Nonlinear localization of light in disordered optical fiber arrays

Light propagating through optical fiber arrays tends to localize in only a few center cores. The recent experiments in two-dimensional single-mode optical fiber arrays suggest that an interplay of deterministic and random linear and nonlinear effects might be responsible for this localization. We study this phenomenon, both analytically and numerically, in a hexagonal optical fiber array similar to that used in the experiments. Our analysis reveals that Anderson localization is evident in the linear and intermediate regimes, where a larger fraction of initial energy is returned to the center fiber due to the stochastic effects. For very high levels of input energy, the system is strongly nonlinear, with the randomness amplifying the Kerr localization.

Figure 1

Schematic representation of the cross section of a disordered hexagonal fiber array: A microscope image of the experimental configuration can be found in Fig. 1 of [19].

Figure 2

Propagation dynamics in center fiber: linear input.

Figure 3

Propagation dynamics in center fiber: intermediate input.

Figure 4

Propagation dynamics in center fiber: nonlinear input.

Figure 5

Propagation dynamics in center fiber: asymptotic localized stationary state.

Figure 6

(Color online) Histogram for linear input in center fiber: Deterministic case.

Figure 7

(Color online) Histogram for linear input in center fiber: Stochastic case.

Figure 8

Energy drop off in transverse direction: Linear input.

Figure 9

(Color online) Histogram for nonlinear input in center fiber: Deterministic case.

Figure 10

(Color online) Histogram for nonlinear input in center fiber: Stochastic case.

Figure 11

(Color online) Histogram for intermediate input in center fiber: Deterministic case.

Figure 12

(Color online) Histogram for intermediate input in center fiber: Stochastic case.

Figure 13

Energy drop off in transverse direction: Intermediate input.

Figure 14

(Color online) Histogram for asymptotic stationary input in center fiber: Deterministic case.

Figure 15

(Color online) Histogram for asymptotic stationary input in center fiber: Stochastic case.