Abstract
We study the temporal imaging with a gradient-index (GRIN) time lens in which both dispersion and time-varying quadratic phase modulation are introduced. The lens is built by using cross-phase modulation between a signal and a parabolic pump pulse in the nonlinear optical fiber with group velocity dispersion. A general theoretical analysis of temporal imaging by the GRIN time lens is performed in detail. Compared to thin lens in previous studies, the introduction of dispersion, benefits periodic self-imaging of both time waveform and frequency spectrum for optical pulses. Interestingly, the temporal and spectral profiles of the input can be exchanged with each other periodically in the GRIN time lens. By combining the GRIN time lens with dispersive elements on both sides, the temporal waveforms of incident optical pulses can be stretched and compressed. For an input signal composed of multiple pulses experiencing different dispersions, the temporal depth imaging of the signal is realized by scanning the timing of the pump pulse applied on the lens. The study may find great applications in ultrafast optical signal processing and measurement.
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