4. Simulation of hybridization of nanodisk sandwiches
4.5. Ultrafast plasmon modes in gold-silica-silver sandwichessandwiches
4.5. Ultrafast plasmon modes in gold-silica-silver
4.5.2 Temporal evolution of E-Field 59 modes, similar to the modes in the gold-silica-gold sandwich. The time averaged electric field of the modes are shown next to the absorption peaks. The modes can also be attributed to TEM 11 - TEM 41 modes. In the time average the modes look similar to the modes enhanced in the top gold disk as shown above. By evaluating the modes for monochromatic excitation at different phases (e.g. the maximum, zero crossing, or minimum) as shown in b) one observes a different behaviour. The resonance located at 625 nm is composed at 160◦ of a minimum/maximum (min/max) pair with opposite sign with respect to the center and outer min/max pair. A phase shift of 45◦ shows four alternating min/max pairs. This pattern does not change significantly within another phase shift of 45◦. Only the amplitudes change. The second resonance at 669 nm obtains four min/max pairs only at a phase of 160◦. A phase shift of 45◦ leads to a reduction to only two clear modes in the center of the disk. In the outer part alternating min/max spots become visible resulting in a built up of a ring mode in the oscillator. Another phase shift of 45◦ leads to a vanishing of the ring mode with three remaining min/max pairs with opposite sign of the center pair. The third resonance at 753 nm composed of three alternating min/max pairs reverses within a phase shift of 90◦ instead of 180◦. In the intermediate state only two min/max pairs with the same sign appear. The outer min/max pair exhibits a circular modulation but without sign changes, too. The fourth resonance at 984 nm features only two min/max pairs that change their sign.
4.5.2. Temporal evolution of E-Field
In the following the appearance of the circular modulation and the formation of ring modes are investigated in more detail. The simulation is summarized in Figure 4.17 When the electric
Figure 4.17.: Simulation parameter for the investigation of the temporal E-field on the gold-silica-silver sandwich surface.
field at the top disk surface is evaluated along a concentric half circle, as shown in Figure 4.18 in a) and b) for radii of22 and48 nm, respectively, one observes significant differences in the mode pattern. In the central ring in a) only a regular dipole mode is visible arising with the excitation and changing its sign consecutively with a sinusoidal superposition resulting in more intense regions and less intense regions. The dipole oscillation is decaying exponentially within 60 fs to 1/e2. The symmetry axis is the 90◦ line, that is the line perpendicular to
Figure 4.18.: Evolution of the electric field on the sandwich surface along a ring with radius 22 a) and48 nmb) showing the volume mode in the inside and the ring modes in the outside appearing after around 35 fs.
the light polarization vector. Whereas in the outer ring close to the edge of the disk after excitation also a dipole mode dominates but after 40 fs an asymmetric circular ring mode emerges. The circular mode can be figured out by the changing polarity along the line at a constant time step close to40 fs and 50 fs. Up to eight poles are appearing. These ring modes lead to the built up of a ring current in the disk sandwich resonator, which is usually excited with the resonant coupling of a propagating plasmon from a wave guide to a ring resonator. Here, a small asymmetry of the electric field of the excitation pulse induces the built up of an asymmetric charge distribution.
The evaluation of the electric field on the top disk surface along they= 0 axis is shown in Figure 4.19 a). The electric field evolution at two specific positions (10 nmand 22 nm) are selected in b). In a) the bending of the minima and maxima determines the propagation di-rection, again. In the beginning the propagation direction is from outside to inside up to25 fs since the minima and maxima are bent to the right. Here a phase variation happens. After-wards the propagation direction switches and the modes are travelling from inside to outside up to30 fs, where the direction changes again. This switching repeats for several times. The temporal evolution along the line shows a splitting of the outer minimum/maximum pair that happens constantly over the whole time window. The splitting of the minimum/maximum pair of the inner dipole mode into two pairs corresponding to a surface mode happens around 18 fs. The splitting lasts for about8 fs until the minimum/maximum pair merges again. Af-terwards the splittings are more irregular. Around 28 fsthe inner minimum/maximum pair splits again but at a position more outside and the two pairs are only slightly shifted with respect to each other. The outer of the two pair is merging around37 fswith the outermost mode. After the phase variation at 30 fs there happens another splitting of the inner pair with only a slight shift. Both pairs exist over the whole time window but the splitting position oscillates locally between19 nmand 27 nm.
In b) the electric field intensity at the position of the volume mode at10 nm (blue line)
4.5.2 Temporal evolution of E-Field 61
Figure 4.19.: Electric field along a line on the surface a) and the field on two positions at10 and22 nm b). The observed line is parallel to the incident field.
and the surface mode at 22 nm(red line) are shown. The top blue and bottom red shaded areas correspond, as in the gold-silica-gold sandwich, 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 phase velocities. In the region < 15 fs the intensity of the volume mode is stronger in the outer part of the mode than in the inner part. After15 fsa surface mode determines the intensity profile and the intensity becomes stronger at the10 nm position compared to22 nm. This lasts up to30 fs. With increasing times the intensity ratio switches again several times indicated by the colour switching from top to bottom. In the gold-silica-silver sandwich a phase variation happens on the attosecond time-scale as well.
To summarize the results of the gold-silica-silver sandwich, the surface modes in the top silver disk have a circular asymmetry in contrast to the top gold disk leading to the build up of ring modes (whispering gallery mode [121]) and the formation of a ring current. This results from the asymmetry of the electric field within the excitation pulse. These ring mode formation should be investigated in more detail with different pulse forms simulating a CEP scan.The ring modes are refined to the outer part of the disk, whereas in the inner part surface and volume modes dominate. The temporal structure shows phase variation features on the attosecond time-scale again.