Lecture I, Xiamen,

Transcription

1 Lecture I, Xiamen, download from Optical properties of free electron metals, bulk and surface plasmons and plasmon polaritons, ATR methods 1)Elementary excitations and polaritons 2)The plasmon as elememtary excitation of metals with quasi free electrons 3)Electron energy loss spectroscopy of plasmons 4)Surface plasmon and surface plasmon polariton (SPP) 5) The excitation of SPP s by attenuated total reflection (ATR)

2 Elementary excitations in Solids and Polaritons an elementary excitation is a wavelike excitation in a solid, with phase velocity v phase =ωλ/2π ω= 2π frequency v phase << c dispersion curve blowing up in next slide direction of increasing λ and increasing v phase 2π/lattice constant 2π/λ = k

3 ω socalled light line: v phase = c v phase > c v phase < c dispersion curve of a transverse elementary excitation What about the interaction between light (always transverse) and a transverse elementary excitation? 2π/λ = k

4 Optical phonons in bulk material, interacting with light optical waves (trans.), historical solution by K.Huang (coworker of M.Born) K.Huang, Proc.Roy.Soc. London A208/(1951)352

5 Modern interpretation: Polaritons, E. Burstein, F. de Martini (eds.), Pergamon Press, New York, 1974 light line examples of elementary excitations in solids: Phonons, magnons, plasmons, excitons upper polariton branch longitudinal elementary excitation, coupling to transverse light only at surface (not in local optics) transverse elementary excitation crossing avoided (no crossing rule) lower polariton branch

6 The elementary excitation in a free electron metal is the plasmon

7 A longitudinal plasma wave ρ int ernal 0 i( kx ωt) = = i( kx ωt) E E0 kunite kunit curle = 0 = ρ e In a longitudinal wave exists no B-field. It is not an electromagnetic wave! k k λ k k = 2π λ Prove by Maxwell s equation curl E = - db/dt. Only compatible with B = const. There are no external charges involved: div D = 0. With D= ε E follows ε E = 0, but E 0! Only compatible with ε(ω) = 0.

8 frequency of a bulk plasma wave and explanation of plasmon For a nearly free electron metal with a Drude like dielectric constant ε(ω) 2 ω p εω ( ) = 1 2 ω + iγω ω ω 2 2 p p = 4 πne / m = " plasma frequency" ε( ω) 0 at ω = ωp Have a look at ε(ω) of Aluminium

9 Optical properties of Aluminum, H.Ehrenreich et al, PR 132 (1963)1918 є 1 (ω)=0 Dielectric constants of Aluminium ε( ω)= ε ( ω) + iε ( ω) 1 2 frequency has been converted into photon energy. What is the significance of the energy loss function Imε -1 in the lower part? ε ( ω) Im εω ( )= ε ( ω ) ε ( ω )

10 Electron energy loss spectroscopy E primary Longitudinal charge waves emitted! Probability P of suffering a loss E P( E) Im ε( E/ h) 1 E=E primary - E peaks at the loss E = hω p A plasmon is excited by the fast electron duality wave-particle: EM wave photon, longitudinal plasma wave plasmon

11 far off the light line, see k values Bulk plasmon in Aluminium H.J.Höhberger, A. Otto. E. Petri, Sol.State Commun. 16(1975) 175 Dispersion of the bulk plasmon at high k, compare to foil one

12 Optical properties of Aluminum, H.Ehrenreich et al, PR 132 (1963)1918 R perpendiular (ω) 1 perfectly reflecting below ω p plasma frequency transparent above ω p 0 0 ω ω p

13 ω bulk plasmon polariton ω p v phase = c bulk plasmon polariton, transverse bulk plasmon (longitudinal) for ω < ω p high reflectivity, no light propagation, no polariton k = 2π/λ

14 z surface plasmon as elementary surface excitation Looking for surface waves with v phase << c. Assuming infinite c, the Maxwell equation become the simple equation of electrostatics with electric potential Φ ( + + ) Φ= 4πρ x y z medium B, ε(b,ω), ρ=0 0 x medium A, ε(a,ω), ρ=0 E = gradφ Try the Ansatz: only surface charge at z = 0, potential decaying in both directions off the interface Φ ( A) =Φ ( e e ) Φ ( B) =Φ ( e e ) ikx+ kz iω( SP) t ikx kz iω( SP) t 0 0 Condition of continuity of normal component of D-field D ( A) = D ( B) at z = 0 ε ( A, ω( SP)) = ε( B, ω( SP)) z z

15 SP s of Aluminum clean Al: ε( Al, ω( SP)) = ε( Vacuum, ω( SP)) = 1 ω( SP) ω / 2 oxidized Al: p ε ( Al, ω( SP)) = ε( Al O, ω( SP)) ω( SP) ω / 1 + ε( Al O p 2 3

16 Small difference between bulk and surface plasmons of silver P.B.Johnson, R.W.Christy, Phys.Rev.B 6(1972)4370 H.Ehrenreich, H.R.Philipp, Phys Rev 128 (1962)1622 SP BP

17 25nm Al coverage silver film thickness 44nm 3.83±0.05eV Ag, bulk plasmon from doctor thesis Andreas Otto, Z.Physik, 185(1965) nm 15.8nm 0 nm Al, bulk plasmon Al/Al 2 O 3 surface plasmon Ag(9.5nm) surface plasmon In Al-Ag-Al sandwitch ε(ω,ag) = -ε(ω,al) cannot be fulfilled, therefore Ag-vacuum surface plasmon is quenched. Bulk silver plasmon becomes visible, intensity increases with Ag thickness.

