Metamaterials: Negative refractive index in microwave and optics

IFIN_Theor_Phys_Dept_111810
Metamaterials:
Negative refractive index in
microwave and optics
Physical principles and perspectives
George Nemeş
ASTiGMATTM, 1457 Santa Clara St. Ste. 6, Santa Clara, CA 95050
gnemes@astigmat-us.com
ASTiGMAT
Acknowledgments:
- Interested attendees
Outline:
1. Goal
2. Terminology, definitions, brief history
3. Metamaterials physics: How can be n < 0?
4. Physical properties of metamaterials having n < 0
5. Veselago-Pendry "ideal lens"
6. Experimental results (2000-2009)
7. Potential applications of utmost interest
8. Comments
9. Conclusion
ASTiGMAT
1. Goal
Introduction to the field of metamaterials
with negative refractive index (n < 0)
ASTiGMAT
2. Terminology, definitions, brief history
2.1. Terminology
- Negative refractive index (NRI) materials
- "Left handed materials" (LHM; the vectors E, H, k are oriented using the
"left-handed" rule rather than the regular "right-handed" rule)
- Metamaterials (MTM; linear materials, quasi - homogeneous, artificially
made, with NRI)
- Photonic crystals (PhC; sometimes used, partially incorrect)
- Other: double negative materials, single negative materials
ASTiGMAT
Metamaterials and photonic crystals - main difference
a - spatial period
(From: V. M. Shalaev, Purdue Univ., Talk at 1st Metamaterials Congress, Rome, 2007)
ASTiGMAT
2.2. Metamaterials: formal definition
•
2001: Rodger Walser, University of Texas, Austin, introduces
(published paper) the term "metamaterial" referring to artificial
composites that "...have performances beyond the limitations of
conventional composites".
•
2001: Valerie Browning, Stu Wolf, DARPA (Defense Advanced
Research Projects Agency), extend the definition in the context of the
DARPA Metamaterials program :
Metamaterials are a new class of ordered nanocomposites that exhibit
exceptional properties not readily observed in nature. These properties
arise from qualitatively new response functions that are: (1) not
observed in the constituent materials and (2) result from the inclusion of
artificially fabricated, extrinsic, low dimensional inhomogeneities.
ASTiGMAT
More definitions
Meta- denotes position behind, after, or beyond, and also something of a higher or
second-order kind. . .
a) Short and general: Metamaterial is an arrangement of artificial structural
elements, designed to achieve advantageous and unusual properties.
b) Long: Metamaterial is an artificial material possessing engineered effective
electromagnetic properties resulting from response functions not found in
constituent materials and not readily observed in nature.*
c) Narrow: Metamaterial is an artificial material whose effective properties cannot
be determined by only material parameters, shape, and concentration of the
constituent inclusions.
* Based
on the definition of J. Pendry, 2000.
(S. Tretyakov, Helsinki University of Technology, SMARAD Centre of
Excellence, September 2006; Director of Metamorphose – European Network of
Excellence)
ASTiGMAT
2.3. Brief history
2.3.1. Known and "acknowledged" ("modern") history
- V. G. Veselago (Lebedev Physics Institute, Moscow) – theory
UFN 92, 517 (1967) (Russian)
Æ εr < 0; μr < 0 Æ n < 0
Sov. Phys. Usp. 10, 509 (1968) (English)
- J. B. Pendry et al (Imperial College, London) – theory to obtain
materials having εr < 0; μr < 0, not for n < 0
Phys. Rev. Lett. 76, 4773 (1996) Æ theory to obtain εr < 0
J. Phys. Condens. Matter 10, 4785 (1998) Æ experiment εr < 0
IEEE Trans. MTT 47, 2075 (1999) Æ theory to obtain μr < 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. Oliner; C. Caloz et al – transmission line
model (nonresonant, wide band structures) (June 2002)
IEEE-MTT Symposium; USNC/URSI Nat. Sci. Radio Meeting
ASTiGMAT
Founders of the modern metamaterials field
Viktor G. Veselago
(Prokhorov Inst. of
General 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 1964
Pendry: The goal is different than to verify Veselago’s theory.
