Preparatory School to the Winter College on Optics and the Winter College on Optics: Advances in Nano-Optics and Plasmonics

38-1 Preparatory School to the Winter College on Optics and the Winter College on Optics: Advances in Nano-Optics and Plasmonics 30 January - 17 February, 01 Optical antennas: Intro and basics J. Aizpurua Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC Spain

Optical antennas: Intro and basics Javier Aizpurua http://cfm.ehu.es/nanophotonics Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC Donostia-San Sebastián, the Basque Country, Spain Winter College on Optics: Advances in Nano-Optics and Plasmonics February 6-17, 01 The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Outline Optical antennas: Basics Playing with modes Optical antennas for Enhanced Spectroscopy: SERS and SEIRA More applications of Optical antennas

Different types of radio antennas /4 antenna Horizontal radiation pattern / Dipole Yagi Vertical radiation pattern Horizontal radiation pattern Omni-directional antenna often used at master station sites Parabolic Directional Yagi antenna Commonly used at remote field sites

Radio Frequency Antennas Half wave dipole antennas Biconical antenna Monopole antenna Combilog antenna Yagi-Uda antenna Horn antenna Parabolic antenna Active loop antenna

Scaling down in size Scaling down in wavelength Visible light Optical antenna Nanoantenna / nanoantenna

Optical nanoantennas Design of plasmonic nanoparticles: size, shape, interactions,... Analogy with radio-wave antennas Mühlschlegel et al. Science 308, 1607 (005)

Optical nanoantennas Applications: biosensing, nonlinear optics / SERS, fluorescence, quantum optics,... Quidant, ICFO Antenna-gap sensing Alivisatos, Giessen Pd-antenna sensor Van Hulst, ICFO - Single molecule, scanning probe Halas, Nordlander Plasmonic photodetector Capasso Antenna QCL

The simplest optical antenna: a metallic particle Scattering E h + - + - + - Extinction Absorption Enhancement of absorption and emission: Bringing effectively the far-field into the near-field

Metal particle plasmons Standard textbooks: - Kreibig, Vollmer, Optical properties of metal clusters, Springer1995 - Bohren, Huffmann, Absorption and scattering of light by small particles, Wiley 1983

Metallic nanorod as a / optical antenna In analogy to a / radiowave antenna, we call a nanosized rod-like metallic structure a / optical antenna. L=/ YES BUT, it is just similar, and not equal because of plasmons

Bulk plasmons A plasmon is a collective oscillation of the conduction electrons Bulk plasmon: The rigid displacement of the electrons induces a dipolar moment and an electric field opposing the displacement + + + + + + - - - - - - Electron density (t): (t) E(t) d nme () t ene() t 4 n e () t => dt Harmonic oscillator p 4 e n e m e All the electrons are involved in the oscillation. The energy of those oscillations in typical metals might be triggered out by external probes.

Surface plasmons Electromagnetic surface waves which exist at the interface between media whose have opposite sign. E z Metal ( 1 = 1 +i 1 ) E x H + + + - - - + + + - - - + + + y Dielectric ( = +i ) x Dispersion relation (1) (1) (1) i( kxxt ) z o E E e k k ik 1 x x x 1 c =ck x p Drude model 1 p k x Surface plasmons s p

e -

Methods of SPP excitation n prism > n L!!

Nano-optics with localised plasmons Characteristics Confined fields: - Nanooptics Resonances dependence with size with shape Enhanced field: - Lighting rod effect Tunability: - Geometry Coupling: Wavelength range: - Visible Infrared with material with coupling Plasmon polariton + + + + k p s ck Confined plasmon + + + k

Light-particle interaction E i + + + k a - - - Quasi-static case: >> a E t t 0 General case: <= a E t t 0 k a x Homogeneous polarization: All points of an object respond simultaneously to the incoming (exciting) field. k a x Helmholtz eq. reduces to Laplace equation: 0 Phase shifts in the particles: retardation, multipole excitations el. field: E

Small sphere The electric fields inside (E 1 ) and outside (E ) the sphere can be obtained from the scalar potentials E1 1 with r,, 1 0 Solve Lapace equation in spherical coordinates: E with 0 scatter 0 Boundary conditions: 1 1 ( r a ) 1 1 r r ( r a) continuity of the tangential electric fields continuity of the normal component of the electric displacement

Small sphere Homogeneous electric field along x-direction: 0 E0x E0r cos The following potentials satisfy the Laplace equation and boundary conditions: From E we obtain The field is independent of the azimuth angle which is a result of the symetry implied by the direction of the applied electric field.

