Energy transport in metal nanoparticle plasmon waveguides

Transcription

1 Energy transport in metal nanoparticle plasmon waveguides Stefan A. Maier, Pieter G. Kik, and Harry A. Atwater California Institute of Technology Thomas J. Watson Laboratory of Applied Physics, Pasadena, CA Sheffer Meltzer, Elad Harel, Bruce E. Koel, and Ari A.G. Requicha University of Southern California Laboratory for Molecular Robotics, Los Angeles, CA

2 Nanophotonics in integrated circuits On-chip integrated laser or light emitting diode Short range nanoscale waveguides Detectors

3 Introduction Nanoparticle waveguides: - individual elements have specific resonance frequency - mode propagation through coupled resonators - propagating modes have frequencies near particle resonance - center frequency tunable by material, shape, size - group velocity tunable by shape, spacing Overview 1. Introduction resonance 2. Model calculations 3. Measurements

4 The surface plasmon resonance Absorption and scattering of light by small particles, Bohren & Huffman low frequency high frequency resonance: electron phase lag 9 field enhancement polarizability: α = 4ε 3 m R ε ε ε + 2ε m res. frequency: ω 2 res = e mε 2 N e ( 1+ 2ε ) m

5 Extinction measurements.8 Ag ( 41 nm) in solution 2 Au ( 3 nm) in solution ε Ag = -2 ε H2O extinction coefficient (a.u.) extinction coefficient (a.u.) wavelength (nm) wavelength (nm) λ res =41 nm λ res =524 nm

6 Inter-particle coupling collective modes Transverse mode at k = blue-shifted resonance Longitudinal mode at k = red-shifted resonance

7 The dipole model excitation frequencies near single particle resonance propagating waves m-3 m-2 m-1 m m+1 m+2 m+3 m+4 m+5 && p & ( p p ) 2 2 i, m = ω pi, m ΓI pi, m γ iω1 i, m 1 + i, m+ 1 2 ω1 ω + 4 ω ω ω Transverse resonant term internal damping near-field (d << λ) coupling; γ d -3 2 ω1 ω 4 ω Longitudinal d 2d 2d k d

8 FDTD Simulations of Particle Interactions Perform Finite Difference Time Domain simulations to obtain ω(k) for finite particle sizes and realistic dielectric response Plane waves to prepare k = mode Monitor spontaneous relaxation ω(k=) E x of k = collective mode Local CW dipole excitation Analyze resulting mode ω(k ) E x of k = /2d mode, t = 51 fs Local pulsed dipole excitation Measure peak position vs. time v g (k=/2d) E x at t = 27.5 fs

9 FDTD Simulation of resonances Material response: modified bulk Drude model for Au FFT of relaxing field gives plasmon resonances Initialization of particle volume with homogeneous electric field 6 4 a).8 D = 5 nm D = 1 nm E x (V/m) 2-2 amplitude (a.u.) time (fsec) energy (ev)

10 Collective Mode: Influence of Chain Length Near-field interactions in particle chains influence the resonance frequency of longitudinal and transverse modes at k= y x longitudinal mode Plasmon peak (ev) Chain of 5 nm Au spheres in air transverse longitudinal transverse mode longitudinal mode particle chain length (spacing 3R) ω T ω ω L d 2d ω L T 2d Bandwidth saturates for 5 particles k d

11 Dispersion Relation Local dipole excitation near E determine of ω(k) 2.6 E=hck Good functional agreement with point-dipole calculations Energy (ev) Maximum transmission at E Information propagation should be possible k (µm -1 ) E end (a.u.) Group velocities: v gl =.6c v gt =.2c

12 Pulse Propagation Pulsed dipole excitation at f = 5.8x1 14 Hz to determine v g (bandwidth 95% of dispersion bandwidth) Position (nm) Time (fs) Group velocities: v * gl =.6c v* gt =.2c

13 Optimization by Particle Design Position (nm) L T Time (fs) Same volume as spheres v 3:1,L =.17c v 3:1,T =.2c Longitudinal mode: v g increases by factor of 3-4

14 Negative Phase Velocity for T - Modes Pulse propagation Phase propagation t = t ω Transverse t = t + t t = t + 2 t Longitudinal d 2d Negative k vectors with positive v g 2d k d Transverse modes propagate with negative phase velocities - wave packet moves away from source - wave fronts move towards source ( one dimensional negative refraction )

15 Fabrication of Plasmon Waveguides 5 nm Au particles on ITO coated glass Shape approximately spherical Good control over size and spacing 1 µm 3 nm Structures fabricated in collaboration with Richard Muller and Paul Maker; Jet Propulsion Laboratory

16 Polarization dependent extinction ω T ω T White light source ω ω L Polarization filter T L 1. d 2d L 2d k d Array.8 U Monochromator Extinction (a.u.) L T Detector Energy (ev)

17 Energy of the collective plasmon modes nm Au particles 2.12 Energy (ev) interparticle spacing d (nm) T mode (exp.) L mode (exp.) T mode (FDTD) L mode (FDTD) Spacing 3R maximum group velocity for energy transport: 4x1 6 m/s

18 Loss in Plasmon Waveguides Decay constant Γhom α B d Homogeneous linewidth Bandwidth Estimated energy decay: 6dB/3nm (Au) Amplitude (a.u.) α Distance (nm) Homogeneous linewidth reduction: Au in 3:1 rod shape: factor of 5 / Ag spheres: factor of 3-4 Bandwidth increase: Closer spacing and/or rod geometries

19 Bandwidth vs. aspect ratio Plasmon resonance energy (ev) a) b) E T E E L E Particle chain length 6 db/2 nm can be achieved, and should be experimentally observable

20 Optimized Plasmon Waveguide 6 ½B 1 mev Linear arrays Single particles E Extinction (a.u.) 4 2 x 13 5 nm Ag rods (9x3x3nm) 5 nm surface spacing Energy (ev) Bandwidth 2 mev predicted max. decay length ~6dB/2nm

21 Near-Field Scanning Optical Microscopy laser fiber-pulled NSOM tip Illuminate at max. group velocity frequency Detect only red-shifted dye emission vs. tip position

22 Local excitation of isolated dye beads Topography Fluorescence 1 µm 1 µm Single dye-beads can be resolved in topography and NSOM images Tip artifact visible in NSOM image

23 Local excitation of plasmon waveguides Topography Fluorescence 1 µm 1 µm Single dye-beads on top of plasmon waveguides Spot elongation along waveguide direction? fit linear cuts

24 Fluorescent Probing of Energy Transport Data cuts along waveguide Data cuts perpendicular to waveguide Fluorescence intensity (a.u.) Control A Control B WG 1 WG 2 Fit widths: 174±17 nm 193±23 nm 329±14 nm 343±27 nm Distance (micron) Control A Control B WG 1 WG 2 Distance (micron) Control spheres: 185±38 nm Waveguide spheres: 336±3 nm 15 nm FWHM increase guiding observed over 5 nm

25 Plasmon waveguides - summary Coupled dipole oscillators localized waveguide modes Far-field spectroscopy reveals splitting of T and L modes (k=) Estimated propagation length - Au nanospheres 6 db / 3 nm - Ag spheroids 6 db / 2 nm Near-field microscopy shows experimental evidence of energy transport over ~.5 µm distance in nanofabricated plasmon waveguides