Partially PT -symmetric lattice solitons in quadratic nonlinear media

Abstract

Partially parity-time-symmetric ($\mathrm{p}\mathcal{PT}$-symmetric) lattice solitons are explored in quadratic nonlinear media. The solution of the model a nonlinear Schr\"odinger (NLS) equation with coupling to a mean term and an additional external potential, is computed by modern numerical methods, and it is shown that $\mathrm{p}\mathcal{PT}$-symmetric lattice solitons can exist in quadratic nonlinear media. The study concentrates on effects generated by the variation of lattice depth and quadratic nonlinearity strength that specify characteristics of the model, and the stability of the model is examined comprehensively by the nonlinear evolution and linear stability spectra of the solitons. It is demonstrated that stable evolution of solitons in a quadratic nonlinear media is possible for self-focusing $\mathrm{p}\mathcal{PT}$-symmetric lattices. Moreover, it is observed that, for the defocusing case of the lattice, fundamental solitons decay into radiation modes, and the decay of these solitons can be delayed by a deeper potential.