Simplified system configuration for real-time Fourier transformation of optical pulses in amplitude and phase

Real-time Fourier transformation (RTFT) of optical waveforms in amplitude and phase (i.e. transform-limited RTFT) is a fundamental operation that enables the realization of many interesting ultrafast signal processing applications, including wavelength-tunable optical pulse filtering, all-optical temporal correlations and convolutions and temporal imaging, among others. In this paper, we demonstrate that under certain conditions, a single time lens (quadratic-phase temporal modulator) followed by a suitable dispersive delay line can be used to implement transform-limited RTFT of optical pulses. The design specifications and constraints of the proposed transform-limited RTFT systems are derived and discussed. As compared with the conventional methods, the proposed design does not require the use of an input dispersive device preceding the time lens or a second time lens after dispersion, thus resulting in a simpler and more practical alternative for implementing TL-RTFT of optical signals. The feasibility of our proposal to operate on picosecond optical waveforms using electro-optic time lenses has been confirmed by numerical simulations.