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.

中文翻译：

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使用色散梯度指数时间透镜的时间成像

我们使用梯度指数 (GRIN) 时间透镜研究时间成像，其中引入了色散和时变二次相位调制。该透镜是通过在具有群速度色散的非线性光纤中使用信号和抛物线泵浦脉冲之间的交叉相位调制来构建的。详细执行了 GRIN 时间透镜的时间成像的一般理论分析。与先前研究中的薄透镜相比，色散的引入有利于光脉冲的时间波形和频谱的周期性自成像。有趣的是，输入的时间和光谱轮廓可以在 GRIN 时间镜头中周期性地相互交换。通过将 GRIN 时间透镜与两侧的色散元件相结合，入射光脉冲的时间波形可以被拉伸和压缩。对于由经历不同色散的多个脉冲组成的输入信号，通过扫描施加在透镜上的泵浦脉冲的时序来实现信号的时间深度成像。该研究可能会在超快光信号处理和测量中找到很好的应用。