Cloaking The Road to Realization

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1 Cloaking The Road to Realization by Reuven Shavit Electrical and Computer Engineering Department Ben-Gurion University of the Negev 1

2 Outline Introduction Transformation Optics Laplace s Equation- Transformation Realization Summary

3 Introduction Metamaterials The prefix meta comes from Greek and means after or beyond. These are engineered composites (usually periodic structures) that exhibit superior properties that are not found in nature and not observed in the constituent materials. Material classification In double negative (DNG) materials the phase velocity is negative, although the group velocity stays positive. Vectors k, E and H will form a left hand set. V.G.Veselago : The Electrodynamics of Substances with Simultaneously Negative Values of P and M, Sov. Phys. Usp., 1968, 10, (4), pp

Introduction History of Metamaterials Frequency Selective

(d ~ λ) Element Distances are on the order of half a

Electromagnetic Band Gap materials (EBG), Artificial

Metamaterials (d << λ) Elements and distances between them

negative permittivity and permeability) Have several names

$negative index of refraction (NIR) materials, etc.$

4 Introduction History of Metamaterials Frequency Selective Surfaces (FSS) and Electromagnetic Band Gap (EBG) materials (d ~ λ) Element Distances are on the order of half a wavelength or more (Periodic medium concepts) Electromagnetic Band Gap materials (EBG), Artificial Magnetic Conductors (AMC), High Impedance Surfaces (HIS) Metamaterials (d << λ) Elements and distances between them are much smaller than a wavelength (simultaneous effective negative permittivity and permeability) Have several names including left-handed materials, backward-wave materials, negative index of refraction (NIR) materials, etc. Woodpile Stacked dielectric layer Dielectric rods Printed elements Split Ring Resonators (SRR) 4

$Refraction Makes a$ Perfect Lens, Phys. Rev.

5 Introduction DNG Structures n sin n sin Snell ' s law 1 1 =-1 ; =-1 (no reflection) J.B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett., vol.85, no.18, pp , Oct

$Refraction,$

6 DNG Lens Introduction Zero index flat Lens R.A. Shelby, D.r. Smith and S. Schultz, Experimental Verification of a Negative Index of Refraction, Science, vol. 9, pp.77-79, April

10.8 GHz D construction! Polarized waves. R. A.

7 Metamaterial Structures Introduction Lattice spacing: 6mm~/5 Double negative band: GHz D construction! Polarized waves. R. A. Shelby, D. R. Smith, S. Schultz, Science 9, 77 (001) 7

8 Split Ring Resonator (SRR) Element Introduction eq L d x 1 eq 1 C 1 1 L C L Cd x ω 1 ω J.B. Pendry, D.Schurig and D.R. Smith, Controlling Electromagnetic Fields, Science, 31, June 006, pp

9 Introduction Optical Invisibility Cloak H.G.Wells, The Invisible Man,

10 Introduction RF Cloak based on tensor type metamaterial No unique solution to the problem 10

11 Transformation Optics E jh Maxwell eqs. are invariant H j E x x x ', y ', z ' x / x ' x / y ' x / z ' y y x ', y ', z ' y / x ' y / y ' y / z ' A Jacobian z z x ', y ', z ' z / x ' z / y ' z / z ' T A' A A' A ; det A det A T 11

Cylindrical D scatterer Transformation Optics b a r r ' a b ' z z' A b a / b 0 0 0 r / r ' 0 0 0 1 Jacobian in cylindrical coordinates r a 0 0 r r 0 0 in

12 Cylindrical D scatterer Transformation Optics b a r r ' a b ' z z' A b a / b r / r ' Jacobian in cylindrical coordinates r a 0 0 r r 0 0 in cylindrical coordinates r a b r a 0 0 b a r r a r r a r r r a r r a r a r r a r r r a r r a 0 0 b r a b a r cos sin sin cos 0 sin cos sin cos 0 in cartesian coordinates 1

