Ptychographic Approach for FROG: Beyond Pulse Reconstruction

Abstract

Frequency-resolved optical gating (FROG) is probably the most commonly used method for full characterization (i.e., amplitude and phase) of ultrashort optical pulses [1]. A FROG apparatus produces a two-dimensional (2D) FROG trace of an input pulse by interacting the pulse with its delayed replica in a nonlinear-optical medium, e.g., second harmonic generation (SHG) crystal. Current FROG reconstruction procedures are based on 2D projection-based phase retrieval algorithms. These algorithms require Fourier relation between the frequency and delay axes for the measured spectrogram resulting in reconstruction resolution limited by delay step. However, it is desirable to develop FROG algorithms that work well even if a significant part of the Fourier related spectrogram is missing or unmeasurable. Implementation of the ptychography– a powerful scanning coherent diffraction imaging method, to pulse diagnostic techniques in which the unknown pulse interacts with another pulse that is fully or partially known [2]–[3], demonstrated the superb robustness of the ptychographic reconstruction approach, both in terms of SNR and the use of only partial spectrograms. However, in these works, ptychographic reconstruction approach, have not been adapted to techniques like FROG, in which the unknown pulse interacts with its exact replica and therefore the reconstruction problem is more difficult.