18 Surface plasmon polariton of silver hω ( ev ) phase velocity parallel surface = c BP SP Surface plasmon-polariton of plane silver with phase velocity parallel surface < c dispersion relation: k parallel ω εω ( ) ( ω) = ( ) c εω ( ) + 1 1/2 k parallel surface

19 c α c Problem and idea phase velocity length surface v phase,pl = c/sin α >c silver c α c v phase,pl = c/n sin α under total reflection c/n c/n n sin α > 1 and v phase,pl < c evanescent field with v phase,pl < c PUT the silver sample in about a wavelength distance BELOW the prism!!!

20 The realization (1968) A. Otto, Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection, Z. Physik 216 (1968) 398, download from SPP resonance only observed for p-polarized light (equivalent to TH polarization) gap width d ~λ measuring D by intererence fringes of white light

21 Experimental results 5 different colours of a mercury lamp used intensity ratios of p- and s-polarized light as function of external angle ß, converted into α by Snellius law of refraction

22 Experimental dispersion ω(mercury lamp) k= sinα(spp-minimum) c

23 More precise adjustment of airgap in Otto configuration Bodesheim J., Diplomarbeit München 1973

24 The Weierstraß prism in Otto configuration: Application in Raman scattering M. Futamata, P. Borthen, J. Thomassen, D. Schumacher, A. Otto, Application of an ATR method in Raman spectroscopy, Applied Spectroscopy 48 (1994)

25 M. Futamata, E. Keim, A. Bruckbauer, D. Schumacher, A. Otto, Enhanced Raman Scattering from CuPc on Pt by use of a Weierstrass Prism, Advantage of Ottoconfiguration, when using transition metals Schematic light scattering configuration under the SPP resonance with the Weierstrass prism (WP). Aplanatic pair of points F and F of a sphere of radius r, and central ray for α i = α SPP (λ L )is depicted. The platinum surface is irradiated with a laser of nm wavelength (1 mw) through a 1:0.7 (Ll) objective. For variation of α i and β i, and p,. the position (y) of the prism (P) is adjusted. The scattered light including the SPP cone is focused on the entrance slit (ES) of the monochromator with the second objective (L2).

26 Advantage of Otto -configuration, when using single crystals A. Bruckbauer, A. Otto, Raman spectroscopy of pyridine adsorbed on single crystal copper electrodes, J. Raman Spectrosc., 29 (1998)

27 On priorities 1) A. Otto, Eine neue Methode der Anregung nichtstrahlender Oberflächenplasmaschwingungen. (A new method of excitations of nonradiative surface plasma oscillations) phys. stat. sol. 26 (1968) K 99, received February 13, 1968 Spring meeting of the Bavarian branch of the DPG, München Prof. H.Raether came from Hamburg, listening to my talk on this new method. 2) A. Otto, Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection, Z. Physik 216 (1968) 398, received 4.July ) E. Kretschmann, H. Raether, Radiative Decay of Non Radiative Surface Plasmons Excited by Light, Z. Naturforschung A23,(1968)2135, received 15.Nov Contains the reference to paper 2, with the remark: His (Otto s) measurments are analogous to the plasma wave absorption whereas ours correspond to the plasma resonance emission of the radiative modes. (a better wording would have been emission into radiative modes. The emission was possible, because Kretschmnann s film was rough.) I found later: First phenomenological observation in Kretschmann-configuration, but without any interpretation T.Turbadar, Proc.Phys.Soc.(London)73(1959)40; Optica Acta 11(1964)207

28 Why did Otto not invent the Kretschmann configuration? First I set up a computer program to see, whether my idea was good, before doing the difficult experiment. The computer said: Go ahead! In the mean time I had also thought about the later Kretschmann configuration. But my computer said: There is no resonance! (I had not taught him to chose the right square root of complex numbers) Why did it arrive, that my name got on my invention? According to second hand gossip, Prof.H.Raether complained to Eli Burstein (Philadelphia, he was a good friend of Stig Lundquist, chairman of the swedish Nobel price comittee) that Otto got all the honors (Schottky-price 1974), but he and Kretschmann nothing. Burstein decided this case by nomenclature: There should be Ottoconfiguration and Kretschmann-Raether-Configuration.

29 Modern applications

30 In 1968, the sensitivity of the ATR SPP resonance was clear, but real surface diagnostic needs were not known, at least to me.