Metamaterials and Metafilms: Overview and Applicationsweb.mst.edu/~jfan/slides/Holloway2.pdf · Metamaterials and Metafilms: Overview and Applications Christopher L. Holloway National

Metamaterials and Metafilms: Overview and Applications

Christopher L. HollowayNational Institute of Standards of Technology (NIST)

EEEL Electromagnetics Division

U.S. Department of Commerce, Boulder Laboratories325 Broadway, Boulder, CO 80305

email: [email protected], Phone: 303-497-6184

Cooperative research effort between NIST and CU

Edward Kuester, James Baker-Jarvis, John Ladbury, Pavel Kabos, Michael D. Janezic, Andrew Dienstfrey, Steven Russek, and Derik Love

Also the DARPA/BOEING Team with NIST, UofA, UCSD, DUKE, UofPenn, UofI

3-D array of inclusions embedded in a background matrix

The most convenient method to analyze these structures is with effective medium theory.

MetaMaterialsMetaMaterials: Novel Synthetic Materials: Novel Synthetic Materials

Material Behavior

Frequency(or Length scale)

Effective Media

Classical mixing theory

Effective Media

Resonances associatedwith individual scatterers

Floquet-Block modes

Resonances associatedwith periodicity

OUTLINEMetamaterials• Discussion on Artificial Composite Materials• Negative Index Materials and Applications• Historical Perspective of Negative Materials• Effective Properties of Spherical Particle Composites• Negative Permittivity and Permeability of Spherical Particle Composites

Metafilm• Define Metafilmn• Derivation of a Generalized Sheet Transition Conditions (GSTCs) for a

Metafilm• Reflection and Transmission Properties• Total Reflection and Transmission Conditions• “Smart” surface: Controllable Scatterers• A New Class of Controllable Surface: YIG Spherical Particles

Composite Materials

• Permittivity arises from the induced electric-dipole response of a large number of small particles.

• Classically, these particles have been atoms or molecules, but in the past 60 years so-called artificial dielectrics have been developed whose “atoms” are small objects, large compared to atomic dimensions, but still small compared to the wavelength.

• The effective or averaged field E, D, H, and B are then related to each other by the usual expressions

ED ε= HB μ=where ε

and μ are related to the polarizability densities of the scatterers in space.

In this description, details of the field behavior on the scale of the scatterer size and separation are lost, and often are not of practical interest.

For many common materials ε

and μ

are positive, but there are exceptions.

Negative εr and μr

When one (but not both) of εr and μr is negative, plane waves decay exponentially, like modes below cutoff in a waveguide. However, when both εr and μr are negative, waves can still propagate in such a medium since the product εμ

remain positive. In this case (“backward wave”), the phase of the wave moves in the opposite direction from that of the energy flow.

• Veselago: Many authors have attributed the first study of such media to Veselago in 1968, but Sivukhin in 1957 briefly examined the properties of these materials.

• Mandelshtam: Veslago and Sivukhim as well as Silin in 1972 give credit to the much earlier work of L.I. Mandelshtam work 1945.

• Lamb: Mandelshtam himself referred to a 1904 paper of Lamb, who may have been the first person to suggest the existence of backward waves (his examples involved mechanical systems rather than electromagnetic waves).

• Schuster: In his 1904 book on optics, Schuster briefly notes Lambs’s work, and gives a speculative discussion of its implications for optical refraction, should a material with such properties ever be found.

• Engineered Materials: More recently, many other authors have studied the properties and potential applications of negative-index materials in detail.

Metamaterial Structures and Their Location in the ε , μ

Phase Space

ε

μ

Majority of isotropic dielectrics

Plasma-like behavior,k < 0, evanescent wave

∑ 20− 1 =

ωωε

2

where

Negative index materials

Propagating waves

me /4 220 Ν= πω

k < 0, evanescent wave

μ

and ε

close to zero

3-D array of inclusions embedded in a background matrix

MetaMaterialsMetaMaterials: Novel Synthetic Materials: Novel Synthetic Materials

• We need to emphasize that when we say metamaterials, we do not JUST mean materials that have negative index behavior.