Small sphere Small sphere: Dipole: E r cos E dipole 0 p cos 4 r 0 1 1 3 a cos r The field outside the sphere is the superposition of the applied field and the field of an ideal dipole at the sphere origin The dipole moment is given by p 3 1 4 0 a E 0 1 Generally the dipole moment is defined by p 0 E 0 Polarizability of the sphere: 3 4a 1 1

Small sphere We can describe the light scattering of a small sphere by plane wave scattering at an ideal point dipole with dipole moment derived on the previous slides. The dipole field is given by: ikr 1 e 1 1 E( r) k 3 4 0 r r r t ik e i n p n n n p p with n r r Near-field zone: kr << 1 (r << E( r) 1 4 3n 3 0 r n p p it e E E 3 a 3 r electrostatic dipole field harmonic time dependency 0 0 a a r Radiation zone: kr >> 1 (r>> E( r) n pn k ikr t r propagating wave 4 0 e

Far- and near-field calculations for a sphere a << E in k a + + + - - - Near-field scattering Far-field scattering (transverse fields) I E in E pa rticle 90 r/a 1 r/a 1 0 0-1 -1 180 0 - - -1 0 1 r/a - - -1 0 1 r/a 70 Pointing vector always radial! Pointing vector is not always radial

Optical cross sections of small spheres Integrating the Poynting vector S sca (S abs ) over a close spherical surface we obtain the totally scattered (absorbed) power P sca (P abs ) from which we can calculate the scattering (absorption) cross section C sca = P sca /I i (C abs = P abs /I i ): Scattering cross section: Absorption cross section: C sca 8 3 k4 a 6 m m k4 6 C abs 3 m 4ka Im m k Im C sca 6 a 4 C abs 3 a - stronger scattering at shorter wavelength (Rayleigh scattering, blue sky) - for large particle extinction is dominated by scattering whereas for small particles it is associated with absorption - scattering of single particles <10nm is difficult to measure (low signal/noise and low signal/background)

Dielectric function of metals Collective free electron oscillations (plasmons) = - plasma frequency (longitudinal oscillation)

Optical cross sections of small spheres Drude model 1 p 0.i 7.5 5.5 -.5-5 0.5 1 1.5 p 3.5 1.5 1 0.5 3.5 1.5 1 0.5 1 0.5 1 1.5 1 Arg opt. field amplitude 0.5 1 1.5 p optical phase of scattered light p 8 6 4.5 1.5 1 0.5 1 C sca 0.5 1 1.5 1 Im C abs 0.5 1 1.5 p p

Excitation of a plasmon by a pulse Rice University, Houston

Localised Surface Plasmon: a swimming pool of e -

The simplest optical antenna: a metallic particle Scattering E h + - + - + - Extinction Absorption Enhancement of absorption and emission: Bringing effectively the far-field into the near-field

Small particle resonances E in + + + k a - - - E 0 enhanced field at E 0 m Ein m 3 m 4a polarizability: m resonance at m E 0 /E in 30 0 10 10 wavelength (m) 1 SiC Phonon polariton resonance 0.5 m 1 Plasmon polariton resonance Ag Au 0 1000 frequency (cm -1 ) 10000

Nanotechnology with plasmonics: before the nanorevolution Lycurgus Cup (British Museum; 4 th century AD) Illumination: from outside (strong absorption at and below 50 nm) from inside

Extinction vs. scattering

Near-field versus far-field Near-field distribution Far-field distribution 50 nm gold nanoparticle Spectral information

Near-field versus far-field

Higher multipole resonances in quasistatic limit In the quasistatic limit the Mie theory yields the resonance positions of the higher multipoles at L medium l 1 l Drude L p 1 1 l 1 l medium 1 L p 1 medium = 1 However, higher multipoles in the quasistatic limit are negligible compared to the dipole contribution (l=1)

Antenna modes: D=80nm,L=00nm; ratio=.5 Dipole response: L / -Q Q - + - - + ~ L Higher order modes: l + + + Aizpurua et al. Physical Review B 71, 3540 (005)

An alternative to excite high order modes in a sphere EELS in nanoparticles Ferrell and Echenique, PRL 55, 156 (1985) l= l a b l=1 v e - ( ) 1 3 l ( ) a ( ) ( l 1)/ l l q a l b lm m l l 0 m0 4 P ( a, b, v) A K Im ( ) v a v v Probability of losing energy h for a 50-keV electron moving at grazing incidence on an aluminum sphere of radius a=10nm

