Towards retrieving the temporal profile of unequal pulse bound states from autocorrelation measurements.

Optical autocorrelators are typically employed to retrieve the temporal information of bound-state lasers; however, they suffer from limitations when multiple sub-pulses coexist with varying intensities and pulse widths. To this end, this study investigates the impact of differences in pulse temporal intensity and width between two unequal pulses in a bound-state laser on the corresponding autocorrelation trace. Maps of autocorrelation trace in terms of the temporal profile of unequal pulse bound state are created to evaluate their internal relationship. Specifically, the autocorrelation peak intensity ratio exhibits an approximatively Gamma cumulative distribution function relationship with respect to either individual variation in the temporal intensity or width ratio. Additionally, we examine the impact of oscillating tail intensity on the autocorrelation trace. These results reveal that variations in pulse temporal characteristics complicates the retrieval of accurate temporal information. To address this, we provide a checklist based on careful examination of the autocorrelation trace to retrieve the temporal profile of bound states with unequal pulses. This work provides guidance for approximately retrieving the temporal information of a bound-state laser with variations in sub-pulse shapes from the autocorrelation trace and underscores the necessity for more sophisticated analytical methods to disentangle the complexities arising from non-uniform pulse parameters.