Vibration focusing in two dimensions: Constructing elliptical mirrors on the nanoscale

Concentrated vibrational energy transfer from one of the focal points of an elliptically shaped Ar island, adsorbed on different metal surfaces, into the second focus at finite temperatures is demonstrated. A comparison to a free Ar cluster of the same shape is made. A possible influence on the electronic quantum mirage effect is discussed.

Figure 1

Stable kinetic energy distribution pattern averaged over $0.1\mathrm{ns}$ for an excitation (along the horizontal) of (a) the atom in the right focus of the ellipse for a free square harmonic lattice of 327 atomic masses with axis of ellipse parallel to the $\left[110\right]$ direction, $I_{foc}∕I_{av}=5.2$, (b) the atom in the right focus of the ellipse for a free lattice of 291 Ar atoms (bound by the LJ potential) in hexagonal structure, $I_{foc}∕I_{av}=5.3$, (c) same as (b) but with excitation displaced one atomic site to the left side from the focus, and (d) same as (b) but with excitation displaced one atomic site to the right side from the focus.

Figure 2

Line scan of the stable vibrational energy distribution for an elliptic island with square lattice [case of Fig. 1a] as a function of the distance along the main ellipse axis. The result originates from a $0.1\mathrm{ns}$ time average of the MD simulation.

Figure 3

Ar island on $\mathrm{Pt}\left(111\right)$ surface. (a) Stable energy distribution pattern averaged over $0.1\mathrm{ns}$ for an excitation of the atom in the top focus of the ellipse, $I_{foc}∕I_{av}=3.3$. (b) Time evolution of the surface normal displacement of the Ar atom in the nonexcited focus of the ellipse in the direction perpendicular to the $\mathrm{Pt}\left(111\right)$ surface (single mode, $\omega =123{\mathrm{cm}}^{-1}$); full scale of $0.1\mathrm{ns}$ is shown in the inset.

Figure 4

Stable energy distribution pattern averaged over $0.1\mathrm{ns}$ for an excitation of the atom in the right focus of the ellipse for (a) a free island of 329 harmonically bound masses, $I_{foc}∕I_{av}=4.8$, (b) an island of 329 Ar atoms in a $\sqrt{2}\times \sqrt{2}R45°$ superstructure on 4161 atoms of the $\mathrm{Cu}\left(100\right)$ surface, $I_{foc}∕I_{av}=5.6$, and (c) the same as (b) but with the ellipse axis rotated $45°$ to the $\left[100\right]$ direction of the surface. (d) shows the energy pattern for the excitation of atom $A$ on a rectangular-shaped island with square lattice (harmonic approximation).