• We mean synthetic (or engineered) materials that have a uniquely designed μ

and/or ε

behavior. That is, μ

and/or ε

of a

material that are not currently available.

• Existing materials can be tweaked, but the designed materials gives us revolutionary possibilities in electromagnetic behavior.

Normal -VS- Negative Materials

Positive Materials Negative Materials

Propagation in Negative Materials

Applications of NIM

x

zmetafilm

conductorconductor

Region A Region B

z=d1 z=-d2z=0

n1>0DNGn2<0

d1 d2

1. Perfect Lens

2. Resonant of Various Sizes

3. Antennas

x

yz

Typical scatterer at rl

4. Controllable “Smart” Surfaces

Other Applications

• THz devices and switches (a 20 ps was just demonstrated)

• bio-medical applications • quantum levitation• new devices• quasi-optical circuits• reducing EMI in radiation or detecting systems• miniaturization devices• enhancement of nonlinear properties• sub-wavelength resolution• superlenses• imaging • impedance matching• dynamic control of materials and optics

Pendry and Smith NIM

In practice, these structures are quite complicated to fabricate.

Composite NIMEffective Medium: The problem of effective-medium theory and modeling the

electromagnetic response of inclusions embedded in a host material has a long history going back to Maxwell and Rayleigh

Lewin’s work: One notable work is that of Lewin [1947], who, by solving the boundary-value problem of spheres a a medium, obtained a description of the effective material properties of a spherical particle medium.

Our Work : Using Lewin’s work, we have illustrated that the effective materials properties (ε

and μ) of a composite composed of spherical particles can become simultaneously negative.

1. We will show that this “new” class of material can behave in a way similar to that of an array of geometrically more complicated conducting scatterers.

2. This results suggests the possibility of developing negative-index materials that could be fabricated much more simply than those that have been proposed up until now.

DNG Materials Composed of Magneto-Dielectric Spherical Particles Embedded in a Matrix

Holloway, et al., IEEE Transactions on AP, October 2003

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−+

+=

fe

e

frre

vbFbF

v

2)(2)(

311

θθ

εε⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−+

+=

fm

m

frre

vbFbF

v

2)(2)(

311

θθ

μμ

2

1

εε

=eb2

1

μμ

=mb 3

3

34

pav f

π=

θθθθθθθθcossin)1(

)cossin(2)(2 +−

−=F

2'20 rrak μεθ =

where

and

and

Functional Behavior of F(θ)

0 1 2 3 4 5 6 7 8 9 10

θ

-20

-15

-10

-5

0

5

10

15

20

θ

θθθθθθθθcossin)1(

)cossin(2)( 2 +−−

=F

We then ask: can this result in negative-index behavior?

This question can be answered by investing ε

and μ

as a function θ.

Negative εr and μr

Recall:

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−−+

+=

fe

e

frre

vbFbF

v

2)(2)(

311

θθεε

We see that εr <0 if:

1

2)(2)(

3−<

−−+

fe

e

f

vbFbF

v

θθ

Since be >0, the following condition on F(θ)

guarantee that εr <0

f

fe

f

fe v

vbF

vv

b21

12)(

12

+−

−<<−+

− θ

F(θ)

MUST be negative, and from the figure above, we see that this is possible!

We find a similar condition on F(θ)

to guarantee that μr <0.

NIM Composed of Spherical Particles

0.02 0.04 0.06 0.08 0.10koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε re

, μre

ε1=1, ε2=40, μ1=1, μ2=200, and f=0.5

εre

μre

Between 0<k0 a<0.1 there are two regions where both e and m become negative simultaneously.

Producing a negative-index material.

It is possible to have εr negative over the same region where μr negative by having:

'2

'1

'2

'1 // rrrr μμεε =

0.02 0.04 0.06 0.08 0.10koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε re,

μ re

ε1=1, ε2=200, μ1=1, μ2=200, and f=0.5

εre

μre

Impedance matched material!

NIM Composed of Spherical Particles

0.02 0.04 0.06 0.08 0.10koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε re

, μre

ε1=1, ε2=40, μ1=1, μ2=200, and f=0.5

εre

μre

The bandwidth of the materials is influenced by vf

, and the product of “εr μr” .

