Fundamentals applications of plasmonics Svetlana V Boriskina Plasmonics

Fundamentals & applications of plasmonics Svetlana V. Boriskina

Plasmonics in EE engineering tens-to-hundreds nm S. V. Boriskina, 2012

Plasmonics in EE engineering Image credit: M. Brongersma & V. Shalaev S. V. Boriskina, 2012

Plasmonics in chemistry & biotechnology Particle synthesis Sensing Image: D. Pacifici, Brown University Spectroscopy Image: Jain et al, Nano Today, 2(1) 2007, 18– 29 Theragnostics Image: Reinhard group, Boston University S. V. Boriskina, 2012 Image: Nanopartz Inc

Plasmonics in art & architecture Rayonnat Gothic rose window of north transept, Notre-Dame de Paris (Jean de Chelles, 13 th century A. D. ) Lycurgus Cup: Roman goblet, 4 th century A. D S. V. Boriskina, 2012

Overview: lecture 1 • Drude model • Theoretical models for plasmonics • Surface plasmon polariton (SPP) waves • Localized SP resonances - plasmonic atoms – Component miniaturization – Sub-resolution imaging • Temporal & spatial coherence of SP modes – Q-factor enhancement mechanisms • Plasmonic antennas & arrays • Plasmonic atoms & molecules – Plasmonic nanorulers & nanosensors S. V. Boriskina, 2012

Drude theory Material response to electric field: electron velocity Collision frequency mean free path Image credit: Wikipedia • • • Electrons in thermal equilibrium with the surrounding No restoring force (free ideal electron gas) No long-range interaction between electrons & ions No short-range interaction between electrons Instantaneous collisions with a fixed probability per unit time dt: dt/τ. (τ - relaxation time; ) • Electrons move with constant velocity S. V. Boriskina, 2012 e. g. , N. W. Ashcroft and N. D. Mermin “Solid state Physics” (Saunders College, PA 1976)

Drude theory Macroscopic polarization (dipole moment per unit volume): Drude permittivity function: S. V. Boriskina, 2012 Frequency-domain solution (monochromatic fields): Definition of the dielectric constant:

Drude-Lorentz theory Au: ω0 Damping factor (mostly radiative) • Drude frequency of metals is in the ultra-violet range • Interband transitions should be taken into account • In the classical model, they are treated as the contribution from bound charges S. V. Boriskina, 2012

Results • Bulk plasmon (SP) oscillation is a longitudinal wave • Light of frequency above the plasma frequency is transmitted, with frequency below that - reflected (electrons cannot respond fast enough to screen light) • Plasmon - a quasiparticle resulting from the quantization of plasma oscillations: Permittivity S. V. Boriskina, 2012 Reflectance

Popular Drude-like materials • Noble metals (Ag, Au, Pt, Cu, Al …) • Drude frequency in the ultra-violet range • Applications from visible to mid-IR • Ordal, M. A. et al, Appl. Opt. , 1983. 22(7): p. 1099 -1119. • Doped silicon • Drude frequency in the infra-red range • Ginn, J. C. et al, J. Appl. Phys. 2011. 110(4): p. 043110 -6. • Oxides and nitrides • Al: Zn. O, Ga: Zn. O, ITO: near-IR frequency range • Transition-metal nitrides (Ti. N, Zr. N): visible range • Naik, G. V. et al, Opt. Mater. Express, 2011. 1(6): p. 1090 -1099. • Graphene • IR frequency range • Jablan, M. et al, Phys. Rev. B, 2009. 80(24): p. 245435. • Vakil, A. & Engheta, N. Science, 2011. 332(6035): pp. 1291 -1294. S. V. Boriskina, 2012

Theoretical models for plasmonics ‘The oversimplification or extension afforded by the model is not error: the model, if well made, shows at least how the universe might behave, but logical errors bring us no closer to the reality of any universe. ’ Truesdell and Toupin (1960) • Classical electromagnetic theory • • Local response approximation Quasi-static approximation Antenna-theory design Circuit-theory design • Quantum theory • Drude model modifications • Ab initio density functional theory e. g. D. C. Marinica, e. g. , Nano Lett. 12, 1333 -1339 (2012). • Hydrodynamical models • Hydrodynamical model for electrons: non-local response • Hydrodynamical model for photons S. V. Boriskina, 2012 Next lecture

