1. Nanoplasmonic structures: Designing electromagnetic fields
Benji Börner

2. Surface Plasmon Polariton (SPP) mathematical
Content
short revision
Surface Plasmon Polariton (SPP) mathematical
SPP excitation by electons
SPP excitation by photons
nanoplasmonic structures
experimental applications

3. surface plasmons on metal surface
Revision
surface plasmons on metal surface
coherent oscillation of free electrons
can be excited by electrons and photons

4. boundary condition by Maxwell for em wave 𝑘 𝑧1 𝜀 1 + 𝑘 𝑧2 𝜀 2 =0
mathematical explanation – dispersion relation
𝐸= 𝐸 0 𝑒 [𝑖 𝑘 𝑥 𝑥+ 𝑘 𝑧 𝑧−𝜔𝑡 ]
boundary condition by Maxwell for em wave
𝑘 𝑧1 𝜀 𝑘 𝑧2 𝜀 2 =0
𝑘 𝑥 2 + 𝑘 𝑧𝑖 2 = 𝜀 𝑖 𝜔 𝑐 𝑖=1,2
mysite.du.edu/~lconyers/SERDP/Figure5.htm

5. mathematical explanation – dispersion relation
𝑘 𝑥 = 𝜔 𝑐 𝜀 1 𝜀 2 𝜀 1 + 𝜀
𝜀 𝜔 =1− 𝜔 𝑃 2 𝜔 𝑤𝑖𝑡ℎ 𝜔 𝑃 = 𝑛 𝑒 2 𝜀 0 𝑚 ∗

6. mathematical explanation – dispersion relation
real part
imaginary part

7. damping due to ohmic losses and electron-core interactions
mathematical explanation – dispersion relation
damping due to ohmic losses and electron-core interactions
manifestation in imaginary part of dielectric function
𝑘 𝑥 = 𝑘 𝑥 +𝑖 𝑘 𝑥 = 𝜔 𝑐 𝜀 1 𝜀 2 𝜀 1 + 𝜀 𝑖 𝜔 𝑐 𝜀 1 𝜀 2 𝜀 1 + 𝜀 𝜀 𝜀

8. intensity decreased by absorption (E²) propagation length: 𝐿= 1 2 𝑘 𝑥
mathematical explanation
intensity decreased by absorption (E²)
propagation length: 𝐿= 1 2 𝑘 𝑥
intensity at distance x: 𝐼= 𝑒 −2 𝑘 𝑥 𝑥
skin depth formula: 𝑧 𝑖 = 𝜆 2𝜋 𝜀 𝜀 2 𝜀 𝑖

9. electron scattering on surface
SPP excitation by electrons
electron scattering on surface
parallel part creates surface plasmon polariton
Yang Zhang et.al. “Edge scattering of surface plasmons excited by scanning tunneling microscopy”, Maier - Plasmonics

10. need to match wavelength and momentum
SPP excitation by photons
need to match wavelength and momentum
tools like prisms or gratings needed

11. prism in Kretschmann configuration
SPP excitation by photons - prism
prism in Kretschmann configuration
different dielectric functions match momentum
evanescent wave excites SPP
Google.de -> Kretschmann configuration

12. prism in Otto configuration SPP excited on top of metal film
SPP excitation by photons - prism
prism in Otto configuration
SPP excited on top of metal film
Minghui Hong et.al „ Maskless multibeam laser irradiation enables large-area nanostructure fabrication“

13. excitation with grating reciprocal grating vector gives imaginary part
SPP excitation by photons - grating
excitation with grating
reciprocal grating vector gives imaginary part
Byoungho Lee et.al. „Shaping and focusing light beams with plasmonics”

14. defects provide free space radiation
SPP excitation
SPP scatter on defects
defects provide free space radiation

15. nanoplasmonic structures – gratings
Yongqi Fu et. al. “Plasmonic Lenses”

16. nanoplasmonic structures – flat gratings

17. nanoplasmonic structures – concave gratings
Byoungho Lee et.al. „Shaping and focusing light beams with plasmonics“

18. nanoplasmonic structures – concentric gratings
Yongqi Fu et. al. “Plasmonic Lenses”

19. nanoplasmonic structures – nanoholes
Carsten Sönnichsen “Plasmons in metal nanostructures”
Maier - Plasmonics

20. investigation of surfaces to find defects identify density changes
experimental applications
investigation of surfaces to find defects
identify density changes
molecular detectors

21. Thank you!