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Fundamentals & applications of plasmonics

Fundamentals & applications of plasmonics. Svetlana V. Boriskina. Plasmonics in EE engineering. tens-to-hundreds nm. Plasmonics in EE engineering. Image credit : M. Brongersma & V. Shalaev. Plasmonics in chemistry & biotechnology. Sensing. Particle synthesis.

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Fundamentals & applications of plasmonics

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  1. Fundamentals & applications of plasmonics Svetlana V. Boriskina

  2. Plasmonics in EE engineering tens-to-hundreds nm

  3. Plasmonics in EE engineering Image credit: M. Brongersma & V. Shalaev

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

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

  6. 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

  7. 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 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)

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

  9. 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

  10. 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

  11. 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:ZnO, Ga:ZnO, ITO: near-IR frequency range • Transition-metal nitrides (TiN, ZrN): 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.

  12. 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 • Quantumtheory • Drude model modifications • Ab initio density functional theory • Hydrodynamical models • Hydrodynamical model for electrons: non-local response • Hydrodynamical model for photons e.g. D. C. Marinica, e.g., Nano Lett. 12, 1333-1339 (2012). Next lecture

  13. Quantum-mechanical effects Velocity definition: electron velocity Classical Drude model of an ideal electron gas: mean free path 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 J. Scholl, A. Koh & J. Dionne, Nature 483, 421, (2012)

  14. Surface plasmon-polariton wave • Planar interface between two media: • Eigensolutions of the Helmholtz equation: Solution:

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

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

  17. SPP excitation Via prisms: Via gratings: a Via localized sources (e.g. tips, molecules):

  18. Miniaturization of photonic components Gramotnev & Bozhevolnyi, Nature Photon 4, 83 - 91 (2010)

  19. 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) 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

  20. 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) 30nm Ag 60nm Ag Extinction=scattering+absorption Image: Wikimedia commons (author: PoorLeno) K.L. Kelly et al, J. Phys. Chem. B 2003, 107, 668-677.

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

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

  23. SP modes characteristic lengthscales W.L. Barnes 2006 J. Opt. A: Pure Appl. Opt. 8 S87

  24. 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: 6-10fs T. Klar, et al, Phys. Rev. Lett. 80, 4249-4252 (1998).

  25. 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 From experimental spectra: For eigenmode: 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 http://www.nanowerk.com/spotlight/spotid=24124.php

  26. Coherence enhancement Coupling to photonic modes: 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. 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: 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. 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

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

  28. 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/ http://www.ehow.com/info_12198356_yagi-antenna.html

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

  30. 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

  31. 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

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

  33. Applications: plasmon nanorulers • Measuring distances below diffraction limit • Stable probes (no photobleaching) N. Liu, et al, Science 332, 1407-1410 (2011) Alivisatos group, UC Berkeley; C. Sonnichsen, et al, Nat Biotech 23, 741-745 (2005)

  34. 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: 10.1021/nl3012227, 2012

  35. 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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