Abstract: The dark state of a three-core waveguide is adapted to study the influence of the nonlineari- ty on the Coherent Population Trapping (CPT) by Silberberg.etc. However, the numerical study of such a waveguide shows that both the CPT and the nonlinear self-trapping can result in the dark states. When both effects occur, the dark states will be destroyed. Thus the destructi- on of dark states are due to the both effects, which means one cannot simply attributed the disappeara- nce of darks states to the CPT solely. In the idea CPT case, the critical power of nonlinearity approach- es to infinity, which means that the nonlinearity of the system does not influence the idea CPT quantum effects.

Key words: nonlinear optics, dark state, numerical simulation, three-core waveguide, coherent population trapping, self-trapping