Nonquadratic Spectral Phase Aberration With Quadratic Temporal Phase Modulation in an Actively Modulated Ultrafast Laser System

Ultrashort pulses can be generated through active modulation techniques, such as the time-lens technique. To achieve better pulse compression, in the time-lens source, quadratic temporal phase modulation was naturally considered as the ideal modulation. However, it is unknown that whether a quadratic temporal phase modulation (equivalently, a linear chirp) translates into a quadratic spectral phase modulation, which can be easily eliminated using compressors. Here, we study this phase transfer both analytically and numerically. Our results indicate that depending on the pulse shape, nonquadratic spectral phase aberration arises even if the temporal phase modulation is quadratic. Consequently, there is observable difference between the compressed pulses with a flat spectral phase and with quadratic spectral phase compensation only. However, both analytical and numerical analyzes show that as quadratic temporal phase modulation increases, nonquadratic spectral phase modulation decreases, and pulse compression with quadratic spectral phase tends to that with a flat spectral phase.