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 E P e χ ε 0 = lity susceptibi electric : e χ Rao, Elements of Engineering Electromagnetics
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Negative Refraction - FCU 20091103ccf.ee.ntu.edu.tw/~ypchiou/Photonic_Crystals/LHM.pdfPendry et al, PRL 76, 4773, 1996 lossless 42 Magnetism from conductors and enhanced nonlinear
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Introduction to
Yih-Peng Chiou (邱奕鵬)
Graduate Institute of Photonics and Optoelectronics &Department of Electrical Engineering
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
?
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HESk ×= // ?
K. Iizuka, Elements of Photonics
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HESk ×= // ?
Not always!
K. Iizuka, Elements of Photonics
Usually not foranisotropic materials
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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
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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= ± = ±
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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.
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
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Sub-diffraction limited focusing
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f = R/(n − 1)
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Negative index focusing lens
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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 −
+=
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Reverse Cerenkov Radiation
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Boundary Conditions
antiparallel
antiparallel
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Localized Surface Wave
65 66
Negative Space
67 68U. Leonhardt et al., Science 323, 110 -112 (2009)
Invisible Cloak
Coordinate transformation
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J. B. Pendry et al., Science 312, 1780 -1782 (2006)
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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
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U. Leonhardt et al., Science 323, 110 -112 (2009)
3D cloaking
Wider Operating Frequency
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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
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
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Planar TL LH Structures
Caloz and Itoh, Electromagnetic Metamaterials82
Composite Right/Left-Handed (CRLH) Metamaterials
Infinite wavelength
Caloz and Itoh, Electromagnetic Metamaterials
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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
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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)