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Fundamentals & applications of plasmonics Svetlana V. Boriskina

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

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

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

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

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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

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S.V. Boriskina, 2012 Drude theory Material response to electric field: 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 ions with a fixed probability per unit time dt: dt/τ. (τ - relaxation time; ) Electrons move with constant velocity e.g., N.W. Ashcroft and N.D. Mermin Solid state Physics (Saunders College, PA 1976) Image credit: Wikipedia Collision frequency electron velocity mean free path

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

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S.V. Boriskina, 2012 Drude-Lorentz theory 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 Au: Damping factor (mostly radiative) ω0ω0

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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 Reflectance

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S.V. Boriskina, 2012 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., (7): p Doped silicon Drude frequency in the infra-red range Ginn, J.C. et al, J. Appl. Phys (4): p Oxides and nitrides Al:ZnO, Ga:ZnO, ITO: near-IR frequency range Transition-metal nitrides (TiN, ZrN): visible range Naik, G.V. et al, Opt. Mater. Express, (6): p Graphene IR frequency range Jablan, M. et al, Phys. Rev. B, (24): p Vakil, A. & Engheta, N. Science, (6035): pp Popular Drude-like materials

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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) 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 Hydrodynamical models Hydrodynamical model for electrons: non-local response Hydrodynamical model for photons Next lecture e.g. D. C. Marinica, e.g., Nano Lett. 12, (2012).

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

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

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

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

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

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

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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 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 More complex geometries require numerical treatment (FDTD, FEM, BEM …) Object much smaller than the light wavelength: all points respond simultaneously Helmholtz equation reduces to the Laplace equation Quasi-static limit: 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)

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S.V. Boriskina, 2012 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) K.L. Kelly et al, J. Phys. Chem. B 2003, 107, Extinction=scattering+absorption 30nm Ag 60nm Ag Image: Wikimedia commons (author: PoorLeno)

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

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S.V. Boriskina, 2012 Applications: sub-resolution imaging Image: S. Kawata, Y. Inouye & P. Verma, Nat Photon 3, (2009).

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S.V. Boriskina, 2012 SP modes characteristic lengthscales W.L. Barnes 2006 J. Opt. A: Pure Appl. Opt. 8 S87

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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: 6-10fs T. Klar, et al, Phys. Rev. Lett. 80, (1998). 2-20μm T.B. Wild, et al, ACS Nano 6, (2012) complex-ω solution: a complex frequency (ω+iγ) as a function of real wave number. SP lifetime:

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S.V. Boriskina, 2012 Q-factor as a measure of temporal coherence 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 Q - the number of oscillations that occur coherently, during which the mode sustains its phase and accumulates energy From experimental spectra: For eigenmode: Why large Q-values are important?

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S.V. Boriskina, 2012 Coherence enhancement Coupling to photonic modes: Blanchard, R. et al, Opt. Express, (22): See also: Y. Chu, et al, Appl. Phys. Lett., (18): ; S. Zou, J. Chem. Phys., (23): Ahn, W., et al. ACS Nano, (1): p See also: Boriskina, S.V. & B.M. Reinhard, Proc. Natl. Acad. Sci., (8): p ; Santiago-Cordoba, M.A., et al. Appl. Phys. Lett., : p Fano resonance engineering: Fan, J.A., et al. Science, (5982): 1135 also: Luk'yanchuk, B., et al. Nat Mater, (9): 707; Verellen, N., et al. Nano Lett., (4): 1663 SP gain amplification: Grandidier, J., et al. Nano Lett (8): p also: Noginov, M. A. et al. Opt. Express 16, 1385 (2008); De Leon, I. & P. Berini, Nat Photon, (6):

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

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S.V. Boriskina, 2012 Antenna-theory design of SP components Phased nanoantenna arrays: Constructive/destructive interference between dipole fields of individual nanoparticles Y. Chu, et al, Appl. Phys. Lett., (18): p Curto, A.G., et al. Science, (5994): p QD

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

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

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

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

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

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

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S.V. Boriskina, 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

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