1. Nanophotonics
Class 2
Surface plasmon polaritons

2. Surface plasmon polariton: EM wave at metal-dielectric interfacez x
For propagating bound waves: - kx is real - kz is imaginary
EM wave is coupled to the plasma oscillations of the surface charges

3. Derivation of surface plasmon dispersion relation: k()
Wave equation:
Substituting SP wave + boundary conditions leads to the
Dispersion relation:
x-direction:
Note: in regular dielectric:

4. Dispersion relation:
x-direction:
z-direction:
Bound SP mode: kz imaginary: em + ed < 0, kx real: m < 0
so: m < -d

5. Dielectric constant of metals
Drude model: conduction electrons with damping: equation of motion
with collision frequency g and plasma frequency
If g << wp, then:
no restoring force

6. Measured data and model for Ag:
Drude model:
Modified Drude model:
Contribution of bound electrons
Ag:

7. Bound SP modes: m < -d
bound SP mode: m < -d

8. Surface plasmon dispersion relation:w
Radiative modes
real kx real kz
(e'm > 0) wp
Quasi-bound modes
imaginary kx real kz
(-ed < e'm < 0)
Dielectric: ed
Metal: em = em' + em" x z
real kx imaginary kz
Bound modes
(e'm < -ed)
Re kx

9. Surface plasmons dispersion:w
large k
small wavelength
3.4 eV
(360 nm)
Ar laser:
vac = 488 nm
diel = 387 nm
SP = 100 nm
X-ray wavelengths
at optical frequencies
Ag/SiO2
Re kx

10. Surface plasmon dispersion for thin films
Drude model
ε1(ω)=1-(ωp/ω) 2
Two modes appear
Thinner film:
Shorter SP
wavelength
Propagation
lengths: cm !!!
(infrared)
Example:
HeNe = 633 nm
SP = 60 nm L-
L-(symm)
L+(asymm)

11. Cylindrical metal waveguidesk E z r E
Fundamental
SPP mode
on cylinder:
Can this adiabatic coupling scheme be realized in practice?
Now when we let a small nanowire extend from this tip, the taper can serve as a coupling element to excite a wave propagating on the nanowire. This design is difficult to fabricate and integrate, however, so instead we will consider a structure that can be fabricated with standard planar lithography techniques, namely a laterally tapered metal stripe waveguide. To understand how to realize a similar adiabatic coupling in this geometry, we need to find the mode in the metal stripe that transforms to the nanowire mode as the stripe narrows.
taper theory first demonstrated by
Stockman, PRL 93, (2004)

12. Delivering light to the nanoscale+
1 µm
|E|
nanoscale
confinement
Field symmetry at tip similar to SPP mode in conical waveguide k E x z
Optics Express 16, 45 (2008)
Ewold Verhagen, Kobus Kuipers

13. Concentration of light in a plasmon taper: experimentAu Er
Al2O3
λ = 1.5 μm
Ewold Verhagen, Kobus Kuipers

14. Concentration of light in a plasmon taper: experiment
60 nm apex diam.
(1490 nm)
Er3+ energy levels
transmission
1 µm
10 µm
PL Intensity (counts/s)
lexc = 1490 nm
Nano Lett. 7, 334 (2007)
Ewold Verhagen, Kobus Kuipers

15. Concentration of light in a plasmon taper: experiment
Detecting upconversion luminescence from the air side of the film (excitation of SPPs at substrate side)
550 nm
660 nm k E x z
Plasmonic hot-spot
Theory: Stockman, PRL 93, (2004)
Optics Express 16, 45 (2008)
Ewold Verhagen, Kobus Kuipers

16. FDTD Simulation: nanofocussing to < 100 nm
sym
asym
Et, H
|E|2
z = -35 nm
1 µm + E
n1 = 1
1 µm
n2 = 1.74
start
tip
Nanofocusing predicted: 100 x |E|2 at 10 nm from tip
3D subwavelength confinement: 1.5 µm light focused to 92 nm (/16)
limited by taper apex (r=30 nm)
Saturating scale
The structure is excited by a SP mode at the substrate side of the film, just like in the experiment. When we look at the resulting field intensity in the plane of the Er ions, we see that SPs are indeed concentrated at the tip, to a dimension much smaller than the wavelength The width of this spot is 92 nm, and this number is limited by the rounding radius that we used to reflect the finite sharpness of the tip in the experiment. At a depth of 10 nm below the tip, the intensity is enhanced by a factor 100, which is btw not visible in this saturated color scale.
Optics Express 16, 45 (2008)
Ewold Verhagen, Kobus Kuipers

17. Coaxial MIM plasmon waveguides

18. FIB milling of coaxial waveguides
<w>=100 nm, L=485 nm
<w>=50 nm, L=485 nm
100 nm
100 nm
Silica substrates with nm thick Ag
Ring width: nm
Two-step milling process
~7° taper angle
Nano Lett. 9, in press (2009)
René de Waele, Stanley Burgos 18

19. Narrow channels show negative index
Excitation above resonance, w>wsp
25 nm-wide channel in Ag filled with GaP
Simulation shows negative phase velocity with respect to power flow
Negative refractive index of -2
René de Waele, Stanley Burgos

20. Positive and negative index modes
René de Waele, Stanley Burgos

21. Plasmonic toolbox: , (), d - Engineer ()
Plasmonic integrated circuits
Plasmonic multiplexer
Plasmonic concentrator
Plasmonic lens
thin section
And much more …..

22. Conclusions: surface plasmon polariton
Surface plasmon: bound EM wave at metal-dielectric interface
Dispersion: (k) diverges near the plasma resonance: large k, small 
Control dispersion: control (k), losses, concentration
Manipulate light at length scales
below the diffraction limit