0.02 0.04 0.06 0.08 0.10koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε re,

μ re

ε1=1, ε2=200, μ1=1, μ2=200, and f=0.5

εre

μre

5.5% Bandwidth800022 =με

1.1% Bandwidth4000022 =με

Also notice that the first resonance in the first figure occurs at k0 a=0.048, while the first resonance in the second figure occurs at k0 a=0.022.

.

Spherical Particle NIM

0.02 0.04 0.06 0.08 0.10koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε re

, μre

ε1=1, ε2=40, μ1=1, μ2=200, and f=0.5

εre

μre

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30koa

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

ε eff,

μef

f

ε1=1, ε2=20, μ1=1, μ2=20, and f=0.5

εeff

μeff

10% bandwidth can be achieved.

In this material has no complicated metallic scatterers and the composite based on a spherical-particle array has the added advantage of being isotropic.

Lossy Spherical Particle DNG Materials

0.06 0.07 0.08 0.09 0.10koa

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

Re[ε

re]

ε1=1, ε2=50, μ1=1, μ2=50, and f=0.5

tanδ=0.00

tanδ=0.01

tanδ=0.02

tanδ=0.04

tanδ=0.20

1) Notice that for this example, the real part of the effective permittivity can still be negative for loss tangents as large as 0.04.

2) However, for larger values of the loss tangents the resonance is damped out and the real partof the effective permittivity remains positive.

3) This shows that if the inclusion (i.e., the spherical particle) becomes too lossy, negative-index properties cannot be realized.

Other Types of Array of Resonant Inclusions

From a scattering-theory viewpoint, negative effective permeability and permittivity of a composite structure are possible if the effective electric and/or magnetic polarizabilities exhibit a characteristic resonant behavior, hence it should be no surprise that the spherical particles, and any magneto-dielectric inclusion for that matter, behave in the same manner as arrays of more complicated conducting scatterers.

This approach can be readily extended to other geometries and to other types of inclusions.

Spherical ParticlesMetamaterials

• We show how a composite medium realized by an array of spherical particles embedded in a background matrix can yield an effective negative permeability and permittivity.

• The type of composite material (magneto-dielectric spherical particles embedded in a matrix) introduces a new class of potential negative-index materials.

• In this approach no complicated metallic scatterers are required and the composite based on a spherical-particle array has the added advantage of being isotropic.

• This approach can be readily extended to other geometries and to other types of inclusions.

Applications

Antennas Composed of Metamaterials

Four-Layer Cylindrical 825 MHz Structure

12 mm loop for 825 MHz antenna

825 MHz antenna: loop with four-layer cylindrical material

Two paddles used

Antenna Under Test (AUT)

Four-Layer Cylindrical 825 MHz Structure

Reverberation Chamber

Comparison to Horn

Comparison to Loops

-25

-20

-15

-10

-5

0

500 550 600 650 700 750 800 850 900 950 1000Frequency (MHz)

Tota

l Rad

iate

d Po

wer

Rel

ativ

e to

Hor

n (d

B)

Four-Layer Cylindrical Structure

12 mm Loop for 825 MHz Antenna

32 mm Loop Antenna

-5

0

5

10

15

500 550 600 650 700 750 800 850 900 950 1000

Frequency (MHz)

Tota

l Rad

iate

d Po

wer

Rel

ativ

e to

825

MH

z Lo

op (d

B)

Ten-Layer Spherical 612 MHz Structure

8 mm Loop for 612 MHz antenna

612 MHz antenna: loop with ten-layer spherical material

Ten-Layer Spherical 612 MHz Structure

Comparison to Horn

Comparison to Loops

-25

-20

-15

-10

-5

0

500 550 600 650 700 750 800 850 900 950 1000

Frequency (MHz)

Tota

l Rad

iate

d Po

wer

Rel

ativ

e to

Hor

n (d

B)

Ten-Layer Spherical Structure8 mm Loop for 612 MHz Antenna32mm Loop Antenna

-10

-5

0

5

10

15

20

500 550 600 650 700 750 800 850 900 950 1000Frequency (MHz)