Quantum-mechanical effects electron velocity mean free path Velocity definition: Classical Drude model of an ideal electron gas: Maxwell-Boltzmann statistics of energy distribution Drude-Sommerfeld model: Fermi energy Fermi-Dirac statistics of energy distribution Quantum size effects (particle size below the mean free path): • Discretized energy levels in conduction band • Free electron gas constrained by infinite potential barriers at the particle edges transitions from occupied (Ei) to excited (Ef ) energy levels S. V. Boriskina, 2012 J. Scholl, A. Koh & J. Dionne, Nature 483, 421, (2012)

Surface plasmon-polariton wave • Planar interface between two media: • Eigensolutions of the Helmholtz equation: Solution: S. V. Boriskina, 2012

Surface plasmon-polariton wave • Planar interface between two media: <λ • Dispersion equation for a surface plasmon-polariton (SPP) wave: Propagating along the interface: real kx Exponentially decaying away from it: imaginary kz S. V. Boriskina, 2012 Should be negative!

Surface plasmon-polariton wave Experimental Au ω ω Propagating: real kz High DOS: ρ(ħω)∝(dω/dk)-1 Surface: imaginary kz Re(kx) P. B. Johnson & R. W. Christy, Phys. Rev. B 6, 4370 (1972) S. V. Boriskina, 2012

SPP excitation Via prisms: Via gratings: a Via localized sources (e. g. tips, molecules): S. V. Boriskina, 2012

Miniaturization of photonic components Gramotnev & Bozhevolnyi, Nature Photon 4, 83 - 91 (2010) S. V. Boriskina, 2012

Localized SPs on metal nanoparticles + boundary conditions Multi-polar Mie theory formulation: Exact series solution: • Sphere (cluster of spheres) – fields expansion in the spherical-wave basis • Circular cylinders - fields expansion in the cylindrical-wave basis More complex geometries require numerical treatment (FDTD, FEM, BEM …) Quasi-static limit: • Object much smaller than the light wavelength: all points respond simultaneously • Helmholtz equation reduces to the Laplace equation Plasmon hybridization method (quasi-static): deformations of a charged, incompressible electron liquid expanded in a complete set of primitive plasmon modes (Peter Nordlander, Rice University) S. V. Boriskina, 2012 C. F. Bohren & Huffman, Absorption and Scattering of Light by Small Particles (Wiley) Novotny, L. & B. Hecht. Principles of Nano-Optics, Cambridge: Cambridge University Press

Localized SPs on metal nanoparticles • Modes with different angular momentum: analogs of electron orbitals of atoms • Higher-order modes have lower radiation losses; do not couple efficiently to propagating waves (dark plasmons) 30 nm Ag 60 nm Ag Extinction=scattering+absorption K. L. Kelly et al, 2012 J. Phys. Chem. B 2003, 107, 668 -677. S. V. Boriskina, Image: Wikimedia commons (author: Poor. Leno)

Tuning LSP resonance Particle shape: Nanosphere size: Cscatt B. Yan, S. V. Boriskina &B. M. Reinhard J Phys Chem C 115 (50), 24437 -24453 (2011) S. V. Boriskina, 2012 W. A. Murray, W. L. Barnes, Adv. Mater. 19, 3771 (2007).

Applications: sub-resolution imaging Image: http: //www. xenophilia. com S. V. Boriskina, 2012 S. Kawata, Y. Inouye & P. Verma, Nat Photon 3, 388 -394 (2009).

SP modes characteristic lengthscales W. L. Barnes 2006 J. Opt. A: Pure Appl. Opt. 8 S 87 S. V. Boriskina, 2012

Coherence of SP modes Solutions of the SP dispersion equation: • complex-k solution: a complex wave number (k+iα) as a function of real frequency ω SP propagation length: 2 -20μm T. B. Wild, et al, ACS Nano 6, 472 -482 (2012) • complex-ω solution: a complex frequency (ω+iγ) as a function of real wave number. SP lifetime: 6 -10 fs S. V. Boriskina, 2012 T. Klar, et al, Phys. Rev. Lett. 80, 42494252 (1998).

