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1. Nonlinear plasmonics

1. Nonlinear plasmonics. IMS 320 Presentation — Vanderbilt University — 6 October 2008. … strongly correlated electrons. Itinerant electrons (Fermi liquid). CORRELATED ELECTRONS. Tradeoff between hopping rate t ij (kinetic energy) and Hubbard U (on-site Coulomb potential).

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1. Nonlinear plasmonics

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  1. 1. Nonlinear plasmonics IMS 320 Presentation — Vanderbilt University — 6 October 2008

  2. … strongly correlated electrons Itinerant electrons (Fermi liquid) CORRELATED ELECTRONS Tradeoff between hopping rate tij (kinetic energy) and Hubbard U (on-site Coulomb potential) Localized electrons (Mott insulator) Kotliar and Volllhardt, Physics Today, March 2004 for review of DMFT

  3. Plasmon – a quasiparticle • A quantum of a collective longitudinal oscillation of the conduction electron gas at + + + - - + + + + - - + + + + - + - + + + + - - - - - + + + - - - + + + - - - + + + - - - + + + • Dielectric function in a lightly-damped electron gas + + + + - - + + + - - + + + + + - - + + + - - + +u - - - - - - - - • Plasmon frequency in a surface -u - - - - - - - - • Bulk plasmon and surface plasmon (SP) are observed by electron energy loss spectroscopy C. J. Powel and J. B. Swan (1960)

  4. Localized surface plasmon resonance Lycurgus Cup 4th Century A.D.The British Museum Chartres Cathedral, FranceKen Pennington, Catholic University hν Einc pind 2a ε εm

  5. photon plasmon e-h pair intraband - - + d band + interband Sönnichsen et al., PRL 88, 077402 Raschkeet al., Nano Letters 3, 935 N. Halas, Rice University, nanoshells

  6. Lithographic array fabrication FIB PMMA Indium Tin Oxide Ag Glass • Coat ITO/glass substrate with PMMA photoresist • Expose with focused ion beam • Develop lithographic mask • Deposit Ag or Au • Liftoff lithographic mask • Nanoparticles remain at FIB-defined sites (~60 nm diameter) *After Liu et al., APL 82 #8 (2003), p. 1281.

  7. No problem, right?

  8. LSPR Sensitivity Example: Ag NP Tarnishing in Air λmax 550 65 nm in36 hrs! McMahon et al., Appl. Phys. B 80 915-921 (2005). t 470 0:00 40:00

  9. SCANNING AUGER Ag → Ag2S Tarnishing • H2S • OCS Mie modeling: coated sphere

  10. Plasmon shape resonances • For ellipsoidal particles, polarization-dependent shape resonances due to standing waves • Think of MNPs as small antennas that can be driven resonantly by an appropriate optical wavelength

  11. Plasmon dispersion relations Maxwell equations yield • At large k,  approaches • Dispersion relation forbids plasmon-photon coupling • If (air) and , then and • kz becomes imaginary (‘evanescent wave’ in z direction H. Raether (1988) • d : decay length in air or glass • m: decay length in metal

  12. Plasmon-photon coupling through hole arrays Incident light z  y I II x d III • Periodic crystal lattice compensates the momentum mismatch • The radiative modes of SPP at normal incidence are No SPP excitation • Spectral positions are determined by pattern geometry and dielectric constants. SPP modes on either film interfaces • Symmetric SPP resonant mode yields highest transmission rate SPP resonant modes on both surfaces in symmetric or asymmetric structure S. A. Darmanyan & A. V. Zayats (2003)

  13. Non-centrosymmetric particles θ Lamprecht, Appl. Phys. B 68, 419 (1999) • SHG • Arises due to an asymmetry • Surface of NPs break symmetry  SHG • Centrosymmetric arrays • Destructive interference of SHG  SHG forbidden for centrosymmetric systems in forward direction • Most SHG studies  asymmetric MNPs • Can measure in forward direction • Alignment easier ITO glass

