Quadratic phase mismatch in multisoliton interferograms based on time-stretched dispersive Fourier transformation

The time-stretched dispersive Fourier transform method (TS-DFT) has been widely used to analyze multisoliton structures in ultrafast lasers, featuring shot-by-shot access to their spectral interferograms. Most exemplary structures consist of two interacting solitons whose spacing and relative phase can be simply retrieved from their interferograms mapped in time domain by TS-DFT. However, such analysis has not been elaborated for structures with more solitons that could result in a complicated TS-DFT signal. Here we report our theoretical inference of a deterministic discrepancy when retrieving structures consisting of more than two solitons with their TS-DFT signal. We unveil the underlying source of these discrepancies as a result of the quadratic phase mismatch induced by TS-DFT and correspondingly propose an improved retrieval method. Our work may provide a theoretical guideline for conducting unambiguous analysis of complex multipulse structures using TS-DFT, particularly when the dispersive stretching ratio is limited.