Towards optical left-handed metamaterials

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1 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 & Technology, Hellas (FORTH) & Univ. of Crete, Greece Ames Lab & Iowa State University (ISU), USA

2 Negative electrical permittivity () Negative magnetic permeability () Veselago (1968) n e e ( / ) negative ikx i n c x e Novel and unique effects and possibilities

$refraction AIR source LHM,$ Perfect lenses

3 Veselago (1968), Pendry (000) Left-handed (LH) materials: Novel phenomena Backwards propagation (opposite phase & energy velocity) S=E H S Negative refraction AIR source LHM, n<0 θ Flat lenses - Perfect lenses (subwavelength resolution) Opposite Doppler effect Opposite Cherenkov radiation Interesting physical system air LHM air Interesting physical system New possibilities for light manipulation important potential applications

Application areas of left-handed materials New solutions and

Exploiting the subwavelength resolution capabilities of LHMs The

(subwavelength guides, optimized/miniaturized antennas &

4 Application areas of left-handed materials New solutions and possibilities in Imaging/microscopy Lithography Data 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).

Phot. (011) Figure from Soukoulis & Wegener, Nature Photonics 5 (011)

5 Negative μ and n towards visible Fore review, see: Soukoulis et. al., Science 315 (007) Shalaev, Nat. Mat. (007) Soukoulis & Wegener, Nat. Phot. (011) Figure from Soukoulis & Wegener, Nature Photonics 5 (011) Leading efforts by Karlsruhe Purdue Stuttgart Berkeley. Hard to achieve optical negative μ

Negative μ and n towards visible Fore review, see: Purdue Soukoulis et. al.

(007) Im( n ) Soukoulis & Wegener, Nat. Phot.

Low losses (Re(n)/Im(n)=3) Karlsruhe &ISU 1.4 μm Karlsruhe FORTH 780 nm Purdue Dolling et.

6 Negative μ and n towards visible Fore review, see: Purdue Soukoulis et. al., Science 315 (007) 580 Re( nm n ) FOM Shalaev, Nat. Mat. (007) Im( n ) Soukoulis & Wegener, Nat. Phot. (011) Leading efforts by Karlsruhe Purdue Stuttgart Berkeley. Low losses (Re(n)/Im(n)=3) Karlsruhe &ISU 1.4 μm Karlsruhe FORTH 780 nm Purdue Dolling et. al., Opt. Lett. (007) 77 nm Chettiar et. al., Opt. Lett. (007) Xiao et. al., Opt. Lett. (009) ω N. Mexico μm Dolling et. al., Opt. Lett. (006) High losses Single functional layer Zhang et. al., PRL (005)

Multilayer metamaterials 5-layers SRRs Negative μ at ~6 6THz 4-layers

5 Stuttgart, Nat. Mat. 7, 31 (008) 400 nm Karlsruhe, Opt. Lett.

7 Multilayer metamaterials 5-layers SRRs Negative μ at ~6 6THz 4-layers SRRs Negative μ at ~10 THz 3-layers fishnet Negative n at ~1.5 μm, FOM=. 5 μm FORTH, Opt. Lett. 30, 1348 (005) 10-layers fishnet Negative index at ~1.7 μm, FOM=3.5 Stuttgart, Nat. Mat. 7, 31 (008) 400 nm Karlsruhe, Opt. Lett. 3, 55 (007) 7-layers fishnet Negative index at ~640 nm, FOM=3.3 Ag & MgF Berkeley, Nature 455, 376 (008) Valencia, Phys. Rev. Lett. 106, (011)

8 Towards 3D-isotropic negative μ and n? Multilayer SRR( (stereometamaterials) t t Figure from Soukoulis & Wegener, Nature Photonics 5 (011) Stuttgart Caltech Jena 3D-SRR (membrane- projected lithography) Chiral metamaterial (DLW+electroplating) Sandia Karlsruhe Ameslab

9 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

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

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

12 Analysis of wave propagation in optical left-handed metamaterials (OLHMs) Optimization (design & material) of OLHMs as to achieve high operation frequency and broad- bandwidth Loss-examination & optimization of OLHMs as to achieve low-losses Alternatives of metal for OLHMs? 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 81 (010) Ph. Tassin, Th. Koschny M. Kafesaki and C. M. Soukoulis, Graphene superconductors and metams: What makes a good conductor for metamaterials, Nature Photonics 6, 59 (01)

