We demonstrate that a time lens (quadratic phase temporal modulator) followed by a dispersive device can be used to implement real-time Fourier transformation (RTFT) of temporal optical pulses without introducing any additional temporal phase distortion. In this so-called transform-limited RTFT operation, the time and frequency domains are fully interchanged from the input to the output of the device; in other words, the temporal waveform of the pulse at the output of the device is a replica of the input energy spectrum and at the same time, the output energy spectrum is proportional to the temporal intensity shape of the input signal. As compared with the conventional methods, the proposed configuration does not require the use of an input dispersive device preceding the time lens, thus resulting in a much simpler and more practical alternative for implementing transform-limited RTFT of optical signals.
Transform-limited RTFT has enormous application in optical signal processing especially for reconfigurable, ultra-fast pulse filtering in the all-optical domain. Ultrafast optical pulse filtering enables other important optical pulse processing operations, such as all-optical temporal correlations or convolutions. We propose and analyze a novel ultra-fast optical pulse filtering design based on the above-simplified configuration for transform-limited RTFT. In this proposed filtering configuration, the time lens process is implemented using a phase electro-optic modulator driven by a RF tone. Our proposal results in a much more compact and practical design than the conventional 4-f ultra-fast optical pulse filtering system. We further carried out the analytical study of the proposed filtering system and demonstrated its simplicity and feasibility.