1 / 64

Surface Plasmons Part 1

Surface Plasmons Part 1. Surface plasmons: outline. Time-line of major discoveries Surface plasmons - surface mode of electromagnetic waves on a metal surface Spectroscopy of SPs in nanostructures: Nanoparticles Gratings, nanostructures

tharold
Download Presentation

Surface Plasmons Part 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Surface Plasmons Part 1

  2. Surface plasmons: outline Time-line of major discoveries Surface plasmons - surface mode of electromagnetic waves on a metal surface Spectroscopy of SPs in nanostructures: Nanoparticles Gratings, nanostructures 4. Applications: sensors, nanophotonics, surface enhanced Raman spectroscopy (SERS) Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  3. Time line SPs allow to localize and guide EM waves!!! First biosensor on SPs Surface Enhaced Raman Spectroscopy 1974 Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012 1993- Nanoplasmonics, extraordinary transmission, etc. 1991 Excitation of SPs with a prism: Raether, Kretschmann 1968 Fano: role of surface waves, surface plasmons 1941 Rayleigh’s explanation (angle-diffraction orders) 1907 Wood anomalies: reflection on gratings (two types) 1902

  4. density of charges Maxwell’s equations (SI units) in a material, differential form density of current Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  5. Wave equation 0 Double vector product rule is used a x b x c = (ac) b - (ab) c Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  6. Plane waves Thus, we seek the solutions of the form: From Maxwell’s equations one can see that is parallel to is parallel to Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  7. Simple system of a metal bordering a dielectric with incident plane wave Incident light Dielectric, refractive index is dielectric permittivity Reflected light Transmitted light Metal (gold) Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  8. Waves at the interface z y In medium 1, z<0, x Assume that incident light is p-polarized, which means that the E-vector is parallel to the incidence plane Then the vector of the magnetic field is perpendicular to the incidence plane and has the form In medium 2, z>0, x Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  9. Boundary conditions z y x Stokes's theorem Stokes's theorem Gauss’s theorem Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  10. Relations in an E-M wave the curl operator Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  11. Derivation of the dispersion equation Assume no external currents or free charges, magnetic permeability. One boundary condition is From the other condition => Therefore we have a system of 2 homogeneous equations and a nontrivial solution is possible only if the determinant of this system is equal to 0. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  12. Surface plasmon dispersion equation We square both sides We introduce , wavenumber of the surface plasmon, then we obtain Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  13. Dispersion equation and properties of surface plasmons We would like to have a solution which is localized to the surface, i.e. it decays with distance from on both sides from the interface. Indeed, then we have waves localizednear the interface This is possible, if Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  14. Dispersion equation analysis This is only possible, if If we look again at the dispersion equation w,k must be real (propagating wave!), then with negative, we see that the condition for surface waves to exist is Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012

  15. Metamaterials Optics Nanotechnology SERS High harmonics generator coherent control imaging nanostructures nanophotonics nanoantennas Plasmonics Biotechnology Electronics molecular interactions nano-sensors proteomics Opto-electronics Relation of Plasmonics to SOME other fields

  16. The Growth of the Field of Surface Plasmons illustrated by the number of scientific articles published annually containing the phrase “surface plasmon” in either the title or abstract PIETER G. KIK and MARK L. BRONGERSMASURFACE PLASMON NANOPHOTONICS, (2007)

  17. Surface plasmons (or surface plasmon polaritons), Part 2: outline Why SP named so? Excitation of SPs: with a prism or a grating Spectroscopy of SPs in nanostructures: Nanoparticles Gratings, nanostructures 4. Applications: sensors, nanophotonics, surface enhanced Raman spectroscopy (SERS) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  18. Dielectric constant of a metal, Drude model For free electrons! Consequently, plasmon frequency Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  19. Remarks to Drude’s formula Bound electrons should be taken into account, then 1-> , which takes into account the contribution of bound electrons. Also the mass of electron should be replaced with the effective mass of electron in the metal, . Plasmons correspond to , these are eigen (free) oscillations of the electronic plasma. Influence of attenuation For g << wp: Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  20. Electrons oscillating in the SP field dielectric Interface metal There is a longitudinal component in the electric field of SP, because E-M field is coupled to oscillations of the electronic density (plasmonic oscillations). This is why tp exite SPs one needs a p-polarization of the incident light. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  21. Graphing dispersion equation of SPs Light line: , w For excitation of SPs we need to slow down light! ( Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  22. Surface plasmon excitation: Coupling of light to SPs with a prism Optical arrangement used to excite the surface-plasmon wave based on the Kretschmann-Raether configuration where a thin metal film is sandwiched between the prism and the sample. E. Kretschmann, Z. Phys. 241, 313-324 (1971). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  23. SPR curves for different wavelengths Gold film (d=47nm) contacting water l =1230 nm 1.0 l =633 nm 0.8 REFLECTION COEFFICIENT 0.6 0.4 l 0.2 =490 nm 0.0 50 60 70 80 90 INCIDENCE ANGLE (deg) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  24. Conditions for the resonance excitation of SPs • Conditions for the resonance excitation of SPs: • a photon is converted into a surface plasmon. • General laws must be observed: • Energy conservation, • (2) Momentum conservation, is changing is not changing Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  25. Resonance excitation with a prism w wp SP k ksp Conditions for the Surface Plasmon Resonance (SPR): phase matching!!! Momentum conservation Energy conservation Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  26. Questions?