13 Analysis of wave propagation in optical left-handed metamaterials (OLHMs) Optimization (design & material) of OLHMs as to achieve high operation frequency and broad- bandwidth Loss-examination & optimization of OLHMs as to achieve low-losses Alternatives of metal for OLHMs? 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 81 (010) Ph. Tassin, Th. Koschny M. Kafesaki and C. M. Soukoulis, Graphene superconductors and metams: What makes a good conductor for metamaterials, Nature Photonics 6, 59 (01)

14 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 magnetic response of the designs as they are scaled down targeting optical negative permeability High frequency Seek for optimization rules Broad-band d Low-loss

15 Slab-pair : Effective RLC circuit C L C C L C Kirchoff s equation 1 d ext LI Idt RI C dt ext i t 0HAe 0 Current, I Magnetic moment, m=ia Magnetization, M=m/V uc =μ 0 (μ-1)h

$1 F m i F ~ volume fraction of the resonator within unit cell$ (determines the resonance strength) 1 m Rtot LC L for all-type losses)

16 Slab-pair magnetic response (RLC circuit description) C L C C L C ( ) 1 F m i F ~ volume fraction of the resonator within unit cell (determines the resonance strength) 1 m Rtot LC L for all-type losses) Tassin et al., Nature Photon. 6, 59 (01) Damping factor (accounts R tot =R+R rad

17 Magnetic resonance frequency vs length scale Al metal, Glass substrate Reducing a Saturation value independent of ohmic losses Saturation value depends on design a: u.c. size depends on design Saturation of magnetic resonance frequency in small length scales (a<500 nm)

18 Magnetic permeability by scaling down the structures Al metal Glass substrate t a k Weakening of magnetic resonance at small scales μ ultimately does not reach negative values

19 Spectral width of negative μ regime Al metal Glass substrate Spectral width depends on geometry Δω/ω min : constant at larger scales tends to zero for smaller scales Spectral width only slightly affected by metal loss Even in the absence of ohmic losses

20 Slab-pair magnetic response (RLC circuit description) C L C C L C ( ) 1 F i 0 F ~ volume fraction of the resonator within unit cell (determines the resonance strength) 0 1 Rtot LC L for all-type losses) Damping factor (accounts R tot =R+R rad Tassin et al., Nature Photon. 6, 59 (01)

21 Slab-pair total resistance R l S m i Material dependent + Geometry dependent 0 p For free electrons (Drude metals) ω p = metal plasma frequency γ m =metal collision frequency Re( R) Im( R) l m l 1 l R i R ohm il S S S 0 p 0 p R ohm L Inductive term (electrons kinetic inductance) due to electrons inertia ( Difficulty to accelerate finite mass particles with such high rates) l S ( ff y f Solymar, Economou, Shevts, Tretyakov, e e

22 High frequency magnetic permeability l S ( ) 1 F m i m 1 LC(1 ) Kinetic inductance factor L e L For uniform scaling: F 1 F 1 ~ a 1 1 ~ L e L 1 Re( 1 R)~ a a Pronounced role in small a C a F: filling 1 l C a ratio Le scales S a: lattice constant 0 p

23 p i 0 i m Explaining the observed response Magnetic resonance frequency saturates to ω m-max -dependent on shape -independent of metal losses a: u.c. size L a, C a, L 1/ a, 1/ a e 1 1 m ~ const. ( L L ) C ca c e 1 Strength parameter F becomes 1 1 proportional to area F F 1 F 11/ -Weakening of magnetic resonance -Vanishing of negative μ regime even if the absence of ohmic losses Upper bound of negative μ regime m 1 1 F m a

24 For high frequency magnetic metamaterials High m 1 LC(1 ) for High operation frequency Broad-band High F 1 F 1 F 0[1 ] m i ratio F: filling Requirements Small capacitance, C Large structure t filling ratio, F Small L e /L (=ξ) Material requirements Geometry requirements 1 0 p f( geometry)

25 Optimizing slab-pair-based systems thick Requirements wide Thick & wide slabs Thick separation layer Metal of high ω p What about losses?