Mie-theory Kreibig/Vollmer Mie-theory is an electrodynamic theory for optical properties of spherical particles. The solution is divided into two parts: the elctromagnetic one which is treated from first principles (Maxwell equations) and the material problem with is solved by using phenomenological dielectric functions taken from experiments or model calculations See also Bohren/Huffman

Mie theory - results Fig..6 shows farfield distribution at the surface of a large sphere centered at the small cluster Kreibig/Vollmer

Scattering characteristics (far-field) Small particle Large particle (Mie calculation) 90 180 0 70 Pointing vector always radial! Strong forward scattering

Spherical plasmons: l l l 1 p a 1 p Drude-like metal l=1 mode

Effect of finite size on the resonant frequency same shape, different size redshift due to higher multipoles Jin et. al., Science 94, 1901 (001)

m xyz m m xyz L abc 3 4 Shape: Polarizability of small ellipsoids geometrical factors 3 1 z y x L L L sphere: z y x L L L generally: 3 resonances at quasistatic approximation: xyz m L 1 1 E in p z y x 0 0 0 0 0 0 For a geometry like above: z y x

Silver ellipsoid illuminated by a plane wave size shifts dipole resonance for E 0 long axis E i E i k i k i E E a b l = 58nm b a E / E 0 10 100 l = 340 nm 80 60 40 0 0 8 4 E 0 long axis 10 nm / 3 nm 100 nm / 30 nm E 0 short axis 0 300 400 500 600 800 100 Calculation by J. Renger, TU Dresden [nm]

Plasmon resonances:dependence on the geometry

More complex geometries Control over the plasmon frequencies by playing with particle shapes and coupling Nanorods, nanoshells, nanorings, dimers,... Apertureless NSOM Coupled systems Nanometrology, sensing, spectroscopy

Numerical solutions to the 3D electromagnetic problem discrete-dipole approximation Purcell+Pennypacker: optical modes of grains Martin: Green-function formulation boundary element method JGA and Howie finite difference in the time domain Joannopoulos photonic crystals plane wave expansions Leung transfer matrix approach Pendry multiple scattering Ohtaka: LEED-like methods to photons Wang, Stefanou, Sheng: photonic crystals JGA: finite systems periodic systems finite geometries convergence for high dielectric contrast (e.g., in metals) effective dimensionality of the problem Donostia International Physics Center (DIPC)

Boundary Element Method E r i A r r c ext d G A r A r s r s h s S j ext r r ds G r s s S j j j j j G j r 1 i c e r j S j r medium j The boundary conditions lead to a set of surface integral equations with the interface currents h j and charges j as variables. For example, the continuity of leads to S j ext ext d s ' G s s ' s ' G s s ' s ' s s 1 1 1, (1 and refer to the interface sides). The surface integrals are now discretized using N representative points s i. This leads to a system of 8N linear equations with h 1 (s i ), h (s i ), 1 (s i ), and (s i ) as unknowns. García de Abajo and Aizpurua, PRB 56, 15873 (1997) García de Abajo and Howie, PRB 65, 115418 (00)

An example of Optical Antenna: Optical properties of metallic nanorings d/a smaller -> red shift Disk Nanoring d a Aizpurua et al. Phys. Rev. Lett. 90, 057401 (003)

Optical properties of metallic nanoshells

Modes in a nanoring. The twisted slab d kd (1 s e ) - + + 1/ - a d d kd n d n L a - + - + - + + + - + - -

Field-enhancement in a nanoring

Radio Frequency Antennas Half wave dipole antennas Biconical antenna Monopole antenna Combilog antenna Yagi-Uda antenna Horn antenna Parabolic antenna Active loop antenna

/ nanoantenna /4 optical antenna wavelength [m] 5.00 3.33.50.00 1.67 1.00 relative transmittance 0.98 0.96 0.94 L 1.5m, D = 100nm, parallel polarsiation, substrate: CaF 000 3000 4000 5000 6000 wavenumber [cm -1 ] Neubrech et al., App. Phys. Lett. 89, 53104 (006) Taminiau et al., Nature Photonics, 34 (008)

Different types of radio antennas Vertical Horizontal radiation pattern Dipole Yagi Vertical radiation pattern Horizontal radiation pattern Omni-directional antenna often used at master station sites Parabolic Directional Yagi antenna Commonly used at remote field sites

Yagi-Uda antenna Taminiau et al., Optics Express 14, 10858 (008)

Parabolic-like optical nanoantennas N. Mirin and N. Halas, Nano Letters 9, 155 (009)

/4 optical antenna Bowtie antennas E Ar Ar - 140 10 100 80 60 40 0 50 nm Taminiau et al., Nature Photonics, 34 (008) Nature 453, 731 (008)

Plasmonic antennas

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