Shows how to obtain ε < 0 and μ < 0, independently
First experimental proof of Veselago’s theory,
synthesis of a material having n < 0
Proves the possibility that materials with complex n
(having absorption) can have Re [n] < 0
ASTiGMAT
Pendry’s structures to obtain:
ε < 0 (up, left) - 1996
μ < 0 (up, right; both right pictures) - 1999
C. Caloz, T. Itoh, Electromagnetic Metamaterials: Transmission Line
Theory and Microwave Applications, Wiley, Hoboken, NJ, 2006
ASTiGMAT
2.3.2. Less known history ("old" results, before Veselago’s; incomplete list)
"Everything 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-scattering.com/negative.html
- S. A. Tretyakov, "Research on negative refraction and backward-wave media: A historical
perspective", EPFL Latsis Symposium 2005, Lausanne, Feb.-Mar. 2005
- C. Caloz, T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave
Applications, 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 Theory of Optics, Edward Arnold,
London, 1904, pp. 313-318 (backward eltm. waves)
- H. C. Pocklington, Nature 71, 607 (1905) (phase velocity oriented
opposite 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. Malyuzhinets, Jh. Tekh. Fiz. 21, 940 (1951) (Russian) (vp anti II vg)
- D. V. Sivukhin, Opt. Spektrosk. 3, 308 (1957) (Russian) (n < 0)
ASTiGMAT
Examples of "old" results
Wire media in the 1960s
W. Rotman, IRE Trans. Antenna Propagation
10, 82 (1962)
Split rings in the 1950s
S. A. Schelkunoff et al, Antennas:
Theory and Practice,
Wiley, NY, 1952
Backward-wave transmission lines
G. D. Malyuzhinets, Jh. Tekh. Fiz. 21, 940 (1951)
ASTiGMAT
2.4. Early dynamics of the metamaterials field related to n < 0
Number of published papers
on materials with n < 0 (until
the end of 2002)
(J. B. Pendry, Opt. Express
11, 639 (2003))
2003: The field "explodes": annual special sessions at conferences, special issues of
scientific 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.infobase.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.infobase.org)
- Progress in Electromagnetic Research 35 (2002); 41 (2003); 42 (2003); 51 (2005);
63 (2006), 70 (2007) (http://ceta.mit.edu/pier/notify.php) – electronic journal, free
ASTiGMAT
Specially dedicated journal
- Metamaterials, Elsevier, 2007 (No. 1, March)
The Journal Metamaterials is associated with the
Metamorphose Network of Excellence (Europe)
Coordinating Editor: Mikhail Lapine
Publisher: Elsevier
ASTiGMAT
Published books (2005-2009):
- G.V. Eleftheriades, K.G. Balmain, Negative-Refraction Metamaterials:
Fundamental Principles and Applications, Wiley, Canada, 2005
- C. Caloz, T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory
and Microwave Applications, Wiley, Hoboken, NJ, 2006
- N. Engheta, R.W. Ziolkowski, Eds., Electromagnetic Metamaterials:
Physics and Engineering Explorations, Wiley, 2006
- V.M. Shalaev, A.K. Sarychev, Electrodynamics of Metamaterials, World
Scientific, Singapore, 2007.
- J.-P. Berenger, Perfectly Matched Layer (PML) for Computational
Electromagnetics, Synthesis lectures on Computational Electromagnetics
Series, Morgan&Claypool Publishers, 2007.
- R. Marqués, F. Martín, M. Sorolla, Metamaterials with Negative Parameters:
Theory, Design and Microwave Applications, Wiley Series in Microwave and
Optical Engineering, Wiley, Hoboken, NJ, 2008.
- L. Solymar, E. Shamonina, Waves in Metamaterials, Oxford Univ. Press, NY, 2009.
- B.A. Munk, Metamaterials: Critique and Alternatives, Wiley, Hoboken, NJ, 2009.
- Y. Hao, R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications,
Artech House, Norwood, MA, 2009.
ASTiGMAT
Metamorphose-organized conferences on Metamaterials
1st International Congress On Advanced Electromagnetic Materials in
Microwaves and Optics, Rome, Italy, 22-26 October 2007 (Metamaterials'07)
(Proceedings - free, from:
http://www.metamorphose-vi.org/index.php?Itemid=193&id=110&option=com_content&task=view)
2nd International Congress on Advanced Electromagnetic Materials in
Microwaves and Optics, Pamplona, Spain, September 21-26, 2008.
3rd International Congress on Advanced Electromagnetic Materials in
Microwaves and Optics, London, UK, Aug. 30th-Sept. 4th, 2009.