26 Analysis of wave propagation in optical left-handed metamaterials (OLHMs) Optimization (design & material) of OLHMs as to achieve high operation frequency and broad- bandwidth Loss-examination & optimization of OLHMs as to achieve low-losses Alternatives of metal for OLHMs? 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 81 (010) Ph. Tassin, Th. Koschny M. Kafesaki and C. M. Soukoulis, Graphene superconductors and metams: What makes a good conductor for metamaterials, Nature Photonics 6, 59 (01)

Loss depends only on ξ, ζ, F Tassin et al.

factor (dimensionless) Le 1 C 1 Im( R) G(geometry) Im(

27 Loss depends only on ξ, ζ, F Tassin et al., Nature Photon. 6, 59 (01) Dissipative loss Dissipative loss (=Re( R) I ) / 0 Incident power 4 ~ F [ (1 ) 1] Kinetic inductance factor (dimensionless) Le 1 C 1 Im( R) G(geometry) Im( ) L L Dissipation factor (dimensionless) 0 1 LC F: filling ratio m C 1 Re( ) Re( R) G(geometry) Re( ) L Q 0 p

28 Magnetic permeability in dimensionless quantities ( ) 1 F (1 ) 1 i 1 ~Im( R)~ G (geometry) Im( ) Kinetic inductance factor / 0 1 F: filling ratio LC 0 ~ Re( R) ~ G(geometry) Re( ) Dissipation factor Permeability also depends only on ξ, ζ, F Tassin et al., Nature Photon. 6, 59 (01)

29 Dissipative power at ω 1 : μ(ω 1 )=-1 ~ 4 F [ (1 ) 1] 1 ~ Im( R) ~ G(geometry) Im( ) ~ Re( R) ~ G(geometry) Re( ) Dissipation depends only on ζ ζ : good quantity to quantify losses (loss figure-of-merit) and compare conductors For low-loss metamaterials small dissipation factor is For low loss metamaterials small dissipation factor is required Small Re(R) Small Re(ρ)

30 FOMs for high-quality magnetic metamaterials? Loss figure-of merit: Dissipation factor ζ For low-loss l metamaterials t small dissipation i factor ζ (~small Re(R)) is required 1 ~Re( R)~ Re( ) t m t m : metal thickness Freq. saturation figure-of-merit: Kinetic m inductance factor ξ Re( ) 0 p For high-freq. metamaterials small ξ (~small Im(R)) is required Im( ) ~Im( R )~ 1 Im( ) t m / 1/ (1 ) Material-dependent part: Re(ρ), Im(ρ) Good quantities to compare conducting materials m m 0 0 p

31 Analysis of wave propagation in optical left-handed metamaterials (OLHMs) Optimization (design & material) of OLHMs as to achieve high operation frequency and broad- bandwidth Loss-examination & optimization of OLHMs as to achieve low-losses Alternatives of metal for OLHMs? 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 81 (010) Ph. Tassin, Th. Koschny M. Kafesaki and C. M. Soukoulis, Graphene superconductors and metams: What makes a good conductor for metamaterials, Nature Photonics 6, 59 (01)

32 Comparing gold with graphene At IR Graphene conductivity from Li et al, Nature Phys. 4, 53 (008) Graphene performs worse than gold Reason?: Small thickness large R weak total current Tassin et al., Nature Photon. 6, 59 (01)

33 Comparing silver with YBCO Resistivity from experimental data High-Tc superconductors perform worse than silver Reason?: No complete screening of free electrons by Cooper pairs in high frequencies Tassin et al., Nature Photon. 6, 59 (01)

34 Comparing losses in different conductors Seeking for smaller resistivity Tassin et al., Nature Photon. 6, 59 (01) Blue: microwaves, Red: infrared, Green: visible Still silver is best at IR and visible!

35 Slab-pair electric resonance Apart of anti-symmetric current mode (magnetic dipole response) Picture by S. Linden Also a symmetric current mode (electric dipole response) ( ) 1 pe e i + - x t E m e E mm e x ω e

36 Electric dipole resonance in small length scales? Resonance saturates in small scales

37 For high-frequency, low-loss quasistatic plasmon resonance For high-frequency: small kinetic inductance factor ξ (~small Im(ρ)) is required For low-loss: small dissipation factor ζ (~small Re(ρ)) is required

38 Summary/Conclusions Magnetic metamaterial behaviour towards optical regime (nm scale): magnetic resonance frequency saturates permeability resonance becomes weaker negative permeability regime vanishes RLC circuit description and metal dispersive response can account for all the above effects and can lead to figures of merit and design rules for high frequency magnetic metamaterials Optimized i high-frequency h response requires metals of small Re and Im part of resistivity Common metals perform better than graphene and YBCO at IR Funding by Silver Thank seems the you best conducting material for visible

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

limitations J. Zhou, E. N. Economou and C. M. Soukoulis Mesoscopic Physics in Complex Media, 01011 (010) DOI:10.1051/iesc/010mpcm01011 Owned by the authors, published by EDP Sciences, 010 Optical metamaterials: Possibilities and limitations M. Kafesaki, R.