limitations J. Zhou, E. N. Economou and C. M. Soukoulis

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1 Mesoscopic Physics in Complex Media, (010) DOI: /iesc/010mpcm01011 Owned by the authors, published by EDP Sciences, 010 Optical metamaterials: Possibilities and limitations M. Kafesaki, R. Penciu, Th. Koschny, N. H. Shen, D. Guney, J. Zhou, E. N. Economou and C. M. Soukoulis Foundation for f Research R h & Technology, T h l Hellas H (FORTH), Crete, Greece Iowa State University (ISU), USA This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited. Article published online by EDP Sciences and available at or

Koschny, N. H. Shen, D. Guney, J. Zhou, E. N. Economou and C. M.

2 FORTH Mesoscopic Physics in Complex Media Cargese, July 010 Optical metamaterials: Possibilities and limitations M. Kafesaki, R. Penciu, Th. Koschny, N. H. Shen, D. Guney, J. Zhou, E. N. Economou and C. M. Soukoulis Foundation for Research & Technology, Hellas (FORTH), Crete, Greece Iowa State University (ISU), USA

Artificial, i structured t (in subwavelength scale) materials Electromagnetic (EM) properties derive from shape and distribution ib ti of constituent units (artificial atoms)

3 Artificial, i structured t (in subwavelength scale) materials Electromagnetic (EM) properties derive from shape and distribution ib ti of constituent units (artificial atoms) EM properties not-encountered in natural materials EM properties encountered in Electrical permittivity Magnetic permeability Possibility to engineer electromagnetic ti properties

4 Negative electrical permittivity () Negative magnetic permeability () Veselago (1968): How a plane wave with <0 & <0? e ikx propagates in media Sov. Phys. Usp. 10, 509 (1968) ) k c n n Negative ε, μ,, n Novel and unique propagation p characteristics in those materials!

$Negative refraction 1 1$ source LHM, n <0 θ Flat

5 Left-handed (LH) materials: Novel phenomena Backwards propagation (opposite phase & energy velocity) k E H S k E H c S=E H Negative refraction 1 1 n AIR n sin sin θ 1 source LHM, n <0 θ Flat lenses - Zero-reflection possibility Perfect lenses Opposite Doppler effect (subwavelength Opposite Cherenkov resolution) radiation air LHM air Interesting physical system New possibilities for light manipulation important potential applications

Application areas of left-handed materials New

Imaging/microscopy Lithography Data D t storage

capabilities of LHMs The trapped rainbow

(subwavelength guides, optimized/miniaturized

6 Application areas of left-handed materials New solutions and possibilities in Imaging/microscopy Lithography Data D t storage Exploiting the subwavelength resolution capabilities of LHMs The trapped rainbow Communications and information processing (subwavelength guides, optimized/miniaturized antennas & filters, improved transmission lines...) Tsakmakidis et. al., Nature 450, 397 (007).

7 Metamaterials beyond negative index High index metamaterials Shrinkage of devices Cloaking Low index metamaterials Pendry et. al., Science 31, 1781 (006) Parallel beam formation

8 Zero -index metamaterials Parallel beam formation Point Source n 1 0 n = 1 0 n 1 sin 1 n sin All th l θ h ld b d th f di l t th All the angles θ should be zero, and therefore perpendicular to the surface

9 Metamaterials beyond negative index High index metamaterials Shrinkage of devices Cloaking Low index metamaterials Pendry et. al., Science 31, 1781 (006) Parallel beam formation Indefinite media Hyperlensing Single-negative media Bi-anisotropic media

10 Most common approach: Merging structures of negative permittivity (ε) with structures of negative permeability (μ) Negative permeability: Structures of resonant loop-currents Negative permittivity: Continuous wires C L j Split Ring Resonator (SRR), Pendry, 1999 E Short-slabspair, Shalaev, 00 E k m 1/ LC