13 Laplace s Equation-Transformation The Laplace equation transformation fits very well arbitrarily scattering shape, because its solution is numerical. The method is used to compute the cloak material parameters. Space transformation from a flat space x to a distorted space x (x ), yields the permittivity and permeability ε μ 0, 1,,3 Ui i x y z U ( x, y, z) 0 ; U ( x, y, z) x ' 1 a a' 1 b b' U ( x, y, z) 0 ; U ( x, y, z) y ' a a' b b' U ( x, y, z) 0 ; U ( x, y, z) z ' 3 a a' 3 b b' U1 / x U1 / y U1 / z T T A' A A' A ; ; A U / x U / y U / z det A det A U3 / x U3 / y U3 / z 13

14 Example: D circular cylinder Laplace s Equation-Transformation 1 1 r 0 ; U i U1 r ', U ', U3 z ' z r r r r z 1 r ' r 0 ; r ' a 0, r ' b b r r r r b r ' blogba / r a a a r ln 0 0 a r ln a r b ln a 0 0 b r ln a r ' b r ' b b r a, ', z z ' a r', ', z' r,, z 14

15 Realization Challenges in realization: Requires anisotropic materials. The required electrical parameters (ε, μ) vary on a very wide range (0 ) in different regions of the cloaking. Implementation requires metamaterials which are: narrow band, dispersive, lossy, sensitive to polarization and incident angle. Simplifications: Consider single polarization TE or TM. Consider normal incidence. Use quantization instead of continuous media with cell size smaller than 0.1λ. 15

16 Realization Quantization Cummer etal, Full Wave Simulations of EM Cloaking Structures, Physical Review E, vol.74,

Realization For TM polarization and normal

parameters TrO Cloaking cloak rr cloak cloak zz

Scatterer Analytical Cloaking Physical Cloaking

17 Realization For TM polarization and normal incidence cloak cloak cloak only,, are relevant parameters TrO Cloaking cloak rr cloak cloak zz rr 1 cloak ;0 rr r a b a r b b b a zz Metal Scatterer Analytical Cloaking Physical Cloaking TM polarization-f=8.5ghz, a=7.1mm (0.76λ), b=58.9mm (1.67λ), h=10mm Schurig etal, Metamaterial Electromagnetic Cloak at Microwaves Frequencies, Science, vol.314,

18 Realization For TE polarization and normal incidence cloak cloak cloak only,, are relevant parameters cloak b r a cloak MG f rr ; 0 rr 1 rr 1 b a r s Lr 1 f cloak cloak zz rr zz TrO Cloaking Maxwell Garnet Model b MG f 1 b a f 1 Lr 1 s MG 1 1 zz 1 s m 1 m 1 permittivity environment h dq h permittiviy of metal d b a Lr ln ; depolarization factor b a d f ; filling factor ( metal) 8rh Q # of cylinders over rotation TE polarization- a=0.m (1.33λ), b=0.4m (.67λ) Rottler etal, Route towards cylindrical cloaking at visible frequencies using an optimization algorithm, Physical Review B, vol.86, 01 18

Realization TrO Cloaking Maxwell Garnet Model cloak b r a cloak

f 1 Lr 1 s MG 1 1 zz Metal Scatterer Analytical Cloaking

67λ) Rottler etal, Route towards cylindrical cloaking at visible

19 Realization TrO Cloaking Maxwell Garnet Model cloak b r a cloak MG f rr ; 0 rr 1 rr 1 b a r s Lr 1 f cloak cloak zz b MG f 1 b a f 1 Lr 1 s MG 1 1 zz Metal Scatterer Analytical Cloaking Physical Cloaking TE polarization- a=0.m (1.33λ), b=0.4m (.67λ) Rottler etal, Route towards cylindrical cloaking at visible frequencies using an optimization algorithm, Physical Review B, vol.86, 01 19

20 Summary It has been demonstrated that cloaking is feasible for both canonical and arbitrary shape targets. Invisible cloak in RF is possible, but further research effort is needed (theoretical and experimental) to comply with polarization and frequency bandwidth requirements. Metamaterials technology constitute a promising road towards implementation. 0

Wavelength Dependent Microwave Devices Based on Metamaterial Technology. Professor Bal Virdee BSc(Eng) PhD CEng FIET

Wavelength Dependent Microwave Devices Based on Metamaterial Technology by Professor Bal Virdee BSc(Eng) PhD CEng FIET EM response of materials are determined by the spatial distribution of its atoms and