Tota

l Rad

iate

d Po

wer

Rel

ativ

e to

Loo

ps (d

B)

Comparison to 8 mm Loop

Comparison to 32 mm Loop

Magnetic Antenna

New Magnetic Antenna Comparison to Horn

Loop Antenna

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

200 250 300 350 400

Frequency (MHz)

Tota

l Rad

iate

d Po

wer

Rel

ativ

e to

Hor

n (d

B)

Magnetic EZ-Antenna: Ground Plane-Center of ChamberMagnetic EZ-Antenna: No Ground Plane-Center of ChamberMagnetic EZ-Antenna: On Chamber Wall3 cm Loop antenna

Duke’s Spiral Structures: Losses are a Problem

20 Layer Structure 10 Layer Structure

4 Layer Structure

Duke’s Spiral Structures

Comparison to Horn

Comparison to Loops

-30

-25

-20

-15

-10

-5

0

500 600 700 800 900 1000

Frequency (MHz)

Tota

l Rat

iate

d Po

wer

Rel

ativ

e to

Hor

n (d

B) Duke's Source Element

Duke's 20 Layer Structure

Duke's 10 Layer Structure

Duke's 4 Layer Structure

-15

-10

-5

0

5

10

15

500 600 700 800 900 1000

Frequency (MHz)

Tota

l Rat

iate

d Po

wer

Rel

ativ

e to

Loo

p (d

B)

Duke's 20 Layer Structure

Duke's 10 Layer Structure

"Duke's 4 Layer Structure"

© Science

n=±(εμ)1/2

Other Applications: Cloaking and Focusing (Optical Frequencies)

Opportunities:•Beyond the diffraction limit•Atom layers are periodic structures

Challenges:•Color•Geometry

Cloaking Objects: i.e., Disappearing Objects

Cloaking Objects: i.e., Disappearing Objects

Cloaking Objects: i.e., Disappearing Objects

Make the cover a metamaterial

Coat object with a material

Cloaking Objects: i.e., Disappearing Objects

Cloaking Objects: i.e., Disappearing Objects

Cloaking Objects: i.e., Disappearing Objects

Make the cover a metamaterial

Environmentalist

I am filing for a patent as soon as the talk is over!!!!

Cloaking: Science Top 10 Achievements for 2006

Schuring et al., Metamaterial Electromagnetic Cloak at Microwave Frequencies,Science Magazine, Oct 2006

Metamaterial over cylinder: NumericalScattering from Cylinder

Metamaterial over cylinder: Experimental Results: cloaking???

Is it Cloaked?? Some people think NOT!RF INVISIBILITY USING METAMATERIALS: HARRY POTTER’S CLOAK OR THE EMPEROR’S NEW CLOTHES?, Per-Simon Kildal et al, IEEE Trans on Antenna and Propagation, 2007.

Enhancing Objects

Magic Dust

Weak tank return

RF - ID

f

f

Electromagnetic Tunneling

R=1 T=0

Fill small waveguide with ε=0 (or approximately 0).

R=0 T=1

Ramifications: Smaller Waveguides and Waveguide Junctions

Quantum Levitation: CASIMIR Effect Enhancement

Attraction Force for very small t

A Quantum Mechanical Effect: Like Black Body Radiation

normal material

normal materialt

( )( ) ⎥

⎦

⎤⎢⎣

⎡

⋅−⋅

= −

−∞

∫ ∫ dK

dK

eRReRRTrK

kddAdF

3

3

221

221

30

2//

2

1222

ππξ

R1,2 for functions of ε and μ of the materials.

Metamaterial

Metamaterialt

Repulsive ForceIf we tune the material propertiesjudiciously we can get a repulsive force. Levitating

Plates

Quantum Levitation: Applications

1) Levitation cars, trains, and planes: probably not.

2) Levitation of atoms and molecules: probably yes.

Metamaterial

Metamaterial

Metafilm: 2-D Equivalent of a Metamaterial

2-D Slice

In general

The scatterers can be any generic shape, i.e., split rings, sphere, or any other shape.

For many applications, metafilms can be used in place of the metamaterials. Metafilms have the advantage of taking less physical space than do full 3-D metamaterial structures.