11 Analyze, understand, optimize and tailor metamaterial response Achieve optical metamaterials reduce losses in metamaterials Achieve three-dimensional isotropic left-handed metamaterials Create switchable and tunable metamaterials t Devise/analyze new designs and approaches for negative index behaviour (chiral or anisotropic metamaterials) To explore novel phenomena and possibilities in metamaterials

12 Analyze, understand, optimize and tailor metamaterial response Achieve optical metamaterials reduce losses in metamaterials Achieve three-dimensional isotropic left-handed metamaterials Create switchable and tunable metamaterials t Devise/analyze new designs and approaches for negative index behaviour (chiral or anisotropic metamaterials) To explore novel phenomena and possibilities in metamaterials

13 Scaling down of structures demonstrated initially in microwaves or THz Metal response is not scalable up to optical regime Examination mainly of the negative permeability components

14 Slab-pair: more suitable than SRR in sub-micron scale Magnetic response for normal incidence id exploitation ti in small length scales Simplified and easy in fabrication k k Shalaev et. al., Opt. Lett. 30, 3356 (005)

15 Slabs & wires E Slabs & wires connected k H unit cell k E H unit cell Fishnet design E k H unit cell Zhang, et. al., Opt. Expr. (005) Ulrich (1966) Fishnet (wide-slabs & connected with wires): Optimized design for left-handed behavior

16 Negative n towards visible Fore review, see: Purdue Soukoulis et. al., Science 315 (007) FOM 580 Re( nm n ) Shalaev, Nat. Mat. (007) Im( n ) Leading efforts by Karlsruhe Purdue Stuttgart Berkeley. Lowest losses (Re(n)/Im(n)=3) Karlsruhe FORTH 780 nm Purdue Karlsruhe 1.4 μm Dolling et. al., Opt. Lett. (007) &ISU 77 nm Chettiar et. al., Opt. Lett. (007) Chettiar et. al., MRS Bul. (008) ω N. Mexico μm Dolling et. al., Opt. Lett. (006) High losses Single functional layer Zhang et. al., PRL (005)

17 Optical metamaterials: Problems/challenges High losses Limited fabrication capabilities Current procedures: difficult/time-consuming expensive unable to produce - complicated patterns - large samples - 3D isotropic designs

18 Optical metamaterials: Facing the challenges High losses Analysis & design optimization Good constituent media Gain media? Novel approaches (anisotropic media, chiral media, EIT) Limited fabrication capabilities Current procedures: difficult/time-consuming g procedures expensive (direct laser writing, unable to produce - complicated patterns - large samples adapted to fabrication capabilities - 3D isotropic designs Advancement of fabrication New fabrication methods nanoimprint lithography) New designs/approaches,

19 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

20 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

21 Unit cells E μ<0 k (a) (b) (c) (d) H Purdue, μ<0 00 Aim ε<0 Fishnet Zhang, et. al. (005) Ulrich (1966) Examine the behavior of the designs as they are scaled down targeting optical negative index response Seek for optimization rules

Slab-pair magnetic response LI (1/ C) Idt

$volume fraction of the resonator within$ μ regime Strength of resonance m 1 LC For

C a γ (loss factor) determines: Strength

22 Slab-pair magnetic response LI (1/ C) Idt RI m m 1 F C L C C L C ( ) 1 F m i F ~ volume fraction of the resonator within unit cell F determines: Width of negative μ regime Strength of resonance m 1 LC For uniform scaling: a: lattice constant R L C a γ (loss factor) determines: Strength of resonance L a m 1 1 ~ LC a m m m 1 1 F 1

23 Magnetic resonance frequency vs length scale Al metal, Glass substrate Penciu et. al., Phys. Rev. B 81, (010) Reducing a Saturation value independent of ohmic losses Saturation value a: u.c. size depends on design Saturation of magnetic resonance frequency in small length scales (a<500 nm)

