Flirting with Invisibility

Transcrição

Cloaking
Own Research
Outlook
Andreas Helfrich-Schkarbanenko
Karlsruhe Institute of Technology (KIT)
March 28th 2013
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Cloaking
Own Research
Outlook
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What is this talk about?
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Which ideas/approaches are there?
Classification of them?
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What is the level of cloaking?
What are the outcoming problems?
Which questions are still open?
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Outlook of invisibility?
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Cloaking
Own Research
Outlook
Transformation Optics
Acoustics
Electromagnetics
Elastodynamics
Survey of Cloaking
Szenario: Incident wave hits an obstacle.
Figure: Incident, scattered and total fieled [numathics.com]
Ambition: Minimize the scattered field.
Any idea?
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Survey of Cloaking - Any Idea?
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Survey of Cloaking - Any further Idea?
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Survey of Cloaking - One more idea?
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Survey of Cloaking - Ideas
Principle 1: passive cloaking
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Metamaterials Guiding the incident waves around the obstacle via transformation
or change of variables for mapping the cloaked region to a point with vanishing
scattering strength. This leads to anisotropic materials (metamaterials) [9] which
can be approximated by bi-layered isotropic media. Isotropy is highly relevant for
the praxis!
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Scattering cancellation approach Idea: intelligent scattering [1, Chap.10]
Principle 2: active cloaking
I Apply additional wave-sources such that the total field features the desired
property [15].
Principles 1 and 2 can be classified in exterior and interior cloaking.
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Passive Cloaking via Metamaterials
(
ϕ(x) :=
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1+
)
1
x
|x|
,
2
|x|
for 0 < |x| ≤ 2
ϕ is smooth except at 0;
ϕ blows up the point 0 to the ball B1 , while mapping the full domain B2 to itself;
ϕ(x) = x at the outer boundary |x| = 2.
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Acoustics
Electromagnetics
Elastodynamics
Cloaking
Own Research
Outlook
Passive Cloaking via Metamaterials
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One can show that if
then
4u(x) = 0
0
in B2 \{0}
0
∇ · (σ (y )∇u (y )) = 0 in B2 \B1 ,
where y = ϕ(x), u 0 (y ) = u(x), σ 0 denotes the 2 × 2 matrix
σ 0 = σ 0 (y ) =
evaluated at x = ϕ−1 (y ) and
Dϕ(x) :=
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(
Dϕ(x)(Dϕ(x))>
|detDϕ(x)|
∂ϕ1
∂x1
∂ϕ2
∂x1
)
∂ϕ1
∂x2
∂ϕ2
∂x2
is the deformation gradient of ϕ, see Worksheet No. 1.
One obtain similar results for Helmholtz Equation representing time-harmonic
regime of wave equation.
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Problems
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Infinitely massive cloak, i.e. bad singularities in material parameters
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Cloaking effect is frequency dependent
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Manufacturing metamaterials is time- and money-consuming
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Chronologic Reference Guide
The very first vanishing
I 1963, RUS, Velesago: Cornerstone in theoretical investigation of negative
permittivity and permeability
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1990-ies till now, USA, Vogelius, Sylvester, Uhlmann: Theory [5]
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2005, USA, Shalaev: Breaktrougth in creation of a cloak for microwaves [11]
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2006, UK, Leonhardt: Theory; Conformal mapping in electromagnetics
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2008, ESP, Torrent: Acoustics, Construction of a bilayered isotropic cloak [13]
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2009, UK, Movchan: Elastic waves [3]
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2011, GER, Wegener, KIT: Physik, Lithography of a cloak for electromagnetic
field; construction of a cloak for elasic waves [12]
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FIN, Lassas: Theory
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Cloaking in Acoustics - Bi-layered Approximation
2D time-harmonic case [13]
∇·
ω2
1
∇p + 2 p = 0
ρ
ρc
p: total acoustic pressure, ρ: material density, c: propagation velocity of the wave
A suitable transformation of the coordinates applied on a ring and the PDE above
affects only the material parameters [8]. The bi-layered isotropic construction leads to
ρ1 (r ) =
r + (2rR1 − R12 )1/2
ρb ,
r − R1
c1 (r ) =
R2 − R1
r
cb ,
R2
r − R1
ρ2 = ρb /ρ1 ,
c2 = c1 .
Figure: Passive, interior cloak of 200 isotropic layers, [13]. The cloak is independent
of the direction of the incident wave.
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Cloaking in Acoustics
Figure: Realized acoustic cloak (left); Rotator [6], Anti-cloak [7] (right)
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Active Exterior Cloaking in Acoustics
Figure: Active exterior cloak on (left) and off (right) [15]
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Cloaking in Electromagnetics
3D cylindric, time-harmonic case [13]: In cylindric coordinates the Transformation
Optics [9] and anisotropic materials permittivity , permeability µ lead to
(
)2
r − R1
r
R2
r − R1
r = µr =
, φ = µφ =
, z = µz =
.
r
r − R1
R2 − R1
r
The effect of the cloak is independent of the incident wave direction.
Figure: Electromagnetic cloak, first realization, [11]
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Figure: Generalization of the cloak geometry [10]