MetafilmA metafilm is a two-dimensional equivalent of a

metamaterial.

These scatterers are assumed to be characterized completely by their electric and magnetic polarizabilities and their density of distribution on the surface.

Metafilm

Metafilm: How do we analyze them?

For a metamaterial we typically use effective medium theory.

What about a metafilm?

d is not uniquely defined!

Thus, the effective material properties are not uniquely defined.

metafilm effective medium

d=?

There are several papers a year being published with this miss-interpretation!

Effective Boundary Condition for a Metafilm

Final form for effective BC when scatterer spacing is small compared to λ(see Kuester, Mohamed, Holloway, IEEE Trans. AP, October 2003):

[ ] 000

0|| ===

∇×−•=×+

− zzzMStzztESzz HaEjHa ααω

[ ] zzzzEStztMSzz

aEHjaE ×∇−•−=× ===

+

− 000

0|| ααωμ

RN

N

RN

N

RN

NzM

zMzMS

yM

yMyMS

xM

xMxMS

21

,

41

,

41 ,

,

,

,

,

,

αα

ααα

ααα

α−

=+

=+

=

RN

N

RN

N

RN

NzE

zEzES

yE

yEyES

xE

xExES

21

,

41

,

41 ,

,

,

,

,

,

αα

ααα

ααα

α+

=−

=−

=

where

We need anefficient modeling approach

A metafilm is characterized by effective transmission-type boundary conditions,as opposed to the effective-medium description used for a metamaterial.

Oblique Incident Plane Wave on a Metafilm

z

x

θ

ayEi ayEr

ayEt

z

x

θ

ayEi ayEr

ayEt

( )

( ) ( )θαθααθ

θααα

θααα

22022

0

22

0

sincoscos2

sin2

1

sin2

1

zMS

xMS

yES

zMS

yES

xMS

zMS

yES

xMS

kjk

k

T−−+−⎟

⎠⎞

⎜⎝⎛+

−⎟⎠⎞

⎜⎝⎛−

=

TE incident wave:

and

( )

( ) ( )θαθααθ

θααα

θαθααθ

22022

0

220

sincoscos2

sin2

1

sincoscos2

zMS

xMS

yES

zMS

yES

xMS

zMS

xMS

yES

kj

k

kj

−−+−⎟⎠⎞

⎜⎝⎛+

−+=Γ

see Holloway et al, IEEE Transactions on EMC, 2005

Oblique Incident Plane Wave on a Metafilm

( )

( ) ( )θαθααθ

θααα

θααα

22022

0

22

0

sincoscos2

sin2

1

sin2

1

zES

xES

yMS

zES

yMS

xES

zES

yMS

xES

kjk

k

T−−−−⎟

⎠⎞

⎜⎝⎛+

−⎟⎠⎞

⎜⎝⎛−

=

( )

( ) ( )θαθααθ

θααα

θαθααθ

22022

0

220

sincoscos2

sin2

1

sincoscos2

zES

xES

yMS

zES

yMS

xES

zES

xMS

yES

kj

k

kj

−−−−⎟⎠

⎞⎜⎝

⎛+

−+=Γ

TM incident wave:

and

z

x

θ

ayHi ayHr

ayHt

z

x

θ

ayHi ayHr

ayHt

see Holloway et al, IEEE Transactions on EMC, 2005

Controllable SurfacesFrom above we saw that the transmission and reflection properties of the surface were a function of the polarizabilities. Thus, by controlling the polarizabilities, one can control the surface and in turn the transmission and reflection properties.

Total Reflection:

( ) 4sin 220 =− θααα z

MSyES

xMSk

( ) 4sin 220 =− θααα z

ESyMS

xESk

for TE

for TM

0sincos 22 =−+ θαθαα zMS

xMS

yES

Total Transmission:

for TE

for TM

Example: normal incidence

Total Reflection:

Total Transmission:

2

0

2

0

2⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

πλαα

kyES

xMS

2

0

2

0

2⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

πλαα

kyMS

xES

for TE

for TM

xMS

yES αα −= for TE

for TMxES

yMS αα −=

0sincos 22 =−+ θαθαα zES

xES

yMS

See Holloway et al, IEEE Trans. on EMC, 2005

Controllable Surfaces: Example 1

0.0E+0 2.0E+8 4.0E+8 6.0E+8 8.0E+8 1.0E+9 1.2E+9Frequency (Hz)