4th Metamaterials'2010 Congress will be held in Karlsruhe, Germany, on
September 13-18, 2010 (The Conference is on September 13-16, and the
Doctoral School on September 17-18).
ASTiGMAT
Comments
- Veselago's theory was experimentally verified in the microwave
spectrum only in 2000 (33 years after it was formulated for
optics), even though the same technology used in 2000
was available back in 1967.
- Papers doubting the existence of n < 0 are published time to time and
perhaps will continue to be published for some time
ASTiGMAT
3. MetaPhysics of metamaterials: How n < 0 is possible?
3.1. Necessary conditions to have n < 0
- Refractive index n to be a quantity with physical meaning (to exist)
Æ the material to be homogeneous or quasi-homogeneous (the spatial
scale of the periodic inhomogeneities, p, to be p << λ, or p < λ/4 )
Ex. of homogeneous materials for visible light (λ ≈ 500 nm): gases,
liquids, transparent solids
Ex. of inhomogeneities with negligible size for visible light : atoms, molecules
Atomic diameters: 0.01 nm - 0.1 nm
Atomic bonds sizes: 0.1 nm - 0.2 nm
(C-C bond size: 0.154 nm; benzene hexagon bond size: 0.280 nm)
Typical oil molecule diameter : ≈ 2.0 nm - 2.5 nm
Compare with λVIS ≈ 500 nm
Æ Refractive and reflective phenomena are dominant (through n)
ASTiGMAT
- Examples of inhomogeneous materials for visible light:
Particles with sizes 100 nm - 10 μm dispersed in homogeneous media:
gases, liquids, solids (fog, smog, oil emulsions in water, colloidal
systems)
- Optical properties of inhomogeneous materials:
Scattering and diffraction phenomena are predominant as compared to
refraction or reflection phenomena Æ n cannot be defined
Scattering takes place at different angles including 1800 (backscattering)
Note: For microwaves (λ ~ 1000 mm - 10 mm), periodic inhomogeneities
with sizes p ~ 1 mm do not matter Æ material is ≈ homogeneous
Æ n does exist
ASTiGMAT
Electromagnetic field spectrum
≈ 800 nm Visible ≈ 400 nm
λ0
1 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
----------------------------------------------------------------------------------------------------------------------------------------------30 G; 300 G; 3 T;
30 T; 300 T; 3 P;
30 P; 300 P
f0 (Hz) 300 k; 3 M; 30 M; 300 M; 3 G;
ASTiGMAT
3.2. Definition 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 in homogeneous, charge-free materials:
(D = εE = ε0εrE; B = μH = μ0μrH; J = σE)
∇ x E = - ∂B/∂t
∇ x H = J + ∂D/∂t
∇D=0
∇B=0
ASTiGMAT
3.2. Definition of n: two possible solutions
- Plane wave-type solution: E(t,r) = E0 exp j(ωt – kr); analogously H(t,r)
∇2E + μσ ∂E/∂t + με ∂2E/∂t2 = 0; analogous for H
∇ = – jk; ∂/∂t = jω;
k x E = + ωμH
k x H = – ωεE
∇2
=–
k2;
∂2/∂t2
=–
H
k
S
H
E, H, k is right-handed for ε > 0; μ > 0
Æ
E
E, H, k is left-handed for ε < 0; μ < 0
- Solution (perfect, absorption-free dielectric):
RHM
E
ω2
k2
=
ω2εμ
=
LHM
k
ω2/vp2
=
S
ω2n2/c2
c2 = 1/(ε0μ0) Æ n2 = εrμr; ε > 0; μ > 0 Æ n > 0 Å usual case
ε = – |ε| = ejπ|ε| < 0; μ = – |μ| = ejπ|μ| < 0; Æ n = ejπ√|εrμr| = – |n| < 0
- Poynting vector: S = E x H; For n > 0 Æ k II S; For n < 0 Æ k anti II S
n = ±√εrμr Å Veselago
ASTiGMAT
3.3. Possibility that n < 0
Plane (ε, μ) (J. B. Pendry, Opt. Express 11, 639 (2003); also Veselago)
ε < 0 naturally occurs in metals at optical
frequencies, or in plasmas, at infrared
frequencies.
μ < 0 naturally occurs in ferro- or antiferromagnetic resonant systems (low frequency
bands, < THz).
