Embedded solitons in second-harmonic-generating lattices

Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling system’s band. An especially challenging topic is seeking for such nonlinear dynamical lattices (discrete systems). We address this problem a system of coupled discrete equations modeling light an array tunnel-coupled waveguides combination intrinsic quadratic (second-harmonic-generating) and cubic nonlinearities. Solutions embedded (DESs) constructed by means two analytical approximations, adjusted, severally, broad narrow DESs, systematic form help numerical calculations. DESs several types, including ones identical opposite signs their fundamental-frequency second-harmonic components, produced. In most relevant case approximation produces very accurate results, comparison findings. case, DES branch extends from band into semi-infinite gap as family regular solitons. The study stability demonstrates that, addition to featuring well-known property semi-stability, there linearly stable which genuinely robust modes.