Time dispersion in dielectric waveguides

In dielectric waveguides operating at optical frequencies, the primary cause of time dispersion of narrow pulses can be mode conversion. In this paper we argue that under certain assumptions a dielectric waveguide acts as a linear system in intensity. That is, given the intensity input, the intensity output is equal to the input convolved with an intensity impulse response. We show that contrary to intuition, the width of the impulse response gets narrower when coupling between guided modes increases. Using the perturbation results of D. Marcuse, we obtain an interesting model of energy propagation down imperfect guides. We conclude that the intensity response width increases as the square root of the guide length for sufficiently long guides and approaches a gaussian shape for sufficiently long guides. We conclude from the theory that the dispersion in dielectric wave-guides may be orders of magnitude below that which was previously expected in guides of sufficiently long length having properly controlled large amounts of mode conversion. These theoretical results have not yet been verified experimentally.