Higher Order Trapped States of a Solitary-Wave Well

We discuss the interaction dynamics of two pulses in distinct regions of anomalous dispersion, group-velocity matched despite a vast interjacent frequency gap. In such a setting, direct optical analogues of quantum mechanical bound-states can be realized [1] . These bound states manifest themselves as pulse compounds consisting of a strong trapping pulse, given by a solitary wave, and a weak trapped pulse. Here we go a decisive step further by clarifying the mutual interaction dynamics of higher order trapped states and by demonstrating their robustness to perturbations. The trapping mechanism is enabled by the propagation dynamics in a nonlinear waveguide and quite different from the usual trapping of a normally dispersive wave by a solitary wave [2] . Specifically, we consider pulse propagation in terms of an unidirectional non-envelope propagation equation for the analytic signal [3] , modelling group velocity and group velocity dispersion as shown in Figs. 1(a,b) .