Q-factor as a measure of temporal coherence Q - the number of oscillations that occur coherently, during which the mode sustains its phase and accumulates energy For eigenmode: From experimental spectra: Why large Q-values are important? • Local fields enhancement: ~ Q • Spontaneous emission rate enhancement: Purcell factor ~ Q • Stimulated emission & absorption rates enhancement ~ Q • Spectral resolution of sensors: ~ Q • Enhancement of Coulomb interaction between distant charges ~ Q S. V. Boriskina, 2012 http: //www. nanowerk. com/spotlight/spotid=24124. php

Coupling to photonic modes: Coherence enhancement Blanchard, R. et al, Opt. Express, 2011. 19(22): 22113. See also: Y. Chu, et al, Appl. Phys. Lett. , 2008. 93(18): 181108 -3; S. Zou, J. Chem. Phys. , 2004. 120(23): 10871. Fano resonance engineering: Fan, J. A. , et al. Science, 2010. 328(5982): 1135 also: Luk'yanchuk, B. , et al. Nat Mater, 2010. 9(9): 707; Verellen, N. , et al. Nano Lett. , 2009. 9(4): 1663 S. V. Boriskina, 2012 Ahn, W. , et al. ACS Nano, 2012. 6(1): p. 951 -960. See also: Boriskina, S. V. & B. M. Reinhard, Proc. Natl. Acad. Sci. , 2011. 108(8): p. 3147 -3151; Santiago-Cordoba, M. A. , et al. Appl. Phys. Lett. , 2011. 99: p. 073701. SP gain amplification: Grandidier, J. , et al. Nano Lett. 2009. 9(8): p. 2935 -2939. also: Noginov, M. A. et al. Opt. Express 16, 1385 (2008); De Leon, I. & P. Berini, Nat Photon, 2010. 4(6): 382 -387.

Antenna-theory design of SP components Au particle Plasmonic nanodimer as a Hertzian dipole Alu & Engheta, Phys. Rev. B, 2008. 78(19): 195111; Nature Photon. , 2008. 2(5): 307 -310 analog of a dipole antenna S. V. Boriskina, 2012 Review: P. Bharadwaj, B. Deutsch & L. Novotny, Optical antennas. Adv. Opt. Photon. , 2009. 1(3): p. 438 -483.

Antenna-theory design of SP components Phased nanoantenna arrays: Constructive/destructive interference between dipole fields of individual nanoparticles QD Y. Chu, et al, Appl. Phys. Lett. , 2008. 93(18): p. 181108 -3 Curto, A. G. , et al. Science, 2010. 329(5994): p. 930 -933. http: //www. haarp. alaska. edu/haarp/ S. V. Boriskina, 2012 http: //www. ehow. com/info_12198356_yagi-antenna. html

Circuit-theory design of SP components Au particle Engheta, N. Science, 2007. 317(5845): p. 1698 -1702. S. V. Boriskina, 2012

Chemical analogs: plasmonic molecules P. Nordlander, et al, Nano Lett. 4, 899 -903 (2004). Bonding LSP mode Anti-bonding mode Credit: Capasso Lab, Harvard School of Engineering & Applied Sciences S. V. Boriskina, 2012

Spectra shaping B. Yan, S. V. Boriskina, & B. M. Reinhard, J. Phys. Chem. C 115, 4578 -4583 (2011); J. Phys. Chem. C 115, 24437 -24453 S. V. Boriskina, 2012

Local field enhancement Diatomic plasmonic molecule: Cscatt |E|2 Spectroscopy applications (next lecture) B. Yan, S. V. Boriskina, & B. M. Reinhard, J. Phys. Chem. C 115, 24437 -24453 (2011) S. V. Boriskina, 2012

Applications: plasmon nanorulers • Measuring distances below diffraction limit • Stable probes (no photobleaching) Alivisatos group, UC Berkeley; C. Sonnichsen, et al, Nat Biotech 23, 741 -745 (2005) S. V. Boriskina, 2012 N. Liu, et al, Science 332, 14071410 (2011)

Applications: cell surface imaging Quantification of cell surface receptors, which are important biomarkers for many diseases S. V. Boriskina, 2012 Wang, Yu, Boriskina & Reinhard, Nano Lett. , Article ASAP, DOI: 10. 1021/nl 3012227, 2012

Overview: lecture 2 • Refractive index, fluorescence & Raman sensing • SP-induced nanoscale optical forces – Optical trapping & manipulation of nano-objects • Near-field heat transfer via SPP waves • Plasmonics for photovoltaics • Hydrodynamical models – Hydrodynamical model for electrons: non-local response – Hydrodynamical model for photons • • Magnetic effects Plasmonic cloaking Quantum effects Further reading & software packages S. V. Boriskina, 2012