Time-domain ptychography

Through dedicated measurements in the optical regime we demonstrate that ptychography can be applied to reconstruct complex-valued object functions that vary with time from a sequence of spectral measurements. A probe pulse of approximately 1 ps duration, time delayed in increments of 0.25 ps, is shown to recover dynamics on a ten times faster time scale with an experimental limit of approximately 5 fs.

Figure 1

Ptychographic iterative scheme for the reconstruction of a complex-valued, time-varying object function $O\left(t\right)$ from a sequence of $N$ spectra $S(\omega ,n\Delta t)$ recorded at probe pulse time delays $n\Delta t$ with $n\in \{1,...,N\}$. After all $N$ spectra have been processed, the first iteration $\left(j=1\right)$ is complete and the next iteration $\left(j=2\right)$ will start until convergence is reached. For all $n$ the top arrow implies that the product of the estimated object function [$O_n\left(t\right)$ in red] with the time-delayed probe pulse [$P(t-n\Delta t)$ in blue] is Fourier transformed to the spectral domain. Then, the modulus of the Fourier transform is replaced by the square root of the measured spectral intensity. The result is Fourier transformed back to the time domain and is used to update the estimated object function.

Figure 2

Schematic illustrating the concept of the experimental setup.

Figure 3

Theoretical (solid curves) and reconstructed (dashed curves) amplitude and phase of the object function defined in Eq. (5) with (a) the plus sign and (b) the minus sign. For convenience, the phase is only shown in regions where the amplitude is larger than 0.1. The top panel shows the probe pulse $P\left(t\right)$ with a duration of approximately 900 fs. The corresponding parameters are $\tau =300$ fs, $M=5$, and $\gamma =1/5$.

Figure 4

Theoretical (solid curves) and reconstructed (dashed curves) amplitude and phase of the object function defined in Eq. (6). The corresponding parameters are $A=1.57$ rad and $\tau =300$ fs.