Theory of self-similar propagation of two coupled optical pulses in nonlinear optical fiber amplifiers: Coexistence and separation

We present a systematic method to investigate the self-similar propagation of two coupled optical pulses in nonlinear optical fiber amplifiers. By taking into account the intrinsic self-similarity of the two coupled nonlinear Schrödinger equations, we cast them into two simple algebraic equations. We then show that the determining of the most stable power profiles for the self-similar evolution of each pulse is equivalent to the finding of the ground-state solution of binary Bose-Einstein condensate mixtures. Based on this, we find a family of asymptotically exact self-similar solutions, including the parabolic similaritons and the piecewise parabolic similaritons. Further, we propose an approximate method to determine the intermediate evolution of initial pulses toward these similaritons. Both the analytical and numerical results show that when the parameter of cross-phase modulation nonlinearity b is smaller (larger) than 1, the two coupled pulses favor the coexistence (separation) state, while when b=1, the collisionless shock waves could emerge.