# Thinfilm Hybrid Nanostructures: A Perspective to Subcycle Opto-Electronics and Coherent Control
## 2 Methods  
The simulations presented in this article were performed using the finite integration technique (FIT) [26] within the Computer Simulation Technology (CST) Studio Suite. Thisapproach is similar to the finite difference time domain (FDTD) technique used for example in MEEP [27] or Lumerical [28]. With this approach the Maxwell's equations in the time domain either in integral form (FIT) or differential form (FDTD) are solved to study the temporal evolution of the local distribution of electromagnetic fields. The target geometry is divided into small subvolumes with optimized shape and the electric and magnetic field is numerically retrieved for each time step. The simulation setup is identical to the one used in [24] and verified against the simulations and results presented in [25]. In [24] the sandwich geometry of a gold-silica-gold sandwich structure was optimized in the corresponding layer thicknesses and diameter ratios to provide a time dependent superposition of a maximum number of modes, excited by an ultrafast fourier limited laser pulse. In the simulation presented here, the final geometry is adapted without any further optimization focussing on the dynamics of the driving laser field and the appearance of whispering gallery modes due to geometrical symmetry breaking. The sandwich is composed of three individual disks with a gold bottom disk, a silica center disk and a silver top disk as depicted in Figure 1. The initial diameters of the bottom and top disks are 88 nm and 108 nm, respectively. The center disk shape is conical and adapts to the disks below and above. The disk thickness of the bottom and center disks are 10 nm and of the top disk 1 nm. We excite the plasmonic oscillation with an ultrafast laser pulse with a Fourier limited pulse duration of below 5 fs covering a spectral range from 550 to 1500 nm in normal incidence (see Figure 2). The carrier envelope phase (CEP) of the electric field is \(\pi/2\) corresponding to a sine-like electric field. Different observation monitors were used to investigate the behavior of the sandwic in energy and time domain:  
* Absorption cross section;
* Electric field;
* Temporal evolution of electric field. In the simulation presented in this paper, the dielectric function for gold is taken from [29]. We want to emphasize that the dielectric properties change [30] for ultrathin films. Especially with respect to physical properties like the formation of islands and the coalescence during the growth process approaching the quantum limit of atomically thin films in particular is not included in our model. Nevertheless, [PERSON] et al. [31] demonstrated experimentally that gold film thicknesses from two to ten nanometers could be carefully treated in the Drude circle regime. They identified the cluster size in film growth as the predominant cause for permitivity changes. [PERSON] et al. [32] support this finding theoretically comparing the permitivity changes to the Lorentz-Drude model for  
Figure 1: A gold-silica-silver nanodisk sandwich is illuminated from above with an linearly polarized ultra short laser pulse (\(\lambda=550\) to 1500 nm, \(\tau\leq 5\) fs) or monochromatically at the resonance wavelength. The sandwich has a total height of 21 nm and a radius of 54 nm of the top thin disk and 44 nm of the bottom thick disk. The geometry is unchanged in all simulations. Only the driving fields are varied in terms of the CE-phase. (**a**) Simulation geometry, adapted with permission from [24] ©The Optical Society; (**b**) Simulation setup. the visible wavelength range. The plasmon in the simulations presented here is excited with an electric field direction in the surface plane corresponding to the direction of extended material where the influence of the film thickness to the permitivity is smaller compared to the out-of-plane component [33]. As a consequence, the presented results rely on the data for the dielectric function that are restricted to a Lorentz-Drude model.