αEαM

-1E-1

-9E-2

-8E-2

-7E-2

-6E-2

-5E-2

-4E-2

-3E-2

-2E-2

-1E-2

0E+0

1E-2

2E-2

3E-2

4E-2

5E-2

αE,

αM

0.0E+0 2.0E+8 4.0E+8 6.0E+8 8.0E+8 1.0E+9Frequency (Hz)

-80

-70

-60

-50

-40

-30

-20

-10

0

Γ (d

B)

Reflection Coefficient: a=10 mm, d=31.31 mm, εp =2, and μp =900

Eα and

Mα || Γ

Controllable Surfaces: Example 2

Reflection Coefficient: a=5 mm, d=10.15 mm, εp =15, and μp =45

Eα and

Mα || Γ

0.0E+0 4.0E+8 8.0E+8 1.2E+9 1.6E+9 2.0E+9Frequency (Hz)

-2.5E-1

-2.0E-1

-1.5E-1

-1.0E-1

-5.0E-2

0.0E+0

5.0E-2

1.0E-1

1.5E-1

2.0E-1

2.5E-1

αE,

αM

αEαM

0.0E+0 5.0E+8 1.0E+9 1.5E+9 2.0E+9 2.5E+9 3.0E+9Frequency (Hz)

-80.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

Γ (d

B)

Metafilm: Full-wave Model Comparison

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

-80

-70

-60

-50

-40

-30

-20

-10

0

| Γ |

(dB

)

Metafilm modelN=1N=7

0.0 0.2 0.4 0.6 0.8 1.0Frequency (GHz)

-70

-60

-50

-40

-30

-20

-10

0

| Γ |

(dB

)

Metafilm modelN=1N=7

A Controllable Surfaces:

0 10 20 30 40 50 60 70 80 90 100μ

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0Γ

aa

Reflection Coefficient: a=10 mm, d=20.31 mm, and εp =15

A Controllable Surfaces: Yttrium Iron Garnet Spherical Particles

400 600 800 1000 1200 1400 1600B Field (G)

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

Re[

μ]

Material AMaterial B

40 50 60 70 80 90 100 110 120H Field (kA/m)

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Im[μ

]

Material AMaterial B

a

400 600 800 1000 1200 1400 1600B Field (G)

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Re[

αe]

and

Re[

αm

]

Re[αm]Re[αe]

A Controllable Surfaces: Yttrium Iron Garnet Spherical Particles

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600B Field (G)

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

|T|

and

|Γ

| (d

B)

|Γ| : Material A|T|: Material A |Γ|: Material B|T|: Material B

2.0 2.5 3.0 3.5 4.0 4.5 5.0Frequency (GHz)

-30

-25

-20

-15

-10

-5

0

|T|

(dB

)H=50 kA/mH=64 kA/m H=78 kA/mH=92 kA/m

As a function of Biasing H field at 2.745 GHz As a function of Frequency

Spherical Particle Metafilm: Measurement Results

400 500 600 700 800 900 1000 1100 1200 1300 1400B-field (G)

-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

|S11

| a

nd

|S12

| (

dB)

|S11|

|S12|

F=2.724 GHz

400 500 600 700 800 900 1000 1100 1200 1300 1400B-field (G)

-30

-25

-20

-15

-10

-5

0

|S11

| a

nd

|S12

| (

dB)

F=3.7 GHz

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8Frequency (GHz)

-35

-30

-25

-20

-15

-10

-5

0

| S12

|

(dB)

No material

B= 625 G

B= 801 G

B= 973 G

B= 1145 G

Comparison to Measurements

30 40 50 60 70 80 90 100 110H-field (kA/m)

-25

-20

-15

-10

-5

0

|S 12

| (

dB)

Material 2: f=2.724 GHz

Theory

Rectang. Waveguide Measurements

30 40 50 60 70 80 90 100 110 120 130 140 150H-field (kA/m)

