Second-harmonic generation in branched optical waveguides: Metric graphs based approach

We consider the second-harmonic generation in branched optical waveguides, by modeling the process in terms of the three-wave interaction system on metric graphs. The vertex boundary conditions are derived from the conservation laws. Soliton solutions of the three-wave interaction system are obtained for the case of star- and tree-branched networks. •Three-wave system of nonlinear equations is integrable and approves soliton solutions under certain constraints.•Second harmonic generation in branched optical waveguides occurs near the branching points.•Generated second harmonics decay during a very short time.•Transmission of fundamental harmonics via the branching point occurs without the backscattering.