
New invisibility cloak allows object to 'see' out through the cloak
PRL 102, 093901 (2009) 76
New invisibility cloak allows object to 'see' out through the cloak
PRL 102, 093901 (2009)
77
Outline
Review of Electromagnetics
Negative Refractive Index
Making Left-Handed (Meta)materials
Some Other Behaviors
Transmission Line Approach
78
Transmission Line (TL) Approach
Equivalent circuit model of SRR
79
Two Different Approaches
Resonant StructureResonantLossyNarrow bandEM wavesNo systematic analysis
Transmission LineNon-resonantLow lossBroad bandCircuitsSystematic analysis
Backward waves have been analyzedMost mathematics are already there
Planar config. Microwave IC
Trade-off between BW and loss
Caloz and Itoh, Electromagnetic Metamaterials80
Incremental circuit model
Caloz and Itoh, Electromagnetic Metamaterials
81
Planar TL LH Structures
Caloz and Itoh, Electromagnetic Metamaterials82
Composite Right/Left-Handed (CRLH) Metamaterials
Infinite wavelength
Caloz and Itoh, Electromagnetic Metamaterials
83
Some Remarks
Photonics crystals or photonic band gap (PBG)Size p ~ nλ/2
Effective homogeneity in LHMSize p < λ/4
Properties of photonic crystals are essentially determined by the lattice, while the (refractive) properties of MTM are determined by the nature of the unit cell
84
Terminology
Left-handed (LH)originally suggested by Veselago
Doubly-negative (DNG)Negative-refractive-index (NRI)Negative index materials (NIM)Backward-wave (BW)Veselago mediumNegative phase velocity medium (NPV)