  27. Surface Plasmon Part 3

  28. Graphing dispersion equation of SPs Light line: , w For excitation of SPs we need to slow down light! ( Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  29. Air -1 » e q D q L ( k cos ) Gold sp 0 0 res Glass The influence of the thickness of the gold film on the properties of SPs • SP resonance curves at 633 nm for different film thicknesses. • The dependence of the attenuation length on the film thickness for 633 nm and 805 nm. The dielectric constants published by Palik are used. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  30. Approximation of small losses A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  31. Examples: changes in the flow cell, bio-molecular binding reactions Example: binding of monoclonal antibody to horseradish peroxidase protein 0.50 550 A B C=0% 500 0.45 C=0.82% B 450 SPR angle (pixels) 0.40 400 NHS/EDC HRP 0.64 deg 350 0.35 B B 300 250 0.30 0 10 20 30 40 50 60 70.50 70.75 71.00 71.25 71.50 Time (min) INCIDENCE ANGLE (deg) A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997). Applied this sensing technique to myofibers and tubulin molecule.

  32. Sensitivity and detection limit(relationships between different quantities) angular resolution -4deg=2 RU changes of the refractive index n-6 average thickness of the protein layer d=0.03 Å surface concentration d=3 pg/mm2 with mprotein=24 Da surface concentration of molecules ns=1010 cm-2 A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, 6539-6547 (1997).

  33. Attenuation lengths of SPs for gold and silver films in contact with air, calculated for a broad spectral range 1. American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, 1972), p. 105. 2. U. Schröder, Surf. Sci. 102, 118-130 (1981). 3. Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic1985). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009)

  34. w w < p Summary of surface plasmons 2 e e w 2 1 2 = Propagatin g wave with k x 2 e + e c 1 2 Z 2 w p e = - e ion of free electrons : , Approximat 1 2 b w E - e < => plasmon frequency; 0 1 Condition of existence: SPs: • Spatially localized to the surface E-M wave • Oscillations of the electronic density. • Have E -longitudinal component • Are excited with p-polarized light and the local field can significantly exceed the field in the exciting beam. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  35. Dependence of the near field intensity enhancement factor on the back side of the gold film vs. the angle for two wavelengths 633 nm and 805 nm A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  36. SP resonance: coupling with a grating (conservation of momentum) θ ki ki θ grating kSP kSP ki sin(θ) ki sin(θ) kg kg kSP= ki sin(θ) + kg kSP= ki sin(θ) - kg +1 order coupling -1 order coupling Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  37. Conditions for the resonance excitation of SPs Light line Light line, suited for resonance excitation , w SP dispersion curve required additional momentum The crossing of the SP curve and the light line means resonance excitation for desired frequency SPs are slower than light, and therefore for the same frequency their momentum is larger. To enable the resonance excitation additional momentum must be provided. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  38. Schematic of experiment on spectroscopy of SP modes in nanostructures :transmission measurements in the far field This setup maps intensity distribution over angle and wavelength and thus reveals SP modes that affect transmission. λ θ Charge Coupled Device (CCD) Laser beam Grating Sample (nanostructure) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  39. AFM image of the nanostructure: Transmission dependence 5° Angle of Incidence Study of the Interaction of 7 fs Rainbow Laser Pulses with Gold Nanostructure Grating: Coupling to Surface Plasmons Intensity 0° -5° 650 Wavelength (nm) 800 The valley area (x-structure) the laser light is efficiently converted into SPs, about 80%. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 A. Kolomenskii et al., Optics Express, 19, 6587-6598 (2011).

  40. Avoided crossing We consider two counter-propagating SP waves with complex amplitudes a and b; the total fields can be presented as linear combinations of these two individual waves. The amplitudes a(z) and b(z) satisfy: where and are the coupling coefficients.

  41. Experimental and calculational results: interaction of SP modes and spectral gap k Kg -Kg Kg SPs travels in two opposite directions. The intersection of the straight line with the dispersion curve gives the point of excitation. Two counter propagating waves interact with each other when they are scattered on 2Kg. K=wavenumber of grating.k=projection of light on plane of propagation

  42. Avoided crossing The coupled-mode equations can be expressed in matrix form: By substituting: We obtain: , I – unit matrix, The two eigenvalues for are: Where: q can be purely imaginary if Spectral gap!

  43. Questions?

  44. Surface Plasmons Part 4

  45. Optical detection of acoustic waves with surface plasmons

  46. Abstract For fast and sensitive detection of acoustic waves the surface plasmon resonance (SPR) can be used, which responds to variations of dielectric properties in close proximity to a metal film supporting surface plasmon waves. When an acoustic wave is incident onto a receiving plate positioned within the penetration depth of the surface plasmons, it creates displacements of the surface of the plate and thus modulates the dielectric properties, affecting SPR and the reflection of the incident light. Here we study characteristics and determine the optimal configuration of such an acousto-optical transducer with surface plasmons for efficient conversion of an acoustic signal into an optical one. We simulate the properties of the transducer and present estimates showing that it can have a large frequency bandwidth and good sensitivity.

  47. Fig. 1. Schematic of the acousto-optical sensor with surface plasmons. The arrangement consists of a glass prism (PR), the adjacent gold film (GF), a spacer (SPA) and a receiving plate (RP). The field of the excited surface plasmon (SP) decays away from the gold film. The acoustic wave (AW) induces displacements of the RP face close to the GF, which results in a quantifiable modification of the SPR curve featuring the resonance by a dip in the dependence of the intensity on the incidence angle . The inset on the right shows a schematic of layers with notations for the dielectric constants and thicknesses of the layers.

  48. Changes of the SPR curve due to RP displacement

  49. Detection limit for the RP displacement Detection of ΔRmin change Detection of ΔR change at the steep slope

More Related