-40

-35

-30

-25

-20

-15

-10

-5

0

|S

12|

(dB

)

Material 2: f=3.7 GHz

Theory

Rectang. Waveguide Measurements

Optically controlled terahertz switch

LANL, Sandia, Phys. Rev. Lett. 2006

Split ring resonator arrays on GaAs

Dynamical control through photo- excitation of free carriers

Concept might be applied to modulators, switches, and other active devices not readily available in THz region (device functionality gap)

Other Applications: Compact, Flexible, Low-Loss Waveguides

z

x

θ

ayEi ayEr

ayEt

z

x

θ

ayEi ayEr

ayEt

For certain scatterers we can design T=0 and R=1.

How do we use this?

Compact, Flexible, Low-Loss Waveguides

zjxjkxjky eeEeEE xx β−− += )( 21

ym

zm

ye

xmok

ααααβ 42 −

= 0)Im( and ] ,[)/Re(for <=> ββ 10ok

dz

x

For bound mode, or |R|=1:

Rof phase theis re whe Rx

R

kd ψψ

=

22 β−= ox kk

1)

2)

3)

Compact, Flexible, Low-Loss Waveguides: Spherical-Particles

zjxjkxjky eeEeEE xx β−− += )( 21

j0.029479-48.49833=β ./or mm 43050 == λdd

dz

x

p 2a

f = 2.58 GHz

Loss = 0.12 dB/m

1etan 20, 10, mm, 25p mm, 10a -322 ===== δμε

With the following spherical particles:

We get the following waveguide design:

THz Applications: Low Loss Waveguides

Metafilm

z

x

θ

ayEi ayEr

ayEt

z

x

θ

ayEi ayEr

ayEt

For certain scatterers we can design T=0 and R=1.

Now, wrap the metafilm into a cylinder to form a tube. The total reflections will act as a PEC tube.

Other Applications: Resonators

It is well known that the smallest size of a resonator is limited by λ/2where λ is the wavelength in the media filling the resonator.

d

dmin =λ/2

Other Applications: Resonators with Metafilms

x

zmetafilm

conductorconductor

Region A Region B

z=d1 z=-d2z=0

022 )(2)22()22()22()22()22( 212211 =−−++− ++++−− ddjdjdjdjdjj eeeeee emememeem βφβφβφβφβφφ

⎟⎠⎞

⎜⎝⎛= −

ce

e 2tan 1 αω

φ⎟⎟⎠

⎞⎜⎜⎝

⎛= −

cm

m 2tan 1 αω

φwhere

and

Other Applications: Resonators with Metafilmsx

zmetafilm

conductorconductor

Region A Region B

z=d1 z=-d2z=0

Let d1 =d2 : i.e., metafilm in the center of resonator

ππφβ nd e ++−=21

πφβ nd m +=1

Special Case: 0≡mφ

⎥⎦⎤

⎢⎣⎡ −=+

πφλ edd

21

221

Thus,221λ

<+ dd if 0>eφ

Other Applications: Resonators with Metafilms

100 150 200 250 300 350Frequency (GHz)

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Res

onat

or le

ngth

: d1+

d 2 (

mm

)

no metafilm (classical limit)Theory: a=100 μmTheory: a=60 μmTheory: a=20 μmFEM: a=100 μmFEM: a=60 μmFEM: a=20 μm

metafilm

d1 d2

a Size reduction

p/2 0 %

100 μm 29.6 %

60 μm 53.5 %

20 μm 74.2 %

10 μm 78.1 %

Resonator with Square PEC Patch Metafilm

l (d = 500 μm) Size/Frequency reduction0 μm 0 %

200 μm 7.3 %300 μm 20.9 %400 μm 38.4 %480 μm 56.1 %

l

l

d

d

Square PEC Patches

HFSS

GSTC (sparse)

GSTC (Lee et al.)

