Spectral Splitting of Optical Pulses Inside a Dispersive Medium at a Temporal Boundary

We show numerically that the spectrum of an optical pulse splits into multiple, widely separated, spectral bands when it arrives at a temporal boundary across which the refractive index suddenly changes. At the same time, the pulse breaks into several temporally separated pulses traveling at different speeds. The number of such pulses depends on the dispersive properties of the medium. We study the effect of second- and third-order dispersion in detail but also briefly consider the impact of other higher order terms. A temporal waveguide formed with two temporal boundaries can reflect the temporally separated pulses again and again, increasing the number of pulses trapped within the temporal waveguide.