24 Magnetic permeability by scaling down the structures Al metal Glass substrate a k Penciu et. al., Phys. Rev. B 81, (010) Weakening of magnetic resonance at small scales μ ultimately does not reach negative values

B 81, 35111 (010) Spectral width only slightly affected

25 Spectral width of negative μ regime Al metal Glass substrate t Penciu et. al., Phys. Rev. B 81, (010) Spectral width only slightly affected by metal loss Δω/ω min : constant at larger scales tends to zero for smaller scales

26 Losses by scaling down the structures Loss per uni it cell a k Loss 1 R T Increase of losses going to smaller scale Penciu et. al., Phys. Rev. B 81, (010)

27 p i 0 i m Explaining ω m saturation and μ-strength reduction Consideration of metal dispersive response in the conductivity: i 0 1 l m l 1 l Rtot i R il S S S p i 0 p 0 m p Zhou et. al., 005 Tretyakov, 007 Solymar, 1976 Shvets et. al., 005 e ω p = metal plasma frequency γ m =metal collision frequency l S Inductive term (electrons inductance) due to electrons inertia ( Difficulty ( to accelerate ate finite ite mass particles with such high rates) E kinetic 1 L I e dv v m dt v qe m

Slab-pair effective permeability in sub-μm scale C m L

$circuit equation ( ) 1 F ~ volume fraction of the$ i m L 1 F F 1 l L L e ~ L L e e m 0 p S R R L L e For

28 Slab-pair effective permeability in sub-μm scale C m L 1 C ( L L ) C e L e is added to L in the effective circuit equation ( ) 1 F ~ volume fraction of the resonator within unit cell ( L L ) I (1/ C) Idt RI e F i m L 1 F F 1 l L L e ~ L L e e m 0 p S R R L L e For uniform scaling: 1 1 R ~ a a l L ~ a C ~ a 0 p S a: lattice constant

29 p i 0 i m Explaining the observed response Magnetic resonance frequency saturates to ω m-max -dependent on shape -independent of ohmic losses -proportional to metal plasma frequency L a, C a, L 1/ a, R 1/ a m e a: u.c. size 1 1 ~ const. ( L L ) C a c e 1 Strength parameter F becomes L a proportional to area Vanishing of F F F L L e a negative μ regime even if the absence of ohmic losses Loss parameter increases for small length scales; R m m -γ depends on shape L Le 1 L / Le 1 a -it saturates to metal collision frequency 1 Penciu et. al., Phys. Rev. B 81, (010)

30 For high frequency magnetic metamaterials High m 1 ( L L ) C e for 1 High F F High operation 1 L / L frequency Broad-band Low-loss F [1 ] i 0 m e Requirements Small capacitance, C Small L e Large metal plasma frequency small collision frequency L?: opposite role in ω m and μ m 1 L / L e Penciu et. al., Phys. Rev. B 81, (010)

31 Electrons inductance at the electric dipole resonance: Resonance frequency l ( ) 1 d Q Q dq dt C dt ( L L ) R E le pe e e i 0 it e 1 1 ~ const. ( L Le ) C a c 1 Saturation C, L ~ a, R, Le ~ 1/ a

32 Electrons inductance at the electric dipole resonance: Resonance strength l ( ) 1 pe e d Q Q dq dt C dt ( L L ) R E le e i Effective epsilon 0 it pe l 1 1 ~ const. 0 0 Vuc L Le a c C, L ~ a, R, Le ~ 1/ a No vanishing resonance strength

e Electrons inductance at the electric dipole resonance features? l ( ) 1 1 1 ~ const.