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Figure: Cloaking ring for microwaves [11]; Cloaking carpet realized at KIT [4]
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Illusion in Electromagnetics
Figure: A cloak that mimics a cup and hides a spoon [16]
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Cloaking in Elastodynamics
Figure: Seismic metamaterial experiment, Grenoble France, August 2012, [2].
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Cloaking
Own Research
Outlook
Acoustics
Electromagnetics
Elastodynamics
Areas of Application
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In general: Sensors disturb the field to measure by their presence. A partly
cloaking could reduce this affect.
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Electromagnetics: Minimizing the affect of metal implantats on electromagnetic
measurements; Invisibility(?), ...
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Acoustics: Acoustic dipole; architekture; automotive industry; better
laudspeaker, ...
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Elasticity: Earthquake-resistant buildings [3], ...
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Thermodynamics: New cooling system e.g. on el. circuit board, Chip cooling;
Routing or focusing of the heat, ...
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Fluiddynamics: Reducing of turbulences [14], ...
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Medicine: Acoustic metamaterial superlens for ultrasonic tomography (Shu
Zhang, 2009)
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Military: Marine; electromagnetic, acoustic, fluiddynamic cloaking, ...
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
Own Research - Ideas
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The efficiency (i.e. the energy of the scattered field) is depending on the
frequency of the incident field.
Idea 1
Face this problem on different scales.
Idea 2
Construct ρ = ρ(p) and c = c(p). Really challenging goal!
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Cloaking is a very young research branch. Thus, general problem settings are not
inverstigated yet (inhomogeneous background medium, tuning for practical
problems, new application, ...).
Idea
Cloaking in a layered medium (i.e. inhomogeneous medium)
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
Own Research - Electrostatics
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Passive Erdölexpolration aus der Luft. Diploma Thesis, A. Sommer, 2013
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Active Cloaking and Illusion in Electrostatics. Paper in work, Prof.
A.Ismail-Zadeh (IAG), A.Sommer, and AHS
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Cloaking in Electrical Impedance Tomography, Looking for Diploma Thesis
Students
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
Own Research - Acoustics
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Bachelor Thesis, Ph. Kaas, Acoustic Isotropic Cloaking in Layered Medium.
Work in process
Figure: Density of a bi-layered isotropic cloak for inhomogeneous background medium
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
Own Research - Electromagnetics
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Cloaking in inhomogeneous media. Collaboration with Muamer Kadic (IAP) in
process.
Figure: Electromagnetic anisotropic cloaking in homogeneous (left) and
inhomogeneous (right) background media.
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
Antonello Andreone (Editor), Selected Topics in Photonic Crystals and Metamaterials, Word
Scientific, 2011
S.Brul, E.H.Javelaud, S.Enoch, S.Guenneau, Seismic metamaterials: how to shake friends
and influence waves?, 2012
Brun, Guenneau, Movchan: Achieving control of in-plane elactic Waves, 2009
T. Ergin, J. Fischer, and M. Wegener, Optical phase cloaking of 700 nm light waves in the
far eld by a three-dimensional carpet cloak, Phys. Rev. Lett. 107, 173901 (2011)
Greenleaf, Kurylev, Lassas, Uhlmann: Invisibility and Inverse Problems, 2008. (127 further
references)
Huanyang Chen and C.T.Chan, Acoustic cloaking and transformation acoustics, TOPICAL
REVIEW, J. Phys. D: Appl. Phys. 43 (2010) 113001 (14pp)
doi:10.1088/0022-3727/43/11/113001
Huijie Shen1, Michael P. Pädoussis, Jihong Wen1, Dianlong Yu1, Li Cai1 and Xisen Wen1,
Acoustic cloak/anti-cloak device with realizable passive/active metamaterials, J. Phys. D:
Appl. Phys. 45 (2012) 285401 (13pp) doi:10.1088/0022-3727/45/28/285401
Ward, Pendry: Refraction and geometry in Maxwells equations, 1996
J.B.Pendry, D.Schurig, and D.R.Smith, Science 312, 1780, 2006
Marco Rahm, David Schurig, Daniel A. Roberts, Steven A. Cummer, David R. Smith, John
B. Pendry, Design of electromagnetic cloaks and concentrators
using
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Cloaking
Own Research
Outlook
Ideas
Acoustics
Electromagnetics
coordinate transformations of Maxwells equations. Photonics and Nanostructures Fundamentals and Applications, Volume 6, Issue 1, April 2008, Pages 8795.
Shalaev: Optical Cloaking with Methamaterials, 2007 (5th most cited paper among all
OPTICS papers)
N.Stenger, M.Wilhelm, M.Wegener, Experiments on Elastic Cloaking in Thin Plates,
Physical Review Letters 108, 014301, 2012
Torrent, Sanchez-Dehesal: Acoustic Cloaking in two Diemensions: a feasible Approach, 2008
Y.A.Urzhumov and D.R.Smith, Fluid flow control with transformation media, Phys. Rev.
Lett. 107, 074501, 2011
F.G.Vasquez, Graeme W. Milton, and Daniel Onofrei, Active Exterior Cloaking,
arXiv:0906.1544v1 [math-ph] 8 Jun 2009
Yun Lai, Jack Ng, HuanYang Chen, DeZhuan Han, JunJun Xiao, Zhao-Qing Zhang and C.
T. Chan, Illusion optics: The optical transformation of an object into another object
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Flirting with Invisibility

Transcrição

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