Plasmonics and Metamaterials Nick Fang University of Illinois

• New Physics of Metmaterials – Artificial Plasma – High Frequency Magnetism – Negative Refraction – Cloaking

• Outlook

Telecom applications

Fang et al. , Science, 2005

Van Duyne et al., MRS bulletin, 2005

Invisibility cloaks

Metamaterials Logeeswaran et al., Appl. Phys. A, 2007

Chen et al., PRL, 2007 • Materials Today’s top 10 advances in material science over the past 50 years • Discover top 100 science stories of the year 2006 ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 3 What are Meta-Materials ? Atomic Crystal Lattice Sub- Meta “Atoms”

1nm 10 nm -100 m

• Definition by a think-tank futurist: “Metamaterials are new materials designated by manipulating extreme magnitudes of physical conditions during synthesis and manufacture.”

• Our Definition: A new class of ordered composites from the inclusion of artificially fabricated, extrinsic, low dimensional inhomogeneities.

Common Natural Metamat’l medium Wave Quantum Waves Classical Waves Propagation Thermal Significant Low? excitation

Rotation, Translation Symmetry 230 crystal lattices Topology …

Atomic Hard or Soft sphere; nearest “Atoms” can be larger Interaction neighbor dominant than lattice

Dopant and Random Controllable Defects

And More

• When  and <0

(from Valerie Browning, DARPA)

In long wavelength limit(a<<), we take the cell as an macroscopic point: all physical properties are smoothed in the cell volume

11   EriGrdVHriGrdVEH()exp(  )   ()exp(  ) ii VVCC 11   D DB(riGrdVB )exp(  )  ( riGrdV )exp(  ) ii VVCC DB The effective  and  can be defined as     ratios of the macroscopic fields: EH

Natural metal exhibit negative  How to lower the plasma frequency? at Optical Frequency: Consider a sparse wire matrix: 2 • “Diluted” electron density: 2 ne 1,  p 2 eff i  n p  m eff 0 eff • Heavy Mass of Electrons (due to magnetic induction): Natural bulk metal 34 mmeff 10 10 e ! a Applications: Tunable optical high 2r pass filter (visible to THz)

Pendry, PRL,1996

•“Diluted” electron density – Lowered filling ratio

• Heavy Mass of Electrons – MtifftMagnetic effect    PmveA

2 2 2 neff e 2c0  p   2 0meff a ln(a / r)

E 1

) 0 

-1 rmittivity ( rmittivity

2 ee P  p -2 1 2  -3

-4 The wire medium exhibits <0 below the plasma -5 frequency. 00.511.52 Frequency (/ ) p

- Pendry, 1998

(H. Raether, Surface Plasmons, Springer- dielectric Verlag, 1988)  E k z

+ + +  + + +  k  x H metal y  =ckx  • EM waves propagating along  the interface between two media p with their  of opposite si gn.

 1/2 • Intensity maximum at interface;  exponentially decays away from k  12 x c   the interface. 12kx

If consider the absorption in metal:  ' '' 1  1  i1

Then, kx become a complex kx=kx’+ikx’’  1   '  2 k '   1  x c   ' 1   1   3  '  2  '' k ''   1  1 x  '  ' 2 c  1 1 2  1 For silver: L=22 m at 514.5nm The propagation length L L=500 m at 1060 nm

1 L  2k '' Potential for Chip Scale x optical interconnects!

The ratio of the electromagnetic energy at two sides of the metal film: 2 H (2 /1) y 2 t01t12 exp(ikz1d1) 2 2  t012  1 r r exp(2ik d ) H y H y0 (0 /1) 01 02 z1 1

 k k  where  zi  z k  1   0 2  i  k  r  tik 1 rik ik  k k   zi z k      i  k    z 2  3 2 2   2 2i  1 2   1  1 T  t012  4  t01 e           0 rad 2  c   1  2   1  2  k  (k  k )   x x x '   1( 0 1) 0   2 1 2 '  T  1 The maximum enhancement: max  1  '  '' For silver, at =350 nm, T~3X102 0 1 1

2r a B e- Atom

Magnetism in natural materials fa des away a bove 100 GHz ! j Array of Split Ring Resonators (Pendry et al, IEEE MTT, 1999)

H0 B - + g - + C - +

The strong capacitive coupling between ind ucti ve c urrent loops leads the magnetic resonance

H inside the cylinder: H0

eff =

0 0<<1, No Resonance

Resonance by Impedance Coupling 1  '()iL     iz C FF  11   2(iiz ( )) 22z  (1 ) 1i r  0 rr00

2z Resonance, Re())0<0 when F 1 r0

R=11, a=25, d=2

Enhanced Coupling by adding more turns, Lower resonant Freq

M. C. K. Wiltshire et al., Science 291, 849 (2001).

0: resonant frequency (->inf)

MP: “Magnetic Plasma” Frequency (=0)

Hampered Performance at Hig her Frequency (Sca le Effect)

Challenges: Fiber-optic communication systems require devices operating in near-IR [λ = 1312nm/229THz (min. dispersion), 1550nm/193THz (min. attenuation)]

50nm!!!

