Linear pulse propagation with high-order dispersion

We present an approximate, but intuitively appealing theoretical study of the linear propagation of optical pulses in media with high-order dispersion. Our analysis, which is fully consistent with numerical simulations, is based on the pulses' full-width at half maximum and shows that the effect of high-order dispersion differs significantly from that of the well-understood second order dispersion. For high dispersion orders m, the central part of the pulses, where the intensity is highest, evolve in the same way, independent of m, though at different rates, with a weak dependence on the initial pulse shape. We also find that all pulses, irrespective of initial pulse shape, eventually evolve to a sinc function. Our treatment allows us to find expressions for the characteristic dispersion lengths for high dispersion orders.