GSTC (new)

l/d

f r, G

Hz

h = 0.5 mm

0 0.2 0.4 0.6 0.8 150

100

150

200

250

300

Resonator with Dielectric Disk Scatterers: Loss Effects

Resonator with dielectric metafilm

2r

p

Metafilm: Oblate Spheroidal

Dielectric Disks

d1 =d2 =0.75 cm; r=0.46 cm; p=1 cm; Disk thickness=0.046 cm; εr =12.0; tan δ=0.04

GSTC model: fr =8.53 GHz, Q=137

d1 +d2

Resonator without metafilm,but uniformly filled with dielectric

Result: fr =2.98 GHz, Q=25

d1 =d2 =0.75 cm; εr =12.0; tan δ=0.04

x

zmetafilm

conductorconductor

z=d1 z=-d1z=0

HFSS: fr =8.61 GHz, Q=114Tradeoff exists betweensize/frequency reduction and Q

Metafilm or Metamaterial Expired Structures

I.A. Ibrahheem and M. Koch, “Coplanar waveguide metamaterilas: The role of bandwidth modifying slots”, Appl. Phys Lett, 2007

Biomedical Applications

Measurement of fluids, cell counts, and contaminants

Booth, Holloway, and Orloff

1 2 3 4 5Frequency (GHz)

-30

-20

-10

0

|S21

| (d

B)

1 mm cover layer: εr=1.0

1 mm cover layer: εr=4.0

1 mm cover layer: εr=88.0

Summary: Metafilm -- the 2-D Equivalent of a Metamaterial

• The surface version of a metamaterial has been given the name metafilm, which consists of arranging electrically small scatterers (characterized by their electric and magnetic polarizabilities) into a two-dimensional pattern at a surface or interface.

• For many applications, metafilms can be used in place of the metamaterials. Metafilms have the advantage of taking less physical space than do full 3-D metamaterial structures.

• We have shown that a metafilm is better characterized by effective transmission-type boundary conditions, as opposed to the effective-medium description used for a metamaterial. The BC is expressed in terms of theelectric and magnetic polarizabilities of the scatterers.

• Numerical comparison show that this BC is valid and accurate in modeling the metafilm.

• We discussed various applications for metafilms.

Summary: NIST’s Role

realistic materials

realistic applications

Reality

??Gain in Passive Materials??

"'"' μμμεεε jandj −=−=

Published Dataset 1

Published Dataset 2

Fresnel Reflection: Is it Valid?

[ ][ ] 0

0=−×

=−×

BAn

BAn

HHaEEa

AB

B

AB

AB

T

R

ηηη

ηηηη

+=

+−

=

2

Obtained by AssumingRegion B

Region A

x

y

Ei Er

Et

εA, μA

εB, μB

Interaction at an Interface of a Composite

which gives

Region B

Region Ax

y

p

p

ε0, μ0

ε0, μ0

∂AB [ ][ ] AeBaveAn

AmBaveAn

EpjHHa

HpjEEa

αω

αω

=−×

=−×

,

,

New Boundary Condition

corFresnel

corFresnel

TpjTT

RpjRR

λ

λ

+=

+=

Ramifications

If p/λ

is small then,

Fresnel

Fresnel

TTRR

⇒⇒

If not, corrections are needed.

•One of the consequence of these correction terms will be apparent in retrieval algorithms used to determine the effective material properties of composites.

•The basic assumption used in developing retrieval algorithms of material properties uses theclassical Fresnel coefficients and/or the assumption that the fields are continues across the material of interest.

•In fact, this could very well explain some of the non-physical results obtained when the effective material properties are measurement in some of the new metamaterials.

•We are presently using the BCs to develop new material properties retrieval algorithms for these new type of metamaterials.

Summary

• We need to emphasize that when we say metamaterials, we do not JUST mean materials that have negative index behavior.

• We mean synthetic (or engineered) materials that have a uniquely designed μ

and/or ε

behavior. That is, μ

and/or ε

of a

material that are not currently available.

• Existing materials can be tweaked, but the designed materials give us revolutionary possibilities in material behavior.

Other Applications

• THz devices and switches (a 20 ps was just demonstrated)

• bio-medical applications • quantum levitation• new devices• quasi-optical circuits• reducing EMI in radiation or detecting systems• miniaturization devices• enhancement of nonlinear properties• sub-wavelength resolution• superlenses• imaging • impedance matching• dynamic control of materials and optics

Other Applications of Metamaterials and Metafilms???