Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems.

Figure 1

The schematic depiction of the multicore fiber.

Figure 2

Four values of $\Gamma$ corresponding to different power splits between cores as functions of total input power; here ${\gamma }_0/{\gamma }_1=0.5$ and $\kappa =1$. The blue long-dashed, green solid, and red dashed-dotted branches are stable while the black short-dashed one is unstable. Here different curves for each branch correspond to $N$ varying from 3 to 12 (from the bottom to the top). For the red short-dashed curve only odd $N$ are shown.

Figure 3

Dependence of the four solutions of Eq. (10) (shown by squares) on $N$. Here $P_t=40$, ${\gamma }_0/{\gamma }_1=1$, and $\kappa =1$. Solid lines are for the analytical solutions valid in the limit $P_t\gg 1$. Blue circles curve: ${\Gamma }_1=2P_t/N$; black squares line: ${\Gamma }_2=\sqrt{{\gamma }_{1}N/{\gamma }_0}$; green triangles line: ${\Gamma }_3={\gamma }_1/\left(2{\gamma }_0{P}_t\right)$; and red inverse triangle line: ${\Gamma }_4=-\sqrt{{\gamma }_{1}N/{\gamma }_0}$.

Figure 4

$Y$ axis (left): The comparison of numerically calculated threshold for energy or power transfer (red markers) and the analytical formula (12) (solid line). $Y$ axis (right): Numerically calculated period of the power oscillations (gray markers) and analytical approximation, $3.23+2.04/N^2$ (solid line). Insets: Energy or power transfer with distance. The complete transfer occurs only at certain distances.