Numerically optimized FROG results for the study of red-shifted spectra in multi-frequency Raman generation

TL;DR

The paper investigates red-shifted spectral features in transient multi-frequency Raman generation driven by two chirped pumps. It combines a double-pulse interference model with FROG and ADAM-based optimization to reconstruct the temporal field and reproduce the first anti-Stokes component, attributing the red-shift to intensity-dependent two-photon dressed-state dynamics. The approach yields good agreement with experiments across energy and time-delay scans, revealing that the red-shifted shoulder grows as the pump energy increases and as the instantaneous frequency separation approaches the Raman frequency. This work provides a practical framework for interpreting complex ultrafast Raman spectra and improves FROG reconstruction for known pulse structures, with implications for controlling and diagnosing transient nonlinear optical processes.

Abstract

When multifrequency Raman scattering is driven in the transient regime by two chirped pump pulses, the resulting anti-Stokes orders exhibit asymmetric spectral broadening toward lower frequencies, leading to a characteristic double-peaked structure in each order. In this Letter, frequency-resolved optical gating (FROG) is used to investigate the spectral evolution of the first anti-Stokes Raman component. To interpret the observed features, we introduce a double-pulse interference model and employ an adaptive learning-based reconstruction algorithm using the Adam optimizer to retrieve the temporal field evolution. The simulation results show good agreement with the experimental measurements. Our analysis indicates that the observed red-shifted spectral component originates from linear Raman processes within the two-photon dressed-state framework.

Figures (11)

• Figure 1: A schematic depiction of the experimental protocol. G, L and M stand for Grating Lens and Mirror, respectively. Figure adapted from xu_time-dependent_2023.
• Figure 2: Overview of our approach.
• Figure 3: Cross-FROG traces comparison. Experimental traces (top row); Reconstructed FROG traces by beta-I model (middle row); Reconstructed FROG traces by beta-I model with pump data (bottom row). The columns represent the energy scans with different pump energies - 1.2 mJ, 1.7 mJ, and 2.2 mJ from left to right. Diff value represents the FROG reconstruction error. A small diff indicates better matching.
• Figure 4: Simulated FROG traces (top row) for the first anti-Stokes Raman component at three different total pump energies: 1.2 mJ, 1.7 mJ, and 2.2 mJ, shown from left to right. For each energy, the corresponding instantaneous frequency of the Raman signal, including the red-shifted contribution (middle row), and the associated spectral profile (bottom row) are also presented.
• Figure 5: Simulated FROG traces (top row) for the first anti-Stokes Raman component obtained at different relative delays between the two pump pulses: $-2/3$ ps, $-1/3$ ps, $0$ ps, $1/2$ ps, and $2/3$ ps, displayed from left to right. For each delay setting, the corresponding instantaneous frequency evolution of the Raman and red-shifted pulse (middle row), along with the associated spectral profile (bottom row), is presented.