Optimal control of light propagation and exciton transfer in arrays of molecular-like noble-metal clusters

We demonstrate theoretically the possibility of optimal control of light propagation and exciton transfer in arrays constructed of subnanometer sized noble-metal clusters by using phase-shaped laser pulses and analyze the mechanism underlying this process. The theoretical approach for simulation of light propagation in the arrays is based on the numerical solution of the coupled time-dependent Schrödinger equation and the classical electric field propagation in an iterative self-consistent manner. The electronic eigenstates of individual clusters and the dipole couplings are obtained from ab initio TDDFT calculations. The total electric field is propagated along the array by coupling an external excitation electric field with the electric fields produced by all clusters. A genetic algorithm is used to determine optimal pulse shapes which drive the excitation in a desired direction. The described theoretical approach is applied to control the light propagation and exciton transfer dynamics into a T-shaped structure built of seven ${\mathrm{Ag}}_8$ clusters. We demonstrate that a selective switching of light localization is possible in $\sim 5\mathrm{nm}$ sized cluster arrays which might serve as a building block for plasmonic devices with an ultrafast operation regime.

Figure 1

A T-shaped structure consisting of seven ${\mathrm{Ag}}_8$ clusters placed at 20 $a_0$ separation irradiated by an external laser pulse ${\varepsilon }_{\text{ext}}\left(\mathbf{r},t\right)$ with the wave vector ${\mathbf{k}}_{\omega }$.

Figure 2

Values of the target functions $f_1$ and $f_2$ at each generation, averaged over all species within this generation.

Figure 3

Electronic state population dynamics of single clusters in the array under the action of the laser pulse P1. Population of the ground state $|C_0^{\left(I\right)}{|}^2$ is shown with black lines, of the $S_{17}$ excited state $|C_{17}^{\left(I\right)}{|}^2$ with blue lines, and of the $S_{18}$ excited state $|C_{18}^{\left(I\right)}{|}^2$ with red lines. The subplots are arranged and numbered according to the array scheme which is presented in inset (a). The temporal profile of the external laser pulse P1 is shown in inset (b). The vertical arrows denote different steps of the excitation propagation up along the side chain of the array.

Figure 4

Spatial distribution of the electric field [${\left|\mathbf{E}\left(\mathbf{r},t\right)\right|}^2$] at selected instants of the simulation time. The snapshots are taken in the plane of the array (XY plane) at the time moments which are specified in the subplots. The magnitude of the electric field ${\left|\mathbf{E}\left(\mathbf{r},t\right)\right|}^2$ is denoted with the color code from blue (the lowest) to red (the highest).

Figure 5

Electronic state population dynamics of single clusters in the array under the action of laser pulse P2. Population of the ground state $|C_0^{\left(I\right)}{|}^2$ is shown with black lines, of the $S_{17}$ excited state $|C_{17}^{\left(I\right)}{|}^2$ with blue lines, and of the $S_{18}$ excited state $|C_{18}^{\left(I\right)}{|}^2$ with red lines. The subplots are arranged and numbered according to the array scheme which is presented in inset (a). The temporal profile of external laser pulse P2 is shown in inset (b). The vertical arrows denote different steps of the excitation propagation straight along the horizontal side of the array.

Figure 6

Spatial distribution of the electric field [${\left|\mathbf{E}\left(\mathbf{r},t\right)\right|}^2$] at selected instants of the simulation time. The snapshots are taken in the plane of the array (XY plane) at the time moments which are specified in the subplots. The magnitude of the electric field ${\left|\mathbf{E}\left(\mathbf{r},t\right)\right|}^2$ is denoted with the color code from blue (the lowest) to red (the highest).

Figure 7

Electric field energies $W_I\left(t\right)$ calculated using Eq. (6) for cluster 5 ($W_5$) and cluster 7 ($W_7$). The results are obtained for the silver cluster array excitation with (a) laser pulse P1, and (b) laser pulse P2. The time interval of optimization of the ratio between these energies is shaded in both pictures.