Breakdown of linear scaling and saturation Zhou et al ., PRL , 2005 of resonant response of SRRs at optical freq

3 2 1 )  0 y ( 2 tt -1  p 1 -2 2 Permittivi  -3 -4 -5 0 0.5 1 1.5 2 Frequency (/ ) 10 p

5 ) 

 ( F 2 1 0  22

0 Permeability -5

-10 00.511.52 Frequency (/ ) p From these buildi ng bloc ks, a r ic h var ie ty o f met amat eri al structures can be developed.

Merger of SRR and Plasmon Wires: -> LHM

Smith et al, PRL, 2000;Science, 2001

Direction of Energy Flow: SEH 

Direc tion of Phase Velocity: kE   B Phase and Energy propagation directions are thus antiparallel: kEB||   EH S “Lef t-hddhanded materiil”als”

, 

t t • Boundary Conditions:

nˆ E H E H k k 1:RH 1t 1t 1n 1n 1t 1n 2:LH E2t H2t E2n H2n k2t k2n

The permittivity and permeability must be causal analytic functions; Kramers -Kronig applies:

1  "x 1   '1x  ' 1 PV dx " PVdx   x    x 

   1 1   

11  UEH 220 medium 44

Shelby, Smith et al, Science, 2001

Controlling Electromagnetic Fields , J. B.Pendry et al,Science 321,2006

Free space field Distorted field

H H    E      E    0 t q 0 t E E    H   0   H     t q 0 t

2 R2 (r R1) r  r  R2  R1 r

R1  r  R2

R2     R2  R1  R2     R2  R1

• “The cloak would act like you've opened up a hole in space," "All light or other electromagnetic waves are swept around the area, guided by the metamaterial to emerge on the other side as if they had passed through an empty volume of space.“

-David Smith ,Duke University

Smith et al, Science 2006

ME 598 © 2006-2009 Nick Fang, University of Illinois. All rights reserved. 34 Towards optical metamaterials Ion/E-beam lithography Nanoimprint Microfabrication Bulk machining Hyperlens (2007) 1000 MDM (2006-07) Superlens Plasmonic (2005-07) Metallic rods

uencies Anisotropic 100 Fishnet (2005) Magnetic (2005-07) LSR (2007) NIM Plasmonic+NIM

z) Semiconductor SiC

ptical freq 10 supp()erlens (2006)

HH metamaterial O (2007) Terahertz resonators (2004) 1 cy (T Terahertz confined nn surface plasmon 0.1 (2008) • SRR: Split-ring resonator

eque • LSR: L-shaped resonator rr • MDM: Metal-dielectric-metal SRR

F 0.01 • NIM: Negative index materials (2000-03)

• The Maxwell Stress Tensor: how the artificial atoms interact

• Moving media: Negative Doppler effect

• High f magnetism: how to demonstrate magnetic effect? – The Meissner effect and phase transition – Magnonic lattice?

• Extremely-Low-Frequency Plasmons in Metallic Mesostructures,J.B. Pendry, A.T. Holden, W.J. Stewart and I. Youngs, Phys. Rev. Lett., 25, 4773 (1996).

• Low Frequency Plasmons in Thin Wire Structures, J.B. Pendry, AJ Holden, DJ Robbins, and WJ Stewart, J. Phys. Cond. Matt., 10, 4785 (1998).

• Magnetism from Conductors, and Enhanced Non-Linear Phenomena, JB Pendry, AJ Holden, DJ Robbins, and WJ Stewart, IEEE transactions on microwave theory and techniques 47,2075 (1999).

• Metamaterials and Negative Refractive Index, DR Smith, JB Pendry, MCK Wiltshire, Science 305 788-92 (2004)

• Metamaterials and the Control of Electromagnetic Fields, JB Pendry, Proceedings of the Ninth Rochester Conference on Coherence and Quantum Optics (2007)