1 Negative refraction & metamaterials Femius Koenderink Center for Nanophotonics FOM Institute AMOLF Amsterdam

2 Optical materials Maxwell’s equationsMaterial properties + Light: plane waveRefractive 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 S1S1 S2S2

7 Snell’s law Negative refraction Exactly what does negative refraction mean ?? (1) k || conservation is required k in k || k two possible solutions ! How does nature choose which solution is physical ?

8 Snell’s law Negative refraction Exactly what does negative refraction mean ?? (1) k || is conserved (2) Causality: carry energy away from the interface k in k || k Energy flux Phase fronts (k) travel opposite to energy if n<0 !

9 Refraction movies Positive refraction n=1n=2 Negative refraction n=1n=-1 W.J. Schaich, Indiania

10 Snell’s law Negative refraction k in k || k Energy flux Plane wave: (1) k, E, B E B k Phase fronts To the right (2) Energy flow S H S Energy flow to the left

11 Negative index slab NIM slab A flat negative index slab focuses 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 violate energy conservation ? No. n=-1 is a resonant effect that needs time to build up

14 More bizarre optics Superlens: we have taken  =  =-1 Question: what if we take  (r),  (r) arbitrary ? `Transformation optics’ Bend light in space continuously by transforming   Sir John Pendry Maxwell equations map onto Maxwell with modified 

15 Negative lens as example Stretch a thin sheet in space into a slab of thickness d

16 Negative lens as example Insert proper  and  to expand space Stretch a thin sheet in space into a slab of thickness d d

17 Negative lens as example n=-1n=+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<R 1 by bending all rays around it Transformation optics: blow up the origin to a sphere of radius R 1 push the fields in r<R 2 into R 1 <r<R 2 Price to pay: (1)  and  smoothly vary with r (2)  and  depend on polarization

19 Perfect cloaking A 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 longer than ray A Phase front comes through flat Isn’t ray B `superluminal’ ? Superluminality is forbidden for energy or information transport i.e. wavepackets A Cloaking does not violate causality (relativity) Cloaking only works at a single frequency, not for pulses Cloaking corresponds to a resonance with a build up time

21 Conclusions 1.Negative  and  transparent, left-handed plane waves 2.Negative refraction 3.Perfect lensMicroscopy, lithography 4.Transformation optics Perfect cloaking 5.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 Polarizable atoms `Meta material’ Artificial ‘atoms’ Magnetic polarizability Form effective medium

24 Length scales /a 1 Photonic crystals (Bragg) 10 Metamaterials Effective medium Conventional materials 1000 Geometrical optics Ray optics 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 metamaterial Copper SRR, 0.7 cm size 1 cm pitch lattice, =2.5 cm Science 2001 Shelby, Smith Schultz cm-sized printed circuit board microwave 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 (MgF 2 ) (50 nm) Wedge experiment at 1500 nm Valentine et al. (Berkeley) Nature 2008

33 Fishnet dispersion Negative index for > 1450 nm Changes with

34 From microwave to visible Soukoulis, Linden, Wegener Science (review) Scaling split rings from: 1 cm to 100 nm NIR / 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 modes Amplify evanscent field Berkeley: image `Nano’ through 35 nm silver slab in photoresist

37 Superlens Object (mask) 2 um scale AFM of resist with superlens AFM of resist Ag replaced by PMMA 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 & dispersion2. Anisotropy Negative  implies absorption Current 1/e decay length ~ 4 A.Planar arrays B.Out-of-plane response Spatial inhomogeneity Vector anisotropy Question: Can we make 3D isotropic NIM’s ?

40 Possible 3D materials Wegener group: split ring bars Extremely difficult to make Giessen group: split ring stacks 3D but anisotropic

41 Conceptual challenges ‘Resonant amplification’ ‘Superluminal rays’ In time: how does -the perfect image form -cloaking set in Time domain Spatial Magnifying super lens Corner cubes Cavities Different cloaks Transformation optics n=-1 Sources Emitters in cloaks Emitters coupled by perfect lenses Emission rate ?