DOI: 10.1007/s00340-006-2187-0 Appl. Phys. B 84, 111–115 (2006) Lasers and Optics Applied Physics B a.-s. grimault a. vial ✉ m. lamy de la chapelle Modeling of regular gold nanostructures arrays for SERS applications using a 3D FDTD method Institut Charles Delaunay – Universit´ e de technologie de Troyes – CNRS FRE 2848, Laboratoire de Nanotechnologie et d’Instrumentation Optique, 12, rue Marie Curie BP-2060, 10010 Troyes Cedex, France Received: 15 December 2005/Revised version: 7 March 2006 Published online: 4 April 2006 • © Springer-Verlag 2006 ABSTRACT We study the localized surface plasmon resonance (LSPR) and the surface-enhanced Raman scattering (SERS) of arrays of gold cylindrical and ellipsoidal nanoparticles with dif- ferent diameters or major axes. The LSPR and SERS gains are calculated with the three dimensional Finite-Difference Time- Domain method using the Drude–Lorentz dispersion model. We find that the maximum of the extinction spectrum and the aver- age SERS gain of each investigated nanostructures are shifted whatever their size and their shape. PACS 42.25.Fx; 71.45.Gm; 78.30.-j 1 Introduction Surface-enhanced Raman scattering (SERS) is a powerful and sensitive spectroscopic technique that pro- vides valuable information about the vibrational properties of adsorbed particles. Also, it allows the observation of very low concentrations of chemical species and even individual molecules [1–3]. Two kinds of enhancement mechanisms have been identified in SERS. The first comes from the in- teraction between the incident electromagnetic field and the topographical features of a metallic surface, e.g., its rough- ness [4, 5]. The second mechanism involves chemical changes of the adsorbate states due to the chemisorption of the ana- lyte [6, 7]. From these two processes, the main contributing mechanism in SERS is the electromagnetic enhancement due to localized surface plasmons [4]. This physical process cor- responds to collective charge oscillations producing a huge local electromagnetic field at the surface of the nanoparti- cles [8–10]. To determine the role of the localized surface plasmon res- onance (LSPR), it is necessary to design some controllable and reproducible samples, which is not possible with metallic island films [11]. Within the past ten years, several techniques such as electron beam or nanosphere lithographies have been proposed to produce well-reproducible samples of nanoparti- cle arrays. Consequently, several studies showing the relation between the position of the LSPR and the Raman enhance- ment have been proposed [9–16]. However, the modelling of ✉ Fax: +33 3 25 71 84 56, E-mail: vial@utt.fr samples fabricated with these kinds of techniques is compli- cated since it needs to take into account a large number of particles. For methods like the finite element method [17] or the discrete dipole approximation [18], each particle has to be part of the computation window, which not only makes the employment of these techniques computationally expensive, but also it restricts their use to 2D systems. In this work, we propose an application of the three di- mensional finite-difference time-domain method (3D-FDTD) to SERS. The 3D-FDTD has proven to be well adapted for spectroscopic studies [19, 20]. Also, since it allows the mod- elling of infinite particles arrays using periodic boundary con- ditions, the results obtained from the numerical simulations are in good agreement with the experimental ones. The ver- satility and flexibility of the 3D-FDTD suggests its possible application not only to the study of the localized surface plas- mon resonance (LSPR), the extinction spectra and the average SERS gain of several kinds of regular arrays of gold nanopar- ticles, but also the influence of different parameters such as the size and the shape of the nanoparticles on the position of the LSPR [21–23] in comparison with the position of the max- imum of the SERS intensity [9, 12–15]. The paper is organized as follows. In Sect. 2, we introduce the model employed for the numerical experiments and we explain its usefulness in the calculation of extinction spectra and for the SERS studies. Then, in Sects. 3 and 4, we show and discuss the results. Finally, in Sect. 5, we present the main conclusions. 2 Formalism: numerical method The three-dimensional finite-difference time- domain (3D-FDTD) method is a direct space method that was originally introduced by Yee in 1966 and is now widely used for solving different kinds of problems in electromag- netism and also in spectroscopy. The operational principles of this technique are based on the resolution of the discrete Curl–Maxwell’s equations by iteration over the time. In this work, we have improved the implementation of the FDTD through the employment of the Drude–Lorentz dispersion model, which accurately describes the dispersion function of gold in the modelling of extinction spectra for wavelengths between 500 and 1000 nm [24]. To model the SERS experi- ments conducted in this work, we consider regular arrays of