Quadrants I, III Æ propagation, transmission
Quadrants II, IV Æ evanescent (decaying) field
Æ no propagation, no transmission
Pendry (1996 -1999) Æ methods to synthesize "solid plasmas" with ε < 0 and
magnetic structures with μ < 0 in GHz frequency range Æ Periodic structures
with adjustable geometrical parameters. ε: parallel metallic rods with spatial
periodicity; μ: metallic split rings = resonant LC circuits at GHz frequencies,
periodically positioned in space (split-ring resonators, or SRR).
ASTiGMAT
3.4. Examples of Pendry periodical structures
(a) Metallic rods (ε < 0 for E II z); (b) Split ring resonators (μ < 0 for H II y).
In both cases p << λ. Anisotropic structures
ASTiGMAT
Effective relative permittivity, εreff, and effective
relative permeability, μreff
- Condition to have the effective material constants εreff,
μreff: p << λ
- Drude - Lorentz model of oscillator
εreff = 1 – ωpe2/(ω2 – ω0e2 + jωΓe) = 1 – ωpe2/(ω2 + jωΓe)
μreff = 1 – ωpm2/(ω2 – ω0m2 + jωΓm)
ω0e - electric-type resonant frequency; ω0e Æ 0; ωpe - electric-type “plasma” frequency
ω0m - magnetic-type resonant frequency; ωpm - magnetic-type “plasma” frequency
The constants ωpe, ωpm, ω0m depend on geometry and size of wires and SRR
The constants ω0e Æ 0, Γe, Γm, depend on material properties
(J. B. Pendry et al, IEEE Trans. MTT 47, 2075 (1999))
ASTiGMAT
Effective relative magnetic permeability (μreff) for the
split-ring resonators structure
Pink band: frequency interval of
interest, μreff < 0
μreff = 1 – ωpm2/(ω2 – ω0m2 + jωΓm)
In the picture Γm ≈ 0
ω0m - magnetic-type resonant frequency; ωpm - magnetic-type “plasma” frequency
(geometry determines these two quantities Æ bandwidth for μreff < 0)
Note: Similar behavior of εreff for the periodic structure using metallic rods
replacing: μreff Æ εreff; ωpm Æ ωpe (electric-type “plasma”); ω0m Æ 0
ASTiGMAT
3.5. Example of elementary cell ("atom") leading to n < 0
Marcoš, Soukoulis, Phys. Stat. Sol. (a) 197, 595 (2003)
Physically 2-D structure (periodical in x, y);
Electromagnetically 1-D structure (II z, anisotropic); E II y; H II x; k II z;
p = several mm; λ0 ≈ 30 mm; f0 ≈ 10 GHz; fpe ≈ 20 GHz.
ASTiGMAT
Idealized hypotheses (initially considered) and the real world
1. The electric and the magnetic properties do not interact to each other
2. Absorption (losses) in the materials is negligible
3. Simple geometrical structures, ignoring anisotropy (1-D, 2-D)
#1 Not valid Æ careful design to match the negative bands for εeff, μeff.
#2 and #3 also not valid Æ much research effort necessary Æ new
"atomic structures" (geometries), new materials, new principles to get
desired effects (some using PhC instead of NRI metamaterials).
