Ultrashort-Soliton Interactions in Optical Fibers

Abstract

It is well-known that in single-mode optical fibers two picosecond-range fundamental bright solitons with the same phase attract each other when they are close; two such solitons with π phase difference are mutually repulsive. However, the scenarios of the interaction between two femtosecond-range solitons are quite different. The behaviors of femtosecond-range solitons in a single-mode fiber differ from those of picosecond-range solitons because of the higher-order dispersion, shock effect, and the more important Raman response function [1]. These effects are included in the generalized nonlinear Schrödinger equation [2]. By numerically solving this equation, it is discovered that the energy is redistributed between the two solitons during the interaction. Also, the two solitons are separate eventually. The energy redistribution between the identical input solitons depends on the initial soliton separation and relative phase. Figures 1 and 2 show the evolution of the interaction between two identical solitons of 1.51 μm wavelength, 40 fsec width and 140 fsec initial separation. It is observed that when the initial relative phase is π as shown in Fig. 1, the leading soliton keeps pumping the trailing one. However, when the initial relative phase is 0, as shown in Fig. 2, the leading soliton first receives the energy pumped by the trailing one until certain distance where the relative phase between the two solitons becomes π. After this distance, the leading soliton keeps pumping the trailing one. Similar results can be observed in the collision of two femtosecond-range solitons with different central wavelengths. Figure 3 demonstrates the interactions of two solitons at 1.5 and 1.51 μm, respectively, with 0 and π initial relative phases. Detailed interpretations about interaction mechanism will be given. The dependences on other input parameters will also be presented.