Power Controlled Soliton Stability and Steering in Lattices with Saturable Nonlinearity

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site ($A$) and between two neighboring sites ($B$), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode $A$, a stable propagation of mode $B$ is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.

Figure 1

Analytically (solid line) and numerically calculated PN potential versus soliton power $P$ for discrete lattices with $\beta =18.2$ and $K=2$.

Figure 2

Amplitude in the central lattice element and its neighbors for both localized modes as a function of soliton power $P$ for discrete lattices with $N=101$, $\beta =18.2$, and $K=2$.

Figure 3

Illustration of the soliton dynamics with $P=21.63$ in the lattice with $N=101$, $\beta =18.2$, and $K=2$. (a)–(d) represent gray scale maps of the intensity profiles over the lattice for (a) stable propagation of the mode $B$, and soliton steering initiated from mode $A$ with different initial phase differences: (b) $\alpha =0.0027$, (c) $\alpha =0.005$, and (d) $\alpha =0.0155$.