Nanoscopic Ultrafast Space-Time-Resolved Spectroscopy

We propose and analyze a scheme for ultrafast spectroscopy with nanometer spatial and femtosecond temporal resolution. The interaction of polarization-shaped laser pulses with a nanostructure allows us to control the spatial and temporal evolution of the optical near field. Employing a learning algorithm, the field is tailored such that pump and probe excitation occur at different positions and at different times. Both excitations can be restricted to subdiffraction extensions and are separable on a nanometer length scale. This enables the direct spatial probing of nanoscale energy transfer or charge transfer processes.

Figure 1

Ultrafast space-time-resolved spectroscopy. (a) Objective: To study charge transfer (CT) or energy transfer (ET) between two quantum systems that are only a short distance $\Delta x$ apart, we create electromagnetic fields with the characteristics shown. The interaction of light with the quantum systems occurs only in spatially limited places with subdiffraction resolution $d$ and femtosecond time resolution $\tau$. Variation of the time delay $\Delta t$ opens the prospect for space-time-resolved spectroscopy on the nanoscale. For example, the field first creates local excitation at ${\mathbf{r}}_1$, and later the transferred excitation is detected at ${\mathbf{r}}_2$, e.g., by photoelectron emission. (b) Proposed scheme: The model nanostructure is illuminated by an optimized polarization-shaped femtosecond laser pulse. The coordinate systems for the nanostructure and for the polarization state of the laser pulse are indicated by arrows. The optimal polarization-shaped laser pulse corresponding to Fig. 3b is shown using an intuitive representation [23], where the ellipses indicate the momentary time-dependent polarization state and amplitude of the electric field oscillations. The gray-shading (color online) shows the momentary oscillation frequency, whereas the shadows represent the amplitude envelopes of components 1 and 2 separately.

Figure 2

Spatiotemporal field control. The spectral response $A_x^{1,2}({\mathbf{r}}_2,\omega )$ for the $x$ component of the local electric field under excitation with 1-polarized (thick dashed line) or 2-polarized light (thick solid line), respectively, is given as (a) amplitude $|A_x^{1,2}|$ and (b) phase $\arg \{A_x^{1,2}\}$. The far-field amplitude is shown in (a) by a horizontal line. The far-field spectral phases (c) of an optimally polarization-shaped laser pulse yield the temporal spatial intensity evolution of the $x$ component of the local electric field shown in (d) and (e). Part (d) shows the intensity evolution at ${\mathbf{r}}_1=(-30,30,27.5)\mathrm{nm}$ (solid line) and at ${\mathbf{r}}_2=(-30,-30,27.5)\mathrm{nm}$ (dashed line) in the geometry of Fig. 1b. The temporal evolution of the intensity $E_x^2$ in arbitrary units along the straight line defined by ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$ is shown in (e) as contour plot.

Figure 3

(a) Nanoscale pump probe. The temporal intensity of the $x$ component of the local electric field is shown for different pump-probe delays at ${\mathbf{r}}_1$ (solid) and at ${\mathbf{r}}_2$ (dashed), displaced vertically for clarity. (b) Nanoscale pump probe with different pulse durations. The evolution of the normalized total electric field intensity at ${\mathbf{r}}_1$ and at ${\mathbf{r}}_2$ is shown by thick solid and dashed lines, respectively. The corresponding temporal target functions are shown as thin lines; the optimized external polarization-shaped laser pulse is shown in Fig. 1b.