Propagating beam analysis of multimode waveguide tapers

We analyze both slowly and rapidly varying tapers with the aid of the propagating beam method. Our results demonstrate that while the optimal longitudinal profile for slowly varying profiles is independent of the taper length, the optimum profile of a taper which varies rapidly with respect to the inverse of the average propagation constant difference of adjacent modes must be determined computationally in each case from the given values of its length and initial and final width parameters. We also analyze the region of validity of local normal mode perturbation theory in representative taper configurations.