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

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

5. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012
Wave equation
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. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012
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. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012
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. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012
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. Surface plasmons, A. Kolomenski, S. Peng, 9/24/2012
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.
This is possible, if
Indeed, then we have waves localized near the interface
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. Relation of Plasmonics to SOME other fields
Metamaterials
Plasmonics
Nanotechnology
Optics
Biotechnology
SERS
High harmonics generator
coherent control
imaging
Electronics
Opto-electronics
molecular interactions
nano-sensors
proteomics
nanostructures
nanophotonics
nanoantennas

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. BRONGERSMA SURFACE 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. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012
Electrons oscillating in the SP field
metal
dielectric
Interface
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, (1971).
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 4

23. SPR curves for different wavelengths
Gold film (d=47nm) contacting water l
=1230 nm
1.0
0.8 l
=633 nm
REFLECTION COEFFICIENT
0.6
0.4
0.2 l
=490 nm
0.0 50 60 70 80 90
INCIDENCE ANGLE (deg)
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012 16

24. Resonance excitation with a prismwp SP k
ksp
Conditions for the Surface Plasmon Resonance (SPR): phase matching!!!
Energy conservation
Momentum conservation
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, (2009)
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

28. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012
The influence of the thickness of the gold film on the properties of SPs
Gold
Glass
Air -1
res )
cos ( q e D k L sp
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
C=0% B
500
0.45
C=0.82% B
SPR angle (pixels)
450
0.40
400
NHS/EDC
HRP
0.64 deg
350
0.35 B B
300
0.30
250
70.50
70.75
71.00
71.25
71.50 10 20 30 40 50 60
Time (min)
INCIDENCE ANGLE (deg)
A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, Applied Optics 36, (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, (1997). 24

31. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012
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, (1981).
3. Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic1985).
A. Kolomenski et al., Applied Optics, Vol. 48, (2009)
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

32. Summary of surface plasmons2 w e e 2 1 2
Propagatin g
wave
with k = x 2 e + e c 1 2 Z 2 w p
Approximat
ion of
free
electrons : e = e - , 1 b 2 E w -
plasmon
frequency; e
< p
< w
=> 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. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012
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, (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
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

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

39. Mie theory and dipole approximation
t=T/2
Electronic cluster
Ionic cluster
Electric field
Light
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, (2007).
Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012

41. Bowtie nano-antenna and measured intensity enhancement
Intensity enhancement vs wavelength
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, (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. Surface Plasmons, Part 2, A. Kolomenski, 9/26/2012
Raman spectroscopy
Photon scattering on molecules
Elastic or
Rayleigh scattering
Inelastic or
Raman scattering
h
h
h(-)
h(+)
Stocks
Anti-Stocks
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, (2004).
Spectra of
individual
n-particles
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.
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