ECE280: Nano-Plasmonics and Its Applications. Week8. Negative Refraction & Plasmonic Metamaterials

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1 ECE8: Nano-Plasonics and Its Applications Week8 Negative Refraction & Plasonic Metaaterials

2 Anisotropic Media c k k y y ω μ μ + Dispersion relation for TM wave isotropic anisotropic k r k i, S i S r θ i θ r,k θ r,s y (H) y t y μ μ μ μ μ t Anisotropic edia with diagonal perittivity and pereability S r k r k i, S i,, < > > y μ Concentrate on the case, in which D. R. Sith and D. Schurig, PRL (3)

3 Anisotropic Media and Equi-frequency Contour isotropic anisotropic k r k μ y k ω + μ y >, >, < μ c Anisotropic y θ i θ r,k θ r,s k r? k i k r? k i, S i S r isotropic Poynting Vector: v S * Use causality constraint to deterine the correct k : t k v ω v e v S v v e > > k r v v e kr < ω * Positive or negative refraction? H v e v S >

4 All-angle Negative Refraction Refraction angle θ tan 1 ( k / k ) Refraction angle (deg.) r, k θ θ r,k r, s tan Incident angle (deg.) θ r,s 1 ( S / S ) tan 1 k ( ) k isotropic anisotropic The hyperbolic equifrequency contour leads to all-angle negative θ r,s θ i k i, S i k r θ r,k θ r,s S r

5 Effective Perittivity of Metal-dielectric Multilayers t t d Two operation frequency regions y (H) // Effective edia theory p) // ( y ) p + (1 p ( ) ( Filling ratio 1 p 1 + ) d p t /( t + td) d Wavelength (n)

$Negative Refraction at Different Wavelengths @$ Ag: 3n 3μ 3μ Effective slab Effective slab

the effective edia theory B. Wood, J. B. Pendry et al.

6 Negative Refraction at Different 3n 5n wavelength H-field SiO : n Ag: 3n 3μ 3μ Effective slab Effective slab Finite-eleent siulations agree ecellently with the effective edia theory B. Wood, J. B. Pendry et al., PRB (6), X. B. Fan, G. P. Wang, PRL (6)

$5n SiO: 17~3n Coparing with PCs, negative refraction$

7 Periodic v.s Rado Multilayers Ag 3n/ SiO n Totally 4 units (u) ± 15% deviation Ag: 5.5~34.5n SiO: 17~3n Coparing with PCs, negative refraction in ultilayer syste is not so sensitive to the iperfection of the structure

Focusing by Multilayer Structures Finite-eleent siulation H Diagra of ray-tracing 6n air ultilayers air air effective slab air A partial focus can be

8 Focusing by Multilayer Structures Finite-eleent siulation H Diagra of ray-tracing 6n air ultilayers air air effective slab air A partial focus can be fored by etal-dielectric ultilayers D. R. Sith et al., APL (4), Z. Jacob Z, L. V. Alekseyev, E. Narianov Opt. Ep. (6) A. Salandrino and N. Engheta, PRB (6)

9 Nanowires as Anisotropic Media d d d y d p p p p p p ) (1 ) (1 ) (1 ) (1 ) ( ) (1 ) ( // Effective perittivity

$Negative Refractin in Nanowires E <S> (a) 1.$

10 Negative Refractin in Nanowires E <S> (a) 1.5 (b) X1-3 Full-wave Siulation (c) 1.5 (d) X1-3 Effective Slab

11 Eperiental Deonstration Science 31, 93 (8)

$Positive Refraction in Nanowire Pris X1-3.5 1.$

12 Positive Refraction in Nanowire Pris X The negative refraction in anisotropic edia is very sensitive to the relative orientation of interface and the optical ais

$Negative Refraction Using Natural Anisotropic Crystals YVO4 Crystal with different orientations of optical ais in$

13 Negative Refraction Using Natural Anisotropic Crystals YVO4 Crystal with different orientations of optical ais in regions A and B k r k i k t S t S r S i k i S i k r S r k t S t Y. Zhang et al, PRL (3); Z. Liu et al, PRB 69, 1154 (4)

14 Surface Plason Polaritons at Sei-infinite Interface Basic properties: a. Surface plasons are the collective ecitation of electrons at the interface between a etal and a dielectric aterial; b. The electric field is highly confined at the interface; W. L. Barnes et al., Nature (3) c. Moentu isatch between the SPPs and the photons at the sae frequency.

