Realization of multiform time derivatives of pulses using a Fourier pulse shaping system

The technique of multiform time derivatives of pulse has been shown necessary to achieve various time-space metrology goals with a precision at or beyond the standard quantum limit. However, the efficient generation of the desired time derivatives remains challenging. In this paper, we report on the efficient realization of multiform time derivatives with a programmable 4-f pulse shaping system. The first-order time derivative of the pulse electric field has been achieved with a generation efficiency of 72.12%, which is more than 20 times higher than that of previous methods. Moreover, the first- and second-order time derivatives of the pulse envelope have been achieved with the generation efficiencies being 11.10% and 3.53%, respectively. In comparison, these efficiencies are three times higher than those for previously reported methods. Meanwhile, the measured fidelities of the three time-derived pulses are reasonably high, with values of 99.53%, 98.37% and 97.32% respectively.