Absorption Æ ε, μ, n - complex quantities: n = n' + jn"; ε = ε' + jε"; μ = μ' + jμ"
Useful effects: n'; Losses: n"; Causality: ε" > 0; μ" > 0
Factor of merit for negative refractive index: F = – n'/n"
Double-negative materials: n' < 0 because both, ε' < 0, μ' < 0 Æ F large
Single-negative materials: n' < 0 only because ε' < 0, and μ' > 0 Æ F small
ASTiGMAT
Transmission line approach to MTM with n < 0
Eleftheriades group
(Univ. Toronto, 2002 and after)
Analogy:
ε<0
⇔ L shunt
μ < 0 ⇔ C series
Advantage: Wide bandwidth
G.V. Eleftheriades, Radio Sci. Bull. 312, 57 (2005)
G.V.Eleftheriades, Talk at 1st Metamaterials Congress, Rome, 2007
ASTiGMAT
Generalized cell for NRI-transmission line MTM
G.V. Eleftheriades, Talk at 1st Metamaterials Congress, Rome, 2007
ASTiGMAT
4. Physical properties of metamaterials with n < 0
What physical (optical) effects appear in a metamaterial with n < 0
as 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
- Negative (reverted) refraction
- Light transmission without reflection is possible at the interface of two
materials with n1 = n > 0 and n2 = – n < 0
- Reverted Doppler effect (blue shift for the source departing from the observer)
- Reverted Cherenkov effect (the cone of emitted light shines 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 Æ New optics/electrodynamics/physics/new technologies
ASTiGMAT
4.1. Negative refraction
Refraction law (Snell's)
n1 sin(θ1) = n2 sin(θ2)
θ1 > 0
θ1 > 0
n1 > 0
n1 > 0
n2 < 0
n2 > n1 > 0
θ2 > 0
Usual case (positive refraction)
|n2| > n1 > 0
θ2 < 0
Negative refraction case
ASTiGMAT
Example of negative refraction (simulation)
G. Dolling et al, Opt. Express 14, 1842 (2006)
ASTiGMAT
4.2. Behavior of convex and concave lenses
Reverted behavior than in the usual case
(a) Convex lens Æ divergent effect
(b) Concave lens Æ convergent effect
Note: Similar behavior does exist in the microwave and the X-ray spectrum
for transparent materials with 0 < n < 1 (not n < 0)
ASTiGMAT
4.3. Possibility that the reflectance to be zero
Supposedly we have at the interface 1-2:
ε2 = – ε1 = – |ε| < 0; μ2 = – μ1 = – |μ| < 0 Æ n1 = n > 0; n2 = – |n| < 0
Impedances of the two media: Æ η = √|μ/ε| = η1 = η2
Reflectances (Fresnel formulae):
Rp,s = [η2cos(θ2,1) – η1cos (θ1,2)] / [η2cos(θ2,1) + η1cos(θ1,2)]
θ2 = – θ1; η2 = η1 Æ Rp = 0; Rs = 0
ASTiGMAT
4.4. Goos-Hänchen shift (effect)
- Takes place at total internal reflection (TIR) with linearly polarized beams
- It is a small (several λ) longitudinal displacement of the beam axis from the
pure geometrical optics (ray) description
- G-H displacement is greater for incidence angles, i, near the critical angle
Normal
n1 > 0
TIR Interface
n2 > 0
n2 < 0
|n2| > n1
Ordinary, forward
i
G-H shift, n2 > 0
Reverted, backward
Geometrical optics,
G-H shift, n2 < 0
no G-H shift
ASTiGMAT
5. Veselago-Pendry "ideal lens"
Ideal lens: plan-parallel plate with
εr = –1; μr = –1, placed in air (vacuum)
Veselago (1967-1968)
Pendry (2000)
Pendry: The spatial resolution of the
image made by the lens is given by the
evanescent field (that vanishes in
vacuum after (1-2)λ).
The lens material "amplifies" the
evanescent field Æ perfect spatial
resolution (~ 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 propagating field. The spatial resolution Δ is limited by
ktrM ≈ ω2/c2, because kz = (ω2/c2 – ktrM2)1/2 needs to be real to account for propagation Æ Δ ≈ λ.
(b) Attenuation of the evanescent field in the medium with n > 0 (classical lens in air or vacuum). The fine
structure of the object (small x, y) is revealed in the very large values of ktrM (by the Fourier transform
theorem), making the field to be evanescent (ktrM > ω/c) Æ kz = j(ktrM – ω2/c2)1/2. The information on the
very fine structure of the object does not exist at the imagine.
(c) Image through the “ideal lens” obtained with propagating field Æ Δ ≈ λ (identical to the case (a)).
