Which observables to characterize multipolar plasmon resonances in a gold nanowire embedded in a silica matrix ? A. Fafin1, J. Cardin1, F. Gourbilleau1, P.E. Coulon2, A. Slablab2, G. Rizza2 and C. Dufour1 1
CIMAP, UMR CNRS/CEA/ENSICAEN/UCBN, 6 boulevard Maréchal Juin, 14050 Caen Cedex 4, France 2 LSI, Ecole PolytechniqueCEA/DSMCNRS, 91128 Palaiseau Cedex, France email:
[email protected]
ADEFDTD METHOD
INDRODUCTION Localized surface plasmon resonances (LSPRs) in metal nanoparticles can enhance the electromagnetic field particularly in quasi onedimensional nanostructures like nanowires. Previous studies of these structures have focused mainly on the fundamental mode. By the ADEFDTD method, we study the optical response of a gold nanowire excited by a plane wave (electric field Einc, incident wave vector k, energy E (eV)). Usual observables like the extinction cross section or the near field electric enhancement (Eloc/Einc) are not sensitive enough to distinguish all modes because the spectrum is dominated by the fundamental mode. We introduce the near field magnetic enhancement (Hloc/Hinc), and the bound charge density ρb, which is ρb=div P , where P is the polarization density.
Finite difference time domain (FDTD) Auxiliary differential equations (ADE)
Solve Maxwell's equations Gold dielectric susceptibility
Figure 1: Gold nanowire and the incident wave. The incident wave vector is in the (x,z) plane with an incidence angle θ with respect to the axis z.
OPTICAL RESPONSE OF A GOLD NANOWIRE IN A SILICA MATRIX 5 1
3
1
3
5 3 5
2
1
Figure 2: Electric field enhancement as a function of the energy E
1
Longitudinal mode, θ=0
2
Figure 3: Magnetic field enhancement as a function of the energy E
Longitudinal mode, θ=0
3
Longitudinal mode, θ=0
4
4
Figure 4: Bound charge density as a function of the energy E
Longitudinal mode, θ=0
5
Transversal mode, θ=90
Figure 5: Pics labelled from 1 to 5 correspond to different plasmon modes, 1 to 4 are longitudinal modes and 5 is a transversal mode
CONCLUSION
ACKNOWLEDGMENT
In conclusion, the ADEFDTD method is a powerful method to study the response of plasmonic structures. The magnetic field enhancement (Hloc/Hinc) does not provides an additional information relative to the electric field enhancement (Eloc/Einc) to find a mode. However a study of the bound charge density ρb, and different incidence angle may reveal more modes than the electric field enhancement.
The authors thank the French National Agency (ANR), which supported this work through the Nanoscience and Nanotechnology program (SHAMAN project ANR09NANO 0334)
