Cross-phase modulation (XPM) is commonly viewed as a nonlinear process that chirps a probe pulse and modifies its spectrum when an intense pump pulse overlaps with it. Here we present an alternative view of XPM in which the pump pulse creates a moving refractive-index boundary that splits the probe pulse into two parts with distinct optical spectra through temporal reflection and refraction inside a dispersive nonlinear medium. The probe even undergoes a temporal version of total internal reflection for sufficiently intense pump pulses, a phenomenon that can be exploited for making temporal waveguides. We investigate the practical conditions under which XPM can be exploited for temporal reflection and waveguiding. The width and shape of the pump pulses as well as the nature of the medium dispersion at the pump and probe wavelengths (normal versus anomalous) play important roles. The super-Gaussian shape of a pump pulse is particularly helpful because of the relatively sharp edges of the super-Gaussian shape. When the pump wavelength lies in the anomalous-dispersion regime, the pump pulse can form a soliton, whose unique properties can be exploited to our advantage. We also discuss a potential application of XPM-induced temporal waveguides for compensating for timing jitter.
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