Comprehensive study on the concept of temporal optical waveguides

Time and space are dual variables which bring a lot of analogies during theoretical study. In this paper, we extend the concept of a spatial optical waveguide to the temporal domain. Here we show that it is possible to confine the optical pulse within a time interval by introducing the temporal index boundaries. The confined pulse will propagate at a speed of the index change in the waveguide, and it will be behind the original optical pulse which propagates without the temporal index variations. In this way, we may offer an approach to broaden the bandwidth of the slow light and to tune the light speed based on the existing slow light devices. The temporal waveguide has modes, which are the temporal waveforms maintaining their shapes during the propagation. In a single-mode temporal waveguide, the pulse retains its shape as the only mode of the waveguide just like an optical soliton. In a multimode temporal waveguide, multimode interference effect exists, which can duplicate a single pulse into multiple copies and be potentially implemented for all-optical signal processing.