The optical soliton transmission amplified by bidirectional Raman pumps with nonconstant depletion

A numerical method to solve the coupled equations between the soliton and bidirectional Raman pump waves is proposed. The pump depletion due to the soliton is obtained without using the constant depletion approximation. With this method, the soliton propagation in a Raman-pumped fiber, can be solved accurately. It is found that the constant depletion approximation is valid at a small depletion rate, which requires low soliton power (or long pulsewidth), small material loss, and a short-pump period. In a periodically Raman-pumped fiber, there exists a stable signal energy which is very sensitive to the pump intensity. The stability of the soliton propagation with nonconstant pump depletion is studied. It is found that the stability predicted by the nonconstant depletion (NCD) and the constant depletion assumption (CDA) are generally different