Soliton dynamics in quadratic nonlinear media with two-dimensional Pythagorean aperiodic lattices

Abstract

The dynamics of two-dimensional Pythagorean lattice solitons are explored in quadratic nonlinear media. The study is focused on variation of sub-lattice depths and the strength of quadratic optical effects that specify characteristics of the considered model. The numerical existence of periodic and aperiodic lattice solitons is demonstrated, and the stability domain of solitons is determined for all parameters in the model. It is shown that, although the existence domain of periodic and aperiodic lattice solitons is identical, the stability region of periodic lattice solitons is narrower than that of aperiodic lattice solitons. It is manifested that stable solitons can exist in both periodic and aperiodic lattices, and decay of unstable solitons can be arrested by increasing the potential depth and decreasing the propagation constant.