Tunneling of optical lattice solitons at interfaces

The nonlinear wave propagation and scattering processes in discrete optical heterostructures is studied both analytically and numerically. The presented theory describes the reflection and tunneling of lattice solitons at interfaces. In particular, the derived expressions allow us to construct the reflected and transmitted pulses from the incident one. In the range of validity, the analytical results are in very good agreement with the numerical simulations. It is demonstrated that optical heterostructures represent an effective tool for controlling and manipulating nonlinear light pulses and beams.

Figure 1

Top: The soliton scattering process at the interface of a heterostructure. Here, $|{\psi }_n\left(t\right)|$ is plotted. Bottom: ${\varepsilon }_n$ as a function of $n$. In this simulation the interface is located at $n=3000$. Values of other parameters and further details are given in the text.

Figure 2

Dependency of $k_r$ on $k_l$ given by Eq. (26). Discussion and the values of other parameters are presented in the text.

Figure 3

Dependency of $\mu A_T^{\left(1\right)}$ on $k_l$. Squares and circles represent the numerically obtained results for the arithmetic mean of the maximum and minimum amplitude in the first and second oscillations of the soliton parameters, respectively. The solid line is the theoretical prediction.

Figure 4

Unstable dynamics of the bound state of two solitons. $k_l=1.2$, and as in Fig. 1, $|{\psi }_n\left(t\right)|$ is plotted. Higher order effects cause the splitting of the transmitted second-order soliton into two pulses with a long dispersive tail.