  14. Optical Setup MONO-CHROMATOR CCD Camera 4.5 W (cw) 532 nm LOW-PASS FILTERS Sample Photon counting module (PMT) VERDI Si PD (ND Filters) Green filter PC LabVIEW KML 10-fs 93 MHz resonator ~800 nm, ~250 mW (time-avg)

  15. Excitation geometry for SHG θ Au rods ITO glass Interface-generated SHG Sample is backlit at normal incidence. First diffracted order of SH light First order of fundamental (2nd order of SH light) Planar view POLARIZATION a

  16. Is Asymmetry required? McMahon et al.Phys. Rev. B 73 041401(R) • No! • NP Arrays  diffraction grating • SHG  observed at high angles

  17. Straight and tilted rods

  18. SHG from aligned rods • Rods here oriented along grating direction (not tilted). • Long axis has SPR that is nearly resonant with 800 nm fundamental; short axis not resonant.

  19. Resonant excitation enhances SHG Off-resonance Resonant e.g., McMahon, Appl.Phys. B 87, 259 (2007)

  20. SHG vs. Intensity • Critical point: 2nd order  apparent 3rd order dependence • Corresponds with onset of reshaping

  21. Reshaping leads to resonance shifts • Thermal reshaping • Surface melting • Laser, hotplate  overall same effect • Shifts resonance, SHG yield • Consistent with Habenicht et al., Science 309 2043 • “Jumping Nanodroplets”

  22. SHG and reshaping • SHG: • Rapid changes • Complicates interferometric Autocorrelation (AC) • No reshaping  low intensity  much lower SHG yield

  23. Coupled Dimers • Coupling for large NPs, large spacing • Consistent with e.g.: • Haynes, J Phys Chem 107, 7337 (2003) • Rechberger, Opt. Comm. 220, 137 (2003)

  24. SHG from coupled dimers • Increasing gap • Decreases field enhacement, coupling • Increases SHG! • Counter-intuitive: • Expect “hot spot” to increase SHG • Canfield, Nano Lett. 7, 1251 (2007) • Shows no simple dependence on gap size

  25. Plasmon decay time • Estimated from extinction linewidth • Dahmer, Nano Lett. 7, 318 (2007) • Lamprecht, Appl. Phys. B 68, 419 (1999)

  26. Future directions • Measure dephasing times using AC techniques • Difficulties: • Low SHG intensity to scatted fundamental • Increasing fundamental intensity  reshaping • Alignment at high angles • Lamprecht, Appl. Phys. B 68, 419 (1999) • Zentgrafs, PRL 93, 243901 (2004) SPIE Optics and Photonics 6641-40

  27. Ex, x-polarization

  28. Ey, y-polarization

  29. Different view, same results • Possible explanation for SHG behavior

  30. All-optical switching based on (3) Electro-optic switch All-opticalswitch • Nonlinear polarization • Absorption/dispersion • n2 needed in waveguide The required value of n2has already been observed. So what next?

  31. Quantum-size effects on intraband transition •Forward phase-matched     DFWM • Cross-polarized pumps • Intraband transition •=532 nm, =30 ps Li Yang et al., JOSA B 1994. • Hot electron (Fermi smearing) and interband transitions are weakly confined. Initial and final states of intraband transitions are strongly confined. • Exciting theintraband transitionimplies staying to thered sideof the interband transitions. • Broad size distribution yields average (3). • Ergo, need small quantum dots (≤5 nm), narrow distribution.

  32. Conclusions • SHG from centrosymmetric arrays of NPs • Observable at angles other than the normal • Strong dependence on polarization and SPR • SHG from dimers • Greatest change in field distribution with gap for short-axis polarization • SHG Suppressed with increase gap • Counter-intuitive • Possibility of oscillation • Time resolved measurements • Indirect measurements of dephasing time  agree with previous work • Direct measurements complicated by low SHG intensity

  33. The end … Picasso “Don Quixote” (in VO2) 2.31 µm Jae Suh René Lopez Matthew McMahon Eugene Donev “The legitimate purpose of research can only be, to make two questions grow where there was only one before.” [Thorsten Veblen] Thanks to the National Science Foundation and the United States Department of Energy for $$$!

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