# Thinfilm Hybrid Nanostructures: A Perspective to Subcycle Opto-Electronics and Coherent Control
## 3 Ultrafast Plasmon Modes in Gold-Silica-Silver Sandwiches
Up to eight poles are emerging, driving a ring current at the outer rim of the structure. These ring modes are usually excited with the resonant coupling of a propagating plasmon from a wave guide to a ring resonator. In the case demonstrated in this paper, a slight asymmetry of the electric field of the excitation pulse induces the build up of an asymmetric charge distribution. This asymmetry in time can be seen in (a, b) close to 35 fs. Figure 6a represents the time dependent behaviour of the electric field at the top disk surface along the \(y=0\) axis. In (b) the electric field evolution at two specific positions (10 nm and 22 nm) and the related field asymmetry is characterized. In (a) the gradient along the field free lines in between the modes determines the propagation direction. A positive gradient represents a propagation from the center to the rim whether a negative gradient represents a propagation from the rim to the center  
Figure 5: Evaluation of the electric field on the sandwich surface along a ring with radius (**a**) 22 nm and (**b**) 48 nm showing the volume mode in the inside and the ring modes in the outside appearing after around 35 fs. Figure 6: Electric field along a line on the surface (**a**) and the field on two positions at 10 and 22 nm (**b**). The observed line is parallel to the incident field. of the disk. Up to 25 fs we see a propagation of the modes towards the center of the disk followed by a phase jump. Afterwards, the propagation direction changes and the modes are propagating from the center to the rim until 30 fs, where the direction changes again. This switching repeats for several times. The temporal evolution along the line shows an outer mode splitting that happens constantly over the whole time window. A mode splitting of the inner volume mode into two surface modes is observed at around 18 fs and lasts for about 8 fs until the modes are uniting again. The modes split up more irregularly after that position. Around 28 fs the inner mode splits again but at a lateral position closer to the rim of the disk and the two modes are only slightly shifted with respect to each other. The outer one is merging around 37 fs with the outermost mode. After the phase jump at 30 fs another splitting of the inner mode with only a slight shift is observed. Both modes exist over the whole time window but the splitting position oscillates laterally between 19 nm and 27 nm. The time dependent intensity envelope, integrating the simulated electrical nearfield of the top disc in the form  
\[f(t,\sigma,\tau) = \int_{0}^{t}e^{\frac{-t^{2}}{2\sigma^{2}}}e^{-\frac{t-t^{\prime}} {2\tau}}dt^{\prime} \tag{1}\] \[= e^{\frac{\sigma^{2}-4\tau t}{8\tau^{2}}}\left[1-\text{erf}\! \left(\frac{\sigma^{2}-2\tau t}{2\sqrt{2}\tau\sigma}\right)\right]\] (2) \[\text{where}\qquad\xi = \sigma\sqrt{\ln(2)} \tag{3}\]  
provides information on the buildup time to be in the order of \(\xi=2.762\) fs and the lifetime of \(\tau=9.605\) fs, respectively. In (b) the electric field intensity at the position of the volume mode at 10 nm (blue line) and the splitting into the surface mode at 22 nm (red line) are shown. The top blue and bottom red shaded areas correspond to the regions where the field at 22 nm is stronger than the field at 10 nm and the other way around. The asymmetry of the area corresponds to different mode velocities. Before 15 fs the intensity of the volume mode is stronger in the outer part. Then the intensity of the inner volume mode increases over time and dominates. At later times the intensity ratio switches again several times indicated by the colour switching of the shaded areas in the graph. In the inset of Figure 6b and the behavior between 30 fs and 40 fs it is shown, that phase jumps and asymmetries in locally distributed field strength happen at attosecond or at least subcycle time-scales in the gold-silica-silver nano sandwich.