Flirting with Invisibility - KIT - Fakultät für Mathematikschkarbanenko/media/invisibility.pdf · Flirting with Invisibility Andreas Helfrich-Schkarbanenko Karlsruhe Institute of

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CloakingOwn Research

Outlook

Flirting with Invisibility

Andreas Helfrich-Schkarbanenko

Karlsruhe Institute of Technology (KIT)

March 28th 2013

Andreas Helfrich-Schkarbanenko Flirting with Invisibility

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I What is this talk about?

I Which ideas/approaches are there?Classification of them?

I What is the level of cloaking?What are the outcoming problems?Which questions are still open?

I Outlook of invisibility?


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Transformation OpticsAcousticsElectromagneticsElastodynamics

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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Survey of Cloaking - Any Idea?


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Survey of Cloaking - Any further Idea?


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Survey of Cloaking - One more idea?


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Survey of Cloaking - Ideas

Principle 1: passive cloaking

I Metamaterials Guiding the incident waves around the obstacle via transformationor change of variables for mapping the cloaked region to a point with vanishingscattering strength. This leads to anisotropic materials (metamaterials) [9] whichcan be approximated by bi-layered isotropic media. Isotropy is highly relevant forthe praxis!

I 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 desiredproperty [15].

Principles 1 and 2 can be classified in exterior and interior cloaking.


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Passive Cloaking via Metamaterials

ϕ(x) :=

(1 +

1

2|x |)

x

|x |, for 0 < |x | ≤ 2

I ϕ is smooth except at 0;I ϕ blows up the point 0 to the ball B1, while mapping the full domain B2 to itself;I ϕ(x) = x at the outer boundary |x | = 2.


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Passive Cloaking via Metamaterials

I One can show that if4u(x) = 0 in B2\{0}

then∇ · (σ′(y)∇u′(y)) = 0 in B2\B1,

where y = ϕ(x), u′(y) = u(x), σ′ denotes the 2× 2 matrix

σ′ = σ′(y) =Dϕ(x)(Dϕ(x))>

|detDϕ(x)|evaluated at x = ϕ−1(y) and

Dϕ(x) :=

(∂ϕ1∂x1

∂ϕ1∂x2

∂ϕ2∂x1

∂ϕ2∂x2

)is the deformation gradient of ϕ, see Worksheet No. 1.

I One obtain similar results for Helmholtz Equation representing time-harmonicregime of wave equation.


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Problems

I Infinitely massive cloak, i.e. bad singularities in material parameters

I Cloaking effect is frequency dependent

I Manufacturing metamaterials is time- and money-consuming


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Chronologic Reference Guide

The very first vanishing

I 1963, RUS, Velesago: Cornerstone in theoretical investigation of negativepermittivity and permeability

I 1990-ies till now, USA, Vogelius, Sylvester, Uhlmann: Theory [5]

I 2005, USA, Shalaev: Breaktrougth in creation of a cloak for microwaves [11]

I 2006, UK, Leonhardt: Theory; Conformal mapping in electromagnetics

I 2008, ESP, Torrent: Acoustics, Construction of a bilayered isotropic cloak [13]

I 2009, UK, Movchan: Elastic waves [3]

I 2011, GER, Wegener, KIT: Physik, Lithography of a cloak for electromagneticfield; construction of a cloak for elasic waves [12]

I FIN, Lassas: Theory


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Cloaking in Acoustics - Bi-layered Approximation

2D time-harmonic case [13]

∇ ·1

ρ∇p +

ω2

ρc2p = 0

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 aboveaffects only the material parameters [8]. The bi-layered isotropic construction leads to

ρ1(r) =r + (2rR1 − R2

1 )1/2

r − R1ρb, c1(r) =

R2 − R1

R2

r

r − R1cb, ρ2 = ρb/ρ1, c2 = c1.

Figure: Passive, interior cloak of 200 isotropic layers, [13]. The cloak is independentof the direction of the incident wave.


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Cloaking in Acoustics

Figure: Realized acoustic cloak (left); Rotator [6], Anti-cloak [7] (right)


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Active Exterior Cloaking in Acoustics

Figure: Active exterior cloak on (left) and off (right) [15]


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Cloaking in Electromagnetics

3D cylindric, time-harmonic case [13]: In cylindric coordinates the TransformationOptics [9] and anisotropic materials permittivity ε, permeability µ lead to

εr = µr =r − R1

r, εφ = µφ =

r

r − R1, εz = µz =

(R2

R2 − R1

)2 r − R1

r.

The effect of the cloak is independent of the incident wave direction.

Figure: Electromagnetic cloak, first realization, [11]


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Figure: Generalization of the cloak geometry [10]


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Figure: Cloaking ring for microwaves [11]; Cloaking carpet realized at KIT [4]


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Illusion in Electromagnetics

Figure: A cloak that mimics a cup and hides a spoon [16]


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Cloaking in Elastodynamics

Figure: Seismic metamaterial experiment, Grenoble France, August 2012, [2].


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Areas of Application

I In general: Sensors disturb the field to measure by their presence. A partlycloaking could reduce this affect.

I Electromagnetics: Minimizing the affect of metal implantats on electromagneticmeasurements; Invisibility(?), ...

I Acoustics: Acoustic dipole; architekture; automotive industry; betterlaudspeaker, ...

I Elasticity: Earthquake-resistant buildings [3], ...

I Thermodynamics: New cooling system e.g. on el. circuit board, Chip cooling;Routing or focusing of the heat, ...

I Fluiddynamics: Reducing of turbulences [14], ...

I Medicine: Acoustic metamaterial superlens for ultrasonic tomography (ShuZhang, 2009)

I Military: Marine; electromagnetic, acoustic, fluiddynamic cloaking, ...


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IdeasAcousticsElectromagnetics

Own Research - Ideas

I The efficiency (i.e. the energy of the scattered field) is depending on thefrequency of the incident field.

Idea 1Face this problem on different scales.Idea 2Construct ρ = ρ(p) and c = c(p). Really challenging goal!

I Cloaking is a very young research branch. Thus, general problem settings are notinverstigated yet (inhomogeneous background medium, tuning for practicalproblems, new application, ...).

IdeaCloaking in a layered medium (i.e. inhomogeneous medium)


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Own Research - Electrostatics

I Passive Erdolexpolration aus der Luft. Diploma Thesis, A. Sommer, 2013

I Active Cloaking and Illusion in Electrostatics. Paper in work, Prof.A.Ismail-Zadeh (IAG), A.Sommer, and AHS

I Cloaking in Electrical Impedance Tomography, Looking for Diploma ThesisStudents


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Own Research - Acoustics

I 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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Own Research - Electromagnetics

I Cloaking in inhomogeneous media. Collaboration with Muamer Kadic (IAP) inprocess.

Figure: Electromagnetic anisotropic cloaking in homogeneous (left) andinhomogeneous (right) background media.


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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. Padoussis, 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 form-invariant


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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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Documents

Flirting with Invisibility - KIT - Fakultät für Mathematikschkarbanenko/media/invisibility.pdf · Flirting with Invisibility Andreas Helfrich-Schkarbanenko Karlsruhe Institute of