Lecture 10: Surface Plasmon Excitation. 5 nm

Transcription

1 Excitation Lecture 10: Surface Plasmon Excitation 5 nm

2 Summary The dispersion relation for surface plasmons Useful for describing plasmon excitation & propagation This lecture: p sp Coupling light to surface plasmon-polaritons sp sp Using high energy electrons (EELS) Kretschmann geometry Grating coupling //, SiO = " d sin# = sp c Coupling using subwavelength features A diversity of guiding geometries E SiO H Θ

3 Dispersion Relation Surface-Plasmon Polaritons Plot of the dispersion relation Last page: x " # $ m d = % & c m + d ' ( 1/ Plot of the dielectric constants: Note: x " when ε m = ε d Define: ω = ω sp when ε m = ε d r Dielectric d " d p sp Metal Low ω: x 1/ " & m ' d " lim ) * d c m #$% m + d c = ( +, sp x = " d c Light line in dielectric Solutions lie below the light line (guided modes) x

4 Dispersion Relation Surface-Plasmon Polaritons Dispersion relation bul and surface plasmons SP, Air " SP, d Metal/air Metal/dielectric with ε d Note: Higher index medium on metal results in lower ω sp p ω = ω sp when: " m = 1# = #" d # = #" p d p = 1 + " d = p 1+ " d

5 Excitation Surface-Plasmon Polaritons (SPPs) with Light Problem SPP modes lie below the light line No coupling of SPP modes to far field and vice versa (reciprocity theorem) Need a tric to excite modes below the light line Tric 1: Excitation from a high index medium Excitation SPP at a metal/air interface from a high index medium n = n h sp = c = c n h e h > sp Air sp h SPP at metal/air interface can be excited from a high index medium How does this wor in practice?

6 Excitation Surface-Plasmon Polaritons with Light Kretschmann geometry (Tric 1) Maes use of SiO prism Create evanescent wave by TIR sp //,SiO From dispersion relation θ Strong coupling when //,SiO to sp Reflected wave reduced in intensity E H SiO = c c = n sp e Note: we are matching energy and momentum Air sp SiO

7 Surface-Plasmon is Excited at the Metal/Air Interface Kretschmann geometry sp, Air Θ SiO sp, SiO Maes use of SiO prism Enables excitation surface plasmons at the Air/Metal interface E H Surface plasmons at the metal/glass interface can not be excited Light line air Light line glass sp, AIR Surface plasmon Metal/Air interface sp, SiO e Air SiO sp, SiO Surface plasmon Metal/Glass interface //, SiO = " d sin# = sp c sp, Air

8 Quantitative Description of the Coupling to SPP s Calculation of reflection coefficient Solve Maxwell s equations for Assume plane polarized light d 1 0 Find case of no reflection E H D Solution (e.g. transfer matrix theory ) R ( z ) ( ) p p p exp r 1 p p p exp z1 E r r i d = = E + r r i d where p r i Plane polarized light are the amplitude reflection coefficients Also nown as Fresnel coefficients (p 95 optics, by Hecht) r " # " # = % $ & % + & ' ( ' ( p zi z zi z i i i Notes: Light intensity reflected from the bac surface depends on the film thicness There exists a film thicness for perfect coupling (destructive interference between two refl. beams) When light coupled in perfectly, all the EM energy dissipated in the film)

9 Dependence on Film Thicness Critical angle R E H laser Θ detector θ Raether, Surface plasmons Width resonance related to damping of the SPP Light escapes prism below critical angle for total internal reflection Technique can be used to determine the thicness of metallic thin films

10 Quantitative Description of the Coupling to SPP s Intuitive picture: A resonating system When >> 1 ' m well below ω sp : r sp " d p metal and << '' m ' m low loss Reflection coefficient has Lorentzian line shape (characteristic of resonators) R 4 i rad = 1" # $ 0 ( x " x ) + ( i + rad ) %' &( Where Γ i : Damping due to resistive heating Γ rad : Damping due to re-radiation into the prism 0 : The resonance wave vector (maximum coupling) x R x Γ i + Γ rad x Note: R goes to zero when Γ i = Γ rad

11 Current Use of the Surface Plasmon Resonance Technique Determination film thicness of deposited films Example: Investigation Langmuir-Blodgett-Kuhn (LBK) films Reflectance Critical angle Incident Angel (degree) Coupling angle strongly dependent on the film thicness of the LBK film Detection of just a few LBK layers is feasible Hiroshi Kano, Near-field optics and Surface Plasmon Polaritons, Springer Verlag