(d) Image through the “ideal lens” obtained with evanescent field amplified by the “ideal lens” Æ
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 and
n = −1, equal thickness d Æ focusing
(b) Group and phase velocity in each
section
(c) Focusing with two complex sections,
with "mirror-like" properties of n
(d) Intuitive explanation of case (c):
total optical path length = 0
Note: Canceling of a positive optical path length can be done also with classical
lenses and free spaces (Sudarshan et al; Nemeş): "negative space" system
ASTiGMAT
Partial conclusion and comments
- Only the "classical" phenomena and configurations were considered
- Negative refraction does not necessarily mean n < 0
Photonic Crystals (PhC) can have negative refraction, though they
do not have n < 0 (they do not have a well-defined neff at all)
- PhC have low loss - can be used to obtain similar effects to those of MTM
- Other approaches toward n < 0 Æ Chirality (handedness) of structures
(Chiral object - asymmetric to its mirror image)
- New structures closer to isotropic MTM are conceived
- Alternating layers of positive and negative index MTM Æ new properties
(discrete or continuous 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
infrared, NIR)
- Recent (2006 - 2009) – NIR and visible
- New results and new trends (2006 - 2009):
- Finding new configurations for desired effects
- Finding useful applications in microwaves
- Race to obtain and extend visible working systems and applications
ASTiGMAT
First experiments (2000-2001)
1-D Metamaterial with n < 0 in microwaves (f ≈ 5 GHz)
(D.R. Smith et al, Phys. Rev. Lett. 84, 4184 (2000))
ASTiGMAT
First experiments
2-D Metamaterial with n < 0 in microwaves
(R. A. Shelby et al, Science, 292, 77 (2001);
J. B. Pendry, D. R. Smith, Phys. Today, June 2004
pp. 37-43); p = 5 mm; λ ~ 30 mm; f ~ 10 GHz
(a) Resonant structure: split-rings and metallic rods
(wires, visible in the back of the vertical holders)
(b) Spectral band where εr < 0 şi μr < 0
(c) Transmitted power spectrum: only metallic rods
(green); only split-rings (blue); both (red)
Æ transmission = propagation
ASTiGMAT
First experiments
Negative refraction in 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 prism
ASTiGMAT
Progress, microwaves
Metamaterial prism for
microwaves
(C. Soukoulis, OPN, June
2006, pp. 16-21)
ASTiGMAT
Progress, microwaves
Experiment to verify the transmission and the negative refraction
(C. Soukoulis, OPN, June 2006, pp. 16-21)
ASTiGMAT
Progress, microwaves
Veselago-Pendry lens for microwaves,
n = –1, spatial resolution < λ
(C. Soukoulis, OPN, June 2006, pp. 16-21)
ASTiGMAT
Progress: from microwaves toward optical spectrum
Example 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-type
ASTiGMAT
Experiments, microwaves: focusing plano-concave lens
Vodo 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 SRR
ASTiGMAT
Progress: from microwaves toward optical spectrum
Magnetic metamaterial for mid-infrared (λ ≈ 4.6 μm)
(S. Zhang et al, PRL 94, 37402 (2005))
ASTiGMAT
Progress: mid-near infrared
Distance between holes: 838 nm;
Holes diameter: 360 nm
Thicknesses Au/Al2O3/Au: 30/60/30 nm
n < 0 at λ = 2 μm
(S. Zhang et al, PRL 95, 137404 (2005))
ASTiGMAT
Progress: near infrared (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 μm
ASTiGMAT
Progress: visible (2007)
ASTiGMAT
Other recent issues (2006-2009)
Using 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 results
λ = 1400 nm
(C. Helgert et al, Opt. Lett. 34, 704 (2009))
ASTiGMAT
Photonic Crystals
- PhC are artificial materials with periodically modulated refractive index
in (1-D), 2-D, 3-D. The spatial period p ~ λ.
ASTiGMAT
Mother Nature and PhC
Quasi-periodical micro-structures performs as pass and stop bands for
light of certain wavelengths Æ different colors
PhC structure of butterly wings and of opal
Negative refraction in the eye of some insects and some
lobsters (D.G. Stavenga, J. Eur. Opt. Soc.- RP 1, 06010 (2006))
(A. Lakhtakia et al, OPN 18, 27 (2007))
ASTiGMAT
Photonic crystal (PhC) approach
PhC is different than MTM - uses diffraction, scattering
PhC has frequency (wavelength) band gaps
Smaller losses than MTM
(Pictures from: C. Lopez, Si PhC, OPN 20, 28 (2009))
ASTiGMAT
7. High-interest potential applications
7.1. Imaging with spatial resolution << λ (super-resolution)
7.2. Objects' camouflage (invisibility; cloaking)
- To radar (microwave spectrum)
- To visible light
- In both targeted areas the progress is remarkable and fast
- Practical applications are expected to emerge in 5 – 10 years
ASTiGMAT
7.1. Toward imaging with spatial resolution << λ
Planar lens for microwaves
f ≈1 GHz
(G.V. Eleftheriades, Talk at 1st Metamaterials Congress, Rome, 2007)
ASTiGMAT
Another slab (Veselago-Pendry-type) lens
(G.V. Eleftheriades, Talk at 1st Metamaterials Congress, Rome, 2007)
ASTiGMAT
New concept for super-resolution lens ("wire medium" lens)
Converting the evanescent field into propagating waves
Spatial resolution: λ/15 in microwaves
P.A. Belov et al, Phys. Rev. B 73, 033108 (2006)
Similar results obtained by the same group in THz regime
λ/20 @ 5 THz; λ/10 @ 30 THz
(Pictures courtesy P. Belov, Talk at Queen Mary Univ. of London, UK, 2006)
ASTiGMAT
7.1. Toward imaging with spatial resolution << λ
A planar lens in photolithography
Structure of the planar lens (left) and the corresponding spatial resolution (right)
Resolution = 145 nm; λ = 365 nm (filtered Hg lamp)
(D.O.S. Melville et al, J. Opt. Soc. Am. B 23, 461 (2006))
ASTiGMAT
7.2. Toward objects' camouflage (invisibility; cloaking)
- Problem: partial or total camouflage?
