Coexistence of a self-induced-transparency soliton and a nonlinear Schrödinger soliton in an erbium-doped fiber

The possibility of observing a self-induced transparency (SIT) in an erbium-doped optical fiber is investigated. A general equation that includes the SIT, the group-velocity dispersion (GVD) of the fiber, and the nonlinear refractive index is discussed. It is shown that for one particular value of waveguide parameters the nonlinear index can balance the GVD, that is, the nonlinear Schrödinger equation (NLS), while maintaining a SIT soliton. This is called a SIT-NLS soliton. The phase change of the SIT-NLS soliton is governed solely by the NLS component, and the pulse delay due to resonance is determined solely by the SIT component when the detuning is zero. Practical parameters for silica-based fibers do not allow the coexistence of a mixed soliton state. A simple derivation of a condition for a SIT-NLS soliton is also presented. The SIT-NLS soliton is computer-run, and it is shown that a stable 2π/N=1 SIT-NLS soliton exists. However, high-order SIT-NLS solitons always split into multiple 2π/N=1 solitons. The NLS property can be preserved when ${\mathit{Z}}_{\mathrm{sp}}$≪${\mathit{L}}_{\mathrm{abs}.\mathrm{}}$ Finally, the NLS soliton that interacts coherently with erbium ions is studied, and the coherent pulsation that produces multiple narrow pulses is described.