15 SPPs on Metallic Fils d (ω) d dielectric etal dielectric d SPPs on the two interfaces interact with each other, giving rise to two new odes antisyetric ode (ω + ) syetric ode (ω ) Charge distribution Dispersion relation d k d d k d ( ω) k + dk tanh( ) ( ω) k + dk coth( ) i i (where k ω ω ) d d / c k, k ( ω) / c k H. Raether, Surface plasons on sooth and rough surfaces and on gratings

16 Dispersion Curve of SPPs air/silver/air A B For thin etallic fils, the anti-syetric ode can have negative group velocity for large wave vectors

17 Propagation Characteristic for Different Modes Mode A is ecited v k v g < Backward SPs air air pris silver v g incident k reflected E V/ Mode B is ecited v k v g > Forward SPs incident k reflected v g E V/ 1-6

the dielectric k J/ s k J/ s air Ag air air Ag air For backward SPs, the

18 Physical Origin of Backward and Forward SPs Tie averaged Poynting vector < S > 1 Re( E H y ) k <S > is always in opposite directions in the etal and the dielectric k J/ s k J/ s air Ag air air Ag air For backward SPs, the net energy flow is negative For forward SPs, the net energy flow is positive

$3D FDTD Siulation of Negative Refraction of$ $Refraction angle agrees with Snell s law$

19 3D FDTD Siulation of Negative Refraction of SPs y SP 1 SP SP inc SP ref k 1 v g1 k v g SP tran θ t sin 1 (6 sin 45 / 5) 58 Refraction angle agrees with Snell s law taking n k sp /k

$Negative Refraction of SPPs in Metal/Insulator/Metal Structure Metal$ diagra of fabricated structure H. Shin and S. H. Fan, PRL (6); A.

20 Negative Refraction of SPPs in Metal/Insulator/Metal Structure Metal Insulator Metal Dispersion diagra of SPPs in MIM structure Scheatic diagra of fabricated structure H. Shin and S. H. Fan, PRL (6); A. Alu and N. Enghta, JOSA (6); H. J. Leec, J. A.Dionne and H. A. Atwater Science, (7)

$Refraction in$

21 Eperiental Deonstration of Negative Refraction in the Visible Region

22 Suary Negative refraction can be deonstrated in various systes Negative refraction takes place when Phase velocity and group velocity are anti-parallel (NIMs, higher band of PCs, surface plasons) Material property is anisotropic (band edge of PCs, etal/dielectric coposites) Negative refraction can be etended to atter waves and acoustic waves Negative refraction can be used to design novel optical devices

23 Engineering Electronic Properties For etal the perittivity is given by Drude odel: Electric plasa frequency: ne ω ep e ( ω) 1 ω ep ω( ω + iγ ) (typically in the UV region) Metallic wire lattice In etallic wire structure: πr dilute electron density : n eff n a μ heavy electron ass : eff ln( a / r) eff ω r e n 1 p, eff ω( ω + i a ω 1 ω p, eff ω( ω + i.1ω p, eff p, eff / πr σ ) for aluinu ) Pendry J.B. et al., Phys. Rev. Lett. 76, 4773 (1996)

Engineer Magnetic Properties Split-ring resonator (SRR) Principle of artificial agnetis: 1) The agnetic-flu induce a current loop, thus produce a agnetic dipole; ) The resonant frequency of such a

24 Engineer Magnetic Properties Split-ring resonator (SRR) Principle of artificial agnetis: 1) The agnetic-flu induce a current loop, thus produce a agnetic dipole; ) The resonant frequency of such a structure depends on the geoetrical capacitance, inductance, and the internal reactance of the ring; 3) The agnetic response is able to etend to TH, or even higher frequency, with large positive or negative μ. Pendry J.B. et al, IEEE MTT 47, 75 (1999) Equivalent circuit of SRR

25 Analytical Forula for Effective μ πr μ a eff + σi μ ωr π μ ω Cr ' " ( ω ) 1 μ eff μ eff 3 Resonance frequency: ω π μcr Magnetic plasa frequency: 3 ω p π μ Cr 3 3 (1 πr / a ) gap between two rings : d outer ring s radius : r. 1 3 lattice constant : a Pendry J.B. et al, IEEE MTT 47, 75 (1999) μ eff versus frequency (loss ay dap the resonance)

Left-handed materials: Transfer matrix method studies

Left-handed materials: Transfer matrix method studies Peter Markos and C. M. Soukoulis Outline of Talk What are Metamaterials? An Example: Left-handed Materials Results of the transfer matrix method Negative