Nonlinear coupled-mode equations

Nonlinear coupled-mode equations governing the modal coupling of a two-mode coupled system (such as twin core couplers) are integrable; power swapping in such a system follows a periodical manner and can be expressed analytically. When three or more modes (for systems such as multiple-core couplers) are involved, the nonlinear coupled-mode equations are no longer integrable and chaotic power swapping is expected. A numerical approach is required, in general, to solve such nonlinear coupled systems involving the coupling of three or more modes. We find, however, that for certain structural configurations, such as triple-core couplers with the cores arranged in the shape of an isosceles triangle, the nonlinear coupled-mode equations for multiple-core couplers can be solved analytically under a resonant condition. The analytical solution indicates that power swapping among, for example, the three cores placed in the shape of an isosceles triangle can be aperiodic at high power, although power may flow from core to core periodically at low power.