1

Negative refraction &metamaterials

Femius Koenderink

Center for NanophotonicsFOM Institute AMOLFAmsterdam

2

Optical materials

Maxwell’s equations Material properties

+

Light: plane wave Refractive index

3

Natural materials

Damped solutions Propagating waves

4

General materials

Damped solutions Propagating waves

Damped solutionsPropagating waves

5

What is special about <0, <0

Veselago (1968, Russian only)

Conventional choice:

If <0, <0, one should choose:

propagating waves with`Negative index of refraction’

6

Snell’s law with negative index

Negative refraction

S1S2

7

Snell’s law

Negative refraction

Exactly what does negativerefraction mean ??

(1) k|| conservation is required

kin

k|| k

two possible solutions !How does nature choosewhich solution is physical ?

8

Snell’s law

Negative refraction

Exactly what does negativerefraction mean ??

(1) k|| is conserved (2) Causality: carry energy away from the interface

kin

k|| k

Energy flux

Phase fronts (k) travel opposite to energy if n<0 !

9

Refraction movies

Positive refraction

n=1 n=2

Negative refraction

n=1 n=-1

W.J. Schaich, Indiania

10

Snell’s law

Negative refraction

kin

k|| k

Energy flux

Plane wave:

(1) k, E, B

E

B

kPhase frontsTo the right

(2) Energy flow S

HS

Energy flowto the left

11

Negative index slab

NIM slab

A flat negative index slabfocuses light

12

Conventional lenses

Ray optics:Image is flipped & sharp

Exact wave optics:Image sharpness limited to /2

Sharp features (large ) don’t reach the lens

13

Perfect lens

The negative index slab creates a perfect image by amplifying the evanescent field via surface modes

Surface modes

Does amplification violateenergy conservation ?

No. n=-1 is a resonant effectthat needs time to build up

14

More bizarre opticsSuperlens: we have taken ==-1Question: what if we take (r), (r) arbitrary ?

`Transformation optics’Bend light in space continuously by transforming

Sir John Pendry

Maxwell equationsmap onto Maxwell

with modified

15

Negative lens as example

Stretch a thin sheet in spaceinto a slab of thickness d

16

Negative lens as example

Insert proper and

to expand space

Stretch a thin sheet in spaceinto a slab of thickness d

d

17

Negative lens as example

n=-1 n=+1

d

The perfect lens(n=-1, d/2 thickness)

‘annihilates’

a slab of n=1, d/2 thick

18

Perfect cloaking

Conceal an object in the sphere r<R1 by bending all rays around it

Transformation optics: blow up the origin to a sphere of radius R1

push the fields in r<R2 into R1<r<R2

Price to pay:(1) and smoothly vary with r

(2) and depend on polarization

19

Perfect cloakingA perfect cloak- keeps external radiation out, and internal radiation inside the cloak- works for any incident wave field- cloaks the object in near and far field- leaves no imprint on the phase of scattered light

Min Qiu, KTH Stockholm

20

Snags in perfect cloaking ?

B

Note that ray B is much longerthan ray A

Phase front comes through flatIsn’t ray B `superluminal’ ?

Superluminality is forbidden forenergy or information transport i.e. wavepackets

A

Cloaking does not violate causality (relativity)Cloaking only works at a single frequency, not for pulsesCloaking corresponds to a resonance with a build up time

21

Conclusions

1. Negative and transparent, left-handed plane waves2. Negative refraction3. Perfect lensMicroscopy, lithography4. Transformation optics Perfect cloaking5. Perfect lenses & cloaks: near-field, resonant phenomena

Questions• How can we realize negative and ?• How can we prove negative and ?• Demonstrations of the perfect lens ?• Was anything cloaked yet ?• What limits cloaking and lensing

22

Metamaterials

Questions• How can we realize negative and ?• How can we prove negative and ?• Demonstrations of the perfect lens ?• Was anything cloaked yet ?• What limits cloaking and lensing

23

How to create arbitrary Conventional material

Polarizableatoms

`Meta material’

Artificial ‘atoms’Magnetic polarizabilityForm effective medium

24

Length scales

/a1

Ph

oto

nic

cry

stals

(B

rag

g)

10

Meta

mate

rials

Eff

ect

ive m

ed

ium

Con

ven

tion

al m

ate

rials

1000

Geom

etr

ical op

tics

Ray o

pti

cs

0.1

25

Metamaterial challenges

Creating negative is easy (any metal)For negative we need

(1) /10 sized artificial atoms with a magnetic response

(2) That do not consist of any magnetic material

We use(3) Localized currents induced by incident radiation

to circulate in loops(4) Resonances to get the strongest magnetic

response

26

Artificial atom - SRR

Split ring resonator has a resonance at

27

How does the SRR work ?

Faraday: flux change sets up a voltage over a loop

Ohm’s law: current depending on impedance

Resonance when |Z| is minimum (or 0)

Circulating current I has a magnetic dipole moment

(pointing out of the loop)

28

Pioneering metamaterialCopper SRR, 0.7 cm size1 cm pitch lattice, =2.5 cm

Science 2001 Shelby, Smith Schultz

cm-sized printed circuit boardmicrowave negative

Calculation Pendry et al, ‘99

29

First demonstration of negative refraction

Idea: beam deflection by a negative index wedge

Measurement for microwaves(10.2 GHz, or 3 cm wavelength)Shelby, Smith, Schultz, Science 2001

30

Smallest split rings

200 nm sized SRR’s, Gold on glass=1500 nm

Karlsruhe (2005) AMOLF (2008)

Can we make smaller split rings for ~ 500 nm wavelength ?

No: at visible metals have a plasmon response

31

Magnetic response from wire pairs

32

Fishnet structures

Fishnet of Ag (30 nm) and dielectric (MgF2) (50 nm)

Wedge experimentat 1500 nm

Valentine et al. (Berkeley)Nature 2008

33

Fishnet dispersion

Negative indexfor > 1450 nm

Changes with

34

From microwave to visible

Soukoulis, Linden, WegenerScience (review) 2007

2000-2006Scaling split ringsfrom:1 cm to 100 nm

2007-2008NIR / visible:

-wire pairs-fishnets

35

Questions

• What about the superlens ?• What about cloaking ?

• Practical challenges for negative and

• Conceptual challenges

36

Superlens

Poor mans superlens: plasmon slab (<0 only)

Surface modesAmplify evanscent field

Berkeley: image `Nano’ through 35 nm silver slab in photoresist

37

Superlens

Object (mask)2 um scale

AFM of resistwith superlens

AFM of resistAg replaced byPMMA

Atomic Force Microscope to detect sub-features in the image

Result: the opaque 35 nm Ag slab makes the image sharper !

38

Cloaking

2-dimensional experiment at microwave frequencies (=3cm)Cloaked object: metal cylinder

No cloak

Cloak

Schurig et al., Science 2006

39

Practical challenges

1. Absorption & dispersion 2. Anisotropy

Negative implies absorptionCurrent 1/e decay length ~ 4

A. Planar arraysB. Out-of-plane response

Spatial inhomogeneityVector anisotropy

Question: Can we make 3D isotropic NIM’s ?

40

Possible 3D materials

Wegener group: split ring barsExtremely difficult to make

Giessen group: split ring stacks3D but anisotropic

41

Conceptual challenges

‘Resonant amplification’‘Superluminal rays’

In time: how does-the perfect image form-cloaking set in

Time domainSpatial

Magnifying super lensCorner cubesCavitiesDifferent cloaks

Transformation optics

n=-1

n=-1

Sources

Emitters in cloaksEmitters coupled byperfect lenses

Emission rate ?