Figure 1

Suggested experimental setup: The beam is injected into the boundary waveguide numbered as $j=0$, $Q_0$ is a linear coupling between boundary and first waveguides, and $Q$ is a coupling constant between the waveguides in the array. $n_0$ and $n$ are linear refractive indexes of boundary and array waveguides, respectively; $z$ is a longitudinal space dimension playing a role of time in the boundary driven DNLS equation (1).Reuse & Permissions

Figure 2

Three dimensional plot of time evolution of the boundary driven DNLS equation for inband driving frequency $\Delta =1.94$ and the very small driving amplitude $A_0=0.01$. As seen, the intensity transmits to remote sites.Reuse & Permissions

Figure 3

Same as in Fig. 2 for band gap driving $\Delta =2.04$. For driving amplitudes below the threshold ($A_{\mathrm{t}\mathrm{h}}=0.202$) the pattern in the upper graph could be described by the standing breather solution (7), while for the driving amplitudes above the threshold (lower graph) the transmission could be described by a train of gap solitons (3). The inset shows the dependence of the driving threshold upon the driving frequency; the asterisks are the results of the numerical simulations on boundary driven DNLS equation (1) and the solid line represents an analytical curve (6). The dashed line divides the range of $A_0$ (left-hand side) for which an analytical approximate semidiscrete approach is given by formulas (3, 7). Moreover within the same range above a threshold, low amplitude semi-discrete envelope solitons participate in band gap transmission (see lower graph). At the right side of the dashed line in the inset high amplitude moving breathers are excited, which are further trapped by the lattice (see Fig. 4), which leads to the suppression of band gap transmission.Reuse & Permissions

Figure 4

Trapping of large amplitude moving gap soliton. For relatively large driving amplitudes the soliton starts to move but further the lattice traps it. This in itself stops the transmission process.Reuse & Permissions

Figure 5

Rescaled waveguide intensity $|{\psi }_j^{\prime }{|}^2$ in the band gap transmission regime. The inset shows longitudinal dimension $z^{\prime }$ dependence of rescaled beam intensity in the boundary waveguide. In creating the solitons the intensity from the boundary waveguide is transferred to other waveguides and as a result the transmission stops when the beam intensity in the boundary waveguide goes below the threshold. The simulations are done for $Q_0/Q=0.1$.Reuse & Permissions