Elimination of Aberrations Due to High-Order Terms in Systems Based on Linear Time Lenses

Signal-processing systems based on linear time lenses are realized by the combination of temporal quadratic phase modulation (which is a time lens) and group-velocity dispersion. In practice, these systems suffer from aberrations due to high-order phase-modulation terms in time lenses and aberrations due to high-order dispersion in dispersive elements. We find that these two kinds of aberrations can counterbalance each other under certain conditions. In this paper we theoretically derive and numerically confirm the aberration-elimination conditions for several time-lens based systems, i.e., temporal imaging, time-to-frequency mapping and frequency-to-time mapping of optical pulse waveforms. In addition, a frequency-time diagram is used to analyze the elimination process in order to illustrate the physical mechanism.