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Surface Plasmons

Surface Plasmons. 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

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Surface Plasmons

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  1. Surface Plasmons

  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 introduced charges in the medium Maxwell’s equations (SI units) in a material, differential form density of currents introduced in the medium 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 along the propagation direction, 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 , 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 to excite 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. 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

  23. 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

  24. 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

  25. Surface Plasmon Part 3

  26. 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

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

  28. 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

  29. 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.

  30. 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).

  31. 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)

  32. 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

  33. 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 (dashed lines – smooth surface, solid lines – surface with roughness) A. Kolomenski et al., Applied Optics, Vol. 48, 5683-5691 (2009) Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  34. 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

  35. Conditions for the resonance excitation of SPs with a grating Light line, suited for resonance excitation Light line , 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

  36. 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

  37. 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

  38. 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).

  39. Mie theory and dipole approximation t=0 t=T/2 Ionic cluster Electric field Light Electronic cluster Electronic plasma oscillations For small nanoparticles (R<<, or roughly 2R< /10): dipole approximation where V is the particle volume,  frequency light, εm and are the dielectric functions of the surrounding medium and the particle material. When is small or varies slowly, the resonance takes place at => Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  40. Extinction spectra of Ag n-particles in solution The oscillations of a n-particle, induced by a pump pulse, modulate (displace) the plasmon absorption band. For efficient detection the probe wavelength was selected at the steeper portion of the slope of this band. S. N. Jerebtsov et al. Phys. Rev. B Vol. 76, 184301 (2007). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  41. Intensity enhancement vs wavelength Bowtie nano-antenna and measured intensity enhancement Fabricated by Electron Beam Lithography (EBL) bowtie antennas. Indium tin oxide substrate. Gap was varied, thickness 20 nm. 3D finite difference time domain (FDTD) simulations Kino et al. In: Surface Plasmon nanophotonics, p.125 (2007). Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  42. Experimental setup for study of “hot spots” for SERS Raman signals from individual Ag n-particles Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004). Raman microscope with sensitive CCD cameras for imaging the sample in scattering and using Raman signal. Notch filters were used to suppress the excitation light. Low concentration of n-particles needed to separate individual particles.

  43. Photon scattering on molecules Elastic or Rayleigh scattering Inelastic or Raman scattering Stocks Anti-Stocks h h(-) h(+) h Raman spectroscopy Raman scattering increases when h produces electronic transition Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

  44. Surface Enhanced Raman Spectroscopy (SERS) of DNA bases Futamata et al. Vibrational Spectroscopy 35, 121-129 (2004). Characteristic stretching modes in heterocycles suited for DNA sequencing : adenine 718 and 893 cm-1;guanine 641cm-1; cytosine 791 cm-1; thymine 616, 743 and 807 cm-1. Spectra of individual n-particles Time evolution (whole scale 1 s) demonstrates Raman peaks and blinking effect, known for single molecule detection. Stongest enhancement ~1010 from pairs of particles with axis parallel to polarization

  45. Energy level diagram for sum-frequency generation (SFG), difference-frequency generation (DFG), and cascaded Raman sideband generation • The lower inset is photograph of Raman sidebands by time delayed linear chirped pulses • Positive chirp(below) • Negative chirp opposite

  46. Beam crossing setup, BS, beam splitter

  47. Raman sideband generation with optical vortices

  48. Line Profiles of Spectral Lines Full width at half maximum

  49. Natural Linewidth Solution: Note: Damping of molecular oscillators is very small From the Fourier Transform:

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