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Negative refraction & metamaterials

Negative refraction & metamaterials. Femius Koenderink Center for Nanophotonics FOM Institute AMOLF Amsterdam . Optical materials. Maxwell’s equations. Material properties. +. Light: plane wave. Refractive index. Natural materials. Damped solutions. Propagating waves.

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Negative refraction & metamaterials

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

  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 Propagating waves Damped solutions

  5. What is special about e<0, m<0 Veselago (1968, Russian only) Conventional choice: If e<0, m<0, one should choose: propagating waves with `Negative index of refraction’

  6. Snell’s law with negative index S2 S1 Negative refraction

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

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

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

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

  11. Negative index slab A flat negative index slab focuses light NIM slab

  12. Conventional lenses Exact wave optics: Image sharpness limited to l/2 Ray optics: Image is flipped & sharp 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 Does amplification violate energy conservation ? No. n=-1 is a resonant effect that needs time to build up Surface modes

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

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

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

  17. Negative lens as example d n=-1 n=+1 The perfect lens (n=-1, d/2 thickness) ‘annihilates’ a slab of n=1,d/2 thick

  18. Perfect cloaking Price to pay: (1) e and m smoothly vary with r (2) e and m depend on polarization • 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

  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 ? A 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 B 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 • Negative e and m: transparent, left-handed plane waves • Negative refraction • Perfect lens Microscopy, lithography • Transformation optics Perfect cloaking • Perfect lenses & cloaks: near-field, resonant phenomena • Questions • How can we realize negative e and m ? • How can we prove negative e and m ? • Demonstrations of the perfect lens ? • Was anything cloaked yet ? • What limits cloaking and lensing

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

  23. How to create arbitrary e,m Conventional material `Meta material’ Polarizable atoms Artificial ‘atoms’ Magnetic polarizability Form effective medium

  24. Length scales Geometrical optics Ray optics Metamaterials Effective medium Photonic crystals (Bragg) Conventional materials 0.1 1 10 1000 l/a

  25. Metamaterial challenges Creating negative e is easy (any metal) For negative m we need (1) l/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, l=2.5 cm Science 2001 Shelby, Smith Schultz cm-sized printed circuit board microwave negative m 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 AMOLF (2008) Karlsruhe (2005) 200 nm sized SRR’s, Gold on glass l=1500 nm Can we make smaller split rings for l~ 500 nm wavelength ? No: at visible w 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 experiment at 1500 nm Valentine et al. (Berkeley) Nature 2008

  33. Fishnet dispersion Negative index for l > 1450 nm Changes with l

  34. From microwave to visible 2000-2006 Scaling split rings from: 1 cm to 100 nm 2007-2008 NIR / visible: -wire pairs -fishnets Soukoulis, Linden, Wegener Science (review) 2007

  35. Questions • What about the superlens ? • What about cloaking ? • Practical challenges for negative e and m • Conceptual challenges

  36. Superlens Poor mans superlens: plasmon slab (e<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-l features in the image Result: the opaque 35 nm Ag slab makes the image sharper !

  38. Cloaking 2-dimensional experiment at microwave frequencies (l=3cm) Cloaked object: metal cylinder No cloak Cloak Schurig et al., Science 2006

  39. Practical challenges 1. Absorption & dispersion 2. Anisotropy • Planar arrays • Out-of-plane • response • Spatial inhomogeneity • Vector anisotropy Question: Can we make 3D isotropic NIM’s ? Negative m implies absorption Current 1/e decay length ~ 4 l

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

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

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