Pulse propagation in a two-mode waveguide

The results of an earlier paper, describing pulse propagation in multimode dielectric waveguides with random coupling, are specialized to the two-mode case. Because of their greater simplicity, the results for this special case provide more insight into the mechanism of pulse shortening due to mode coupling. The two-mode theory yields a formula for the width of a pulse carried by coupled guided modes that is found to hold also for four modes, so that it may be true for an arbitrary number of modes. This formula [eq. (23)] contains only the measurable distance required to establish the steady-state power distribution and the length of uncoupled pulses. The pulse length formula is identical with Personick's important result. Our treatment suggests that the characteristic length appearing in this formula may be accessible to measurement.