General temporal self-imaging phenomena

Using the space–time duality theory, we introduce and analyze theoretically the temporal equivalent of the spatial self-imaging phenomena under point-source illumination (spherical wave-front illumination). This temporal effect can be produced by passing a given periodic optical pulse sequence through a time lens followed by a dispersive medium. The time lens (quadratic phase modulator) implements the time-domain equivalent of spherical wave-front illumination. Based on this temporal effect, we demonstrate that a system composed of a time lens followed by a dispersive medium can be configured to operate over a periodic optical pulse sequence of finite duration (i) as a conventional temporal imaging system, providing a distortionless temporal compression or expansion of the original pulse sequence, or (ii) as an advanced temporal imaging system, combining the capabilities of a conventional imaging system with those of the fractional temporal self-imaging effect, i.e., multiplication of the original pulse-repetition rate.