33 e Electrons inductance at the electric dipole resonance features? l ( ) ~ const. ( L L ) C a c e 1 d Q Q dq dt C dt ( L L ) R E le pe e e i Saturation 0 it l 1 1 pe 0Vuc L Le a c ~ const. 0 No vanishing resonance strength Spectral width of negative ε: independent of L e and length-scale

34 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

35 Connected structures for direct laser writing 1D Gold in polyimide Re(n)/Im(n) n = -1 = 5 Double ~00 THz (1.5 μm) D Double ~160 THz Calculations by D. Guney D. Guney et.al., Opt. Lett. 34, 506 (009)

36 Connected structure realization M.Wegener s group, Karlsruhe

37 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

$Negative refractive$ Chiral structure:

38 Negative refractive index in chiral media Chiral structure: not-identical to its mirror image n Different index for left- and right- handed d circularly l polarized waves Alternative path to achieve negative index (Pendry, Tretyakov) D E i H B H i E Besides negative index: Polarization rotation Circular dichroism Twisted cross Zhou et. al., Phys. Rev. B 79, 11104R (009) Negative index Large polarization rotation Large circular dichroism

39 Chiral optical structures Twisted gold crosses 1- μm Large polarization rotation Large circular dichroism M. Wegener s group, Opt. Lett. (009)

40 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

41 Elliptic Superlenses dispersion for anisotropic metamaterials media? Perfect lensing conditions: Propagating components: Omnidirectional total transmission Evanescent components: Excitation of dispersionless surface plasmon modes x Aim: Examine these conditions for anisotropic materials z Work done by N.H. Shen

42 Superlensing Elliptic dispersion conditions metamaterials for anisotropic media For p-polarizationpolarization E x 1 y 1 For isotropic media:, x z > 0 1 > 0 x z,, 0 x z y Easy to implement conditions with planar technologies

43 Elliptic Lens dispersion formula for anisotropic metamaterials lenses d d ( / ) d 1 1 Source Image x 1,, 1, 1 d Image Isotropic lens: d d d Source Image Possibility for thin lenses! (less influenced by losses) x d Source z d

44 Anisotropic perfect lens: Negative refraction & focusing Negative refraction by an anisotropic double negative slab Focusing in an anisotropic double negative slab d 0. resolution /5

45 Optical metamaterials: Facing the challenges Analysis & design optimization High losses Good constituent media Gain media? Novel approaches (anisotropic media, chiral media,, EIT) Limited fabrication capabilities Current procedures: Advancement of fabrication difficult/time-consuming g procedures expensive New fabrication methods (direct laser writing, unable to produce nanoimprint lithography) - complicated patterns New designs/approaches, - large samples adapted to fabrication - 3D isotropic designs capabilities

Work thanks to C. Soukoulis E. Economou T.

Foteinopoulou D. Guney J. Zhou B. Wang M.

Shen Relevant publications R. S. Penciu, M.

M. Soukoulis, Magnetic response of nanoscale

Soukoulis, Connected bulk negative index

34, 506 (009). N. H. Shen, S. Foteinopoulou, M.

superlens based on anisotropic left-handed

46 Work thanks to C. Soukoulis E. Economou T. Koschny R. Penciu Thank you! S. Foteinopoulou D. Guney J. Zhou B. Wang M. Wegener s group at Karlsruhe N.H. Shen Relevant publications R. S. Penciu, M. Kafesaki, Th. Koschny, E. N. Economou, and C. M. Soukoulis, Magnetic response of nanoscale left-handed metamaterials, Phys. Rev. B (010). D. Guney, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, Connected bulk negative index photonic metamaterials, Opt. Lett. 34, 506 (009). N. H. Shen, S. Foteinopoulou, M. Kafesaki, Th. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, Compact planar far-field field superlens based on anisotropic left-handed metamaterials, Phys. Rev. B 80, (009). J. Zhou, J. Dong, B. Wang, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, Negative refractive index due to chirality, Phys. Rev. B 79, 11104(R) (009).

Towards optical left-handed metamaterials

FORTH Tomorrow: Modelling approaches for metamaterials Towards optical left-handed metamaterials M. Kafesaki, R. Penciu, Th. Koschny, P. Tassin, E. N. Economou and C. M. Soukoulis Foundation for Research