Partial invisibility – perhaps easier to obtain
Total invisibility – perhaps more useful
ASTiGMAT
Example of partial camouflage, obtained by techniques
different than using metamaterials
Site Prof. Susumu Tachi, Japan
www.projects.star.t.utokyo.ac.jp/projects/MEDIA/xv/oc.html
oc-okugai3.mpg
Mirror.mpg
Oc-s.mpg
Bone2.mpg
ASTiGMAT
Example of microwave (not visible) camouflage
Stealth fighter – "black" (low cross-section) in microwaves, yet visible
ASTiGMAT
Total invisibility by using geometrical transforms (theory)
and metamaterials (theory and experiment)
Principle: Surround the object desired to be invisible by a metamaterial specially
designed to distort the light ray paths through the metamaterial (red lines below)
by-passing the object, and then to restore them after the object exactly as they
were before by-passing the object (same positions and slopes) Æ invisible object
Site Prof. Ulf Leonhard, St. Andrews Univ., UK
http://www.standrews.ac.uk/~ulf/invisibility.html
ASTiGMAT
Results: invisibility using metamaterials
Theoretical concept illustrated for non-specialists
(ray paths in black - upper picture;
in red - lower picture)
J.B. Pendry et al, Science Express, 25 May 2006
ASTiGMAT
Results: invisibility using MTM. Simulations
Cloaking of a sphere of ≈ 0.2 m in diameter by a "shell" of metamaterial
ASTiGMAT
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 they
flow around a "hidden" object inside with
little distortion, making it appear almost as
if nothing were there at all.
Metamaterial for microwaves, "swiss roll" configuration,
first camouflage experiment, microwaves
ASTiGMAT
New (2008) cloaking experiments, visible (500 nm)
Design and simulations
Results. (a)-device; (b)-cloaked area
I.I. Smolyaninov et al, Opt. Lett. 33, 1342 (2008)
ASTiGMAT
Cloaking: new theoretical simulations, arbitrary-shaped object
Nicolet et al, Opt. Lett. 33, 1585 (2008)
ASTiGMAT
New (2009) reported cloaking experiment in microwaves
P. Alitalo, S. Tretyakov, Materials Today 12, 22 (2009)
ASTiGMAT
8. Comments
To start the involvement in the MTM field implies simultaneously tackling:
1. Theory
- Understanding specific phenomena involved
- Design of structures behaving as MTM
- Simulations
- Developing new ideas
2. Technology
- Obtaining the designed structures (various techniques for micro- and
nano- structuring)
3. Theory and experiments
- Measurement of physical parameters of interest (n, transmission bands, etc)
ASTiGMAT
9. Conclusion
- MTM is a fascinating "new" field, with > 100 years of theoretical history
and about 10 years of practical experiments Æ Physics, engineering.
Mother Nature designed PhC and perhaps also MTM much earlier.
- Periodic structures in different materials give rise to new, unexpected
behavior, desired or not, in the microwave, THz, and optical spectrum.
- MTM and PhC are complementary, and sometimes intertwining concepts.
The difference consists in the scale of spatial periodicity versus λ.
- Many microwave applications use already MTM concepts.
- Major expected applications:
Super-resolution optics
Cloaking at microwave and optical frequencies
- The dynamics of the field is fast and the money involved is huge.
ASTiGMAT