Topological Filters for Solitons in Coupled Waveguides Networks

We study the propagation of discrete solitons on chains of coupled optical waveguides where finite networks of waveguides are inserted at some points. By properly selecting the topology of these networks, it is possible to control the transmission of traveling solitons: we show here that inhomogeneous waveguide networks may be used as filters for soliton propagation. Our results provide a first step in the understanding of the interplay/competition between topology and nonlinearity for soliton dynamics in optical fibers. The discovery of solitons in optical fibers, three decades ago [1], stimulated a huge amount of work aimed at using solitons for high speed communications [2]. Many experiments evidenced the role of the Kerr nonlinearity in allowing for the propagation over long-distances of solitons in optical fibers [2,3]; however, this nonlinear paradigm has not yet demonstrated decisively its advantages over other more conventional signal propagation schemes. If one introduces a spatial inhomogeneity in the field equations by the linear compression mechanism, one could stabilize the soliton propagation [4]. Motivated by this, one is lead to investigate the so-called dispersion-managed nonlinear Schrödinger equation [5] i ∂E ∂z = − 2 ∂E ∂t2 − ν | E | E, (1)