Electromagnetic modeling of plasmonic properties of gold nanoparticles embedded within a dielectric matrix deformed by swift heavy ions 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]

INDRODUCTION An innovating and powerful technique for manipulating matter at the nanometer scale by ion­shapping has been investigated [1]. This technique allows the deformation of gold spherical particles embedded within an ion­deformable amorphous host matrix into nanowires. We study the local electric field Eloc for a sphere and nanowires with different aspect ratios (AR) excited by a plane wave of amplitude Einc . We determine the plasmon resonances energies of spheres with different diameters. We show that the energies deduced from near field enhancement (Eloc/Einc) peaks determined by our ADE­FDTD method is in accordance with peaks of extinction efficiency Qext calculated using far­field method [2]. We present the energies of longitudinal plasmon modes for different values of AR from 1 to 15. We show a cross section view Eloc/Einc of these modes for nanowire (AR=15). [1] G. Rizza and al, Nanotech. 22,175305,2011 [2] B.T. Draine & al, J. Opt. Soc. Am. A, 11, 1491,1994

COMPARE THE NEAR­FIELD ENHANCEMENT AND THE EXTINCTION EFFICIENCY

ADE­FDTD METHOD

Finite difference time domain (FDTD) Auxiliary differential equations (ADE)

Solve Maxwell's equations Gold dielectric suscpetibility

a

Figure 1: Presentation of the object and the incident wave. The field propagates along the z axis, and is polarized in the y­axis. Only the longitudinal mode will be studied.

b

Figure 2: For 3 gold spheres, embedded in a medium with refractive index 1.45, with different diameters, 20nm 40nm and 60nm, we compare (a) the field enhancement Eloc/Einc and (b) the extinction efficiency Qext. Pics are located at the same position. When the radius increases, the energy of the plasmon mode shifts to lower energies

STUDY OF LOCAL FIELD ENHANCEMENT ACCORDING TO THE ASPECT RATIO AR E=0.55 eV

E=1.27 eV

E=0.96 eV

E=1.54 eV

E=1.84 eV

Figure 3: Cross­section view of the field enhancement for a nanowires with AR=15

AR=15

We study the local field enhancement for different AR. We are interested here only in the longitudinal modes, when the excitation light is polarized along Y axis. Figure 3 presents 5 modes with different maximum values of Eloc/Einc. The first mode (m=0), present a field enhancement important at the extremity of nanowires (Eloc/Ein≈80). For the second mode (m=1), the field enhancement is maximum in the center of the nanowires, and minimum in the extremities. Figure 4 presents the energy modes according to the AR. ­The number of modes increase with the AR. For sphere (AR=1) only one plasmon mode exist. ­The energies of mode decrease when the AR increases ­The first mode is the lowest energy

Figure 4: Evolution of energy modes depending on the AR

CONCLUSION

ACKNOWLEDGMENT

In conclusion, the ADE­FDTD method is a powerful method to study the response of plasmonic structures. It is possible to find energy modes and have a cross­section view of these modes. For an important AR, the field enhancement may be high, and have applications in plasmonics. By changing the AR, we can control the energy of plasmon modes.

The authors thank the French National Agency (ANR), which supported this work through the Nanoscience and Nanotechnology program (SHAMAN project ANR­09­NANO­ 0334)