12 Surface Plasmon Sensors Advantages Evanescent field interacts with adsorbed molecules only Coupling angle strongly depends on ε d Use of well-established surface chemistry for Au (thiol chemistry)

13 Near-field optics is essential Tip taps into the near-field Imaging SPP waves

14 Direct Measurement of the Attenuation of SPP s Local excitation using Kretchmann geometry Imaging of the (decay length of the) SPP 14 µm Width resonance pea gives same result P. Dawson et al. Phys. Rev. B 63, (001)

15 Excitation Surface-Plasmon Polaritons with Gratings (tric ) Grating coupling geometry (tric ) Bloch: Periodic dielectric constant couples waves for which the -vectors differ by a reciprocal lattice vector G Strong coupling occurs when where: //, SiO = e = d sin sp G " # $ m d = % & c m + d ' ( = P Graphic representation " # c 1/ G //,SiO = sp ± m sp H E e θ //,SiO = c sp P e " P //,SiO P //

16 Excitation Surface-Plasmon Polaritons with Dots (Tric 3) Dipolar radiation pattern E d = 00nm h = 60nm 700 nm E E-fields Strong coupling: = ± //,SiO sp dot Radiation Spatial Fourier transform of the dot contains significant contributions of Δ dot values up to π/d H. Ditlbacher, Appl. Phys. Lett. 80, 404 (00) Dipole radiation in direction of charge oscillation Reason: Plasmon wave is longitudinal

17 Other Excitation Geometries Radiation pattern more directional 00nm Divergence angle determined by spot size 700nm 60nm Illumination whole line radiation to line Pattern results from interference dipoles H. Ditlbacher, Appl. Phys. Lett. 80, 404 (00)

18 Excitation Surface-Plasmon Polaritons from a Scattering Particle Atomic Force Microscopy Image Near-field Optical Microscopy Image 00 nm nm Scatter site 0 nm Distance (µm) Distance (µm) Excitation direction 0 Scattering site created by local metal ablation with a 48 nm excimer laser (P=00 GW/m ) Scattering site braes translational symmetry Enables coupling to SPP at non-resonant angles I.I. Smolyaninov, Phys. Rev. Lett. 77, 3877 (1996)

19 Excitation SPPs on stripes with d < λ Excitation using a launch pad Atomic Force Microscopy image 00 nm Al Near Field Optical Microscopy image End stripe Note oscillations J.R. Krenn et al., Europhys. Lett. 60, (00)

20 Excitation SPPs on stripes with d < λ Atomic Force Microscopy image Intensity (a.u.) Near Field Optical Microscopy image End stripe Distance (µm) Note oscillations Note: Oscillations are due to bacreflection

21 D Metallo-dielectric Photonic Crystals Full photonic bandgap for SPPs Hexagonal array of metallic dots metal glass 300 nm 300 nm Scanning Electron Microscopy image (tilted) Array causes coupling between waves for which: sp = π/p or λ sp =π/ sp = P Gap S.C. Kitson, Phys Rev Lett. 77, 670 (1996) sp e = c Gap Gap opens up at the zone boundary " P " P P P //

22 Guiding SPPs in D metallo-dielectric Photonic Crystals Guiding along line defects in hexagonal arrays of metallic dots (period 400 nm) Scanning electron microscopy images Linear guides Close-up Y-Splitter SPP is confined to the plane Full photonic bandgap confines SPP to the line defect created in the array S.I. Bozhevolnyi, Phys Rev Lett. 86, 3008 (001)

23 Guiding SPPs in D metallo-dielectric Photonic Crystals First results Scanning electron microscopy images Atomic Force Microscopy image Near-field Optical Microscopy image Dot spacing: d = 380 nm Excitation: λ e = 75 nm SPP: λ sp = 760 nm = d S.I. Bozhevolnyi, Phys Rev Lett. 86, 3008 (001)

24 Summary Coupling light to surface plasmon-polaritons Kretchman geometry //, = " sin# = c Grating coupling SiO d sp //,Air = sp ± mg E H Θ Coupling using a metal dot (sub-λ structure) Guiding geometries Stripes and wires Line defects in hexagonal arrays (d photonic